We investigate multiuser detection under uplink asynchronous scenario, where the triangular successive interference cancellation (T-SIC) detection scheme is exploited. As the existing analysis was conducted under some ideal assumptions for simplicity, the asynchronous scenario is analyzed under rigorous assumptions in this paper so that important insights are revealed for practical systems. Specifically, the average symbol error rate (SER) formulas are derived for a two-user system with arbitrary$M$-ary quadrature amplitude modulation ($M$-QAM) over Rayleigh fading channels. These solutions are shown to have higher accuracies compared to the existing solutions. Furthermore, a novel iterative detection algorithm is proposed, i.e., the parallel T-SIC method, which is more efficient and effective compared to the iterative T-SIC method. Insightful discussion is conducted in terms of the potentials of the concerned iterative detection method. Simulation results show that the most significant improvement of the iterative detection reflects on the SER for the strongest user, and the reduction is always within 50% of the SER compared to the primary detection. The gains obtained by the iterative detection is negligible for higher order$M$-QAM cases.

This paper presents a novel and effective deep reinforcement learning (DRL)-based approach to addressing joint resource management (JRM) in a practical multi-carrier non-orthogonal multiple access (MC-NOMA) system, where hardware sensitivity and imperfect successive interference cancellation (SIC) are considered. We first formulate the JRM problem to maximize the weighted-sum system throughput. Then, the JRM problem is decoupled into two iterative subtasks: subcarrier assignment (SA, including user grouping) and power allocation (PA). Each subtask is a sequential decision process. Invoking a deep deterministic policy gradient algorithm, our proposed DRL-based JRM (DRL-JRM) approach jointly performs the two subtasks, where the optimization objective and constraints of the subtasks are addressed by a new joint reward and internal reward mechanism. A multi-agent structure and a convolutional neural network are adopted to reduce the complexity of the PA subtask. We also tailor the neural network structure for the stability and convergence of DRL-JRM. Corroborated by extensive experiments, the proposed DRL-JRM scheme is superior to existing alternatives in terms of system throughput and resistance to interference, especially in the presence of many users and strong inter-cell interference. DRL-JRM can flexibly meet individual service requirements of users.

Sums of lognormal random variables can be used to model a wide range of real-life phenomena, and their probability distribution left tails are of crucial interest. Meanwhile, the probability distribution left tail of the sum of lognormal random variables has no closed-form expressions. A closed-form first-order Marcum Q-function lower bound for the probability distribution left tail of the lognormal two-sum is derived. The derivation of the lower bound is based on studying the geometry of the nonzero probability mass region in the Gaussian plane, rather than in the lognormal plane. It is proved that the boundary of the nonzero probability mass region in the Gaussian plane does not change shape and is identical for different lognormal two-sum cumulative distribution function (CDF) arguments, other than for a translation of the boundary curve that is determined by the CDF argument. The first-order Marcum Q-function lower bound becomes an increasingly good approximation for the probability distribution left tail of the lognormal two-sum, as the sum CDF argument approaches zero. A recently reported empirical observation that the Marcum Q-function can be used as an approximation of the left tail probability of the lognormal sum distribution is explained and partially quantified. Simulation results show that the new first-order Marcum Q-function lower bound is tighter than an existing lognormal sum distribution left tail lower bound when the sum CDF argument is sufficiently small.

Idle slots cause identification inefficiency in Aloha-based RFID algorithms. An idle slot prediction and elimination technique is proposed. The algorithm is dubbed idle predicting dynamic frame-slotted Aloha (IP-DFSA). In IP-DFSA, the reader reads a slot for RN16 as well as the idle prediction bits. Using only a few prediction bits, IP-DFSA can predict and eliminate a significant number of successive idle slots following the current time slot. Whereas previous schemes only achieve 36% efficiency on average, simulation results show that IP-DFSA with 1, 2, 3, and 4 idle slot prediction bits achieves 45%, 52.5%, 56%, and 60% system efficiencies, with 83%, 86%, 88%, and 89% time efficiencies, respectively. The system efficiencies of IP-DFSA range from 9% higher to 24% higher than previous schemes for 1 prediction bit to 4 prediction bits. The number k of idle prediction bits is optimized, and it is revealed that koptimal=4 for tag numbers n≥6.

It is challenging to satisfy the critical requirements of ultrareliable and low-latency communications (URLLCs) in the Internet of Things (IoT) under severe channel fading. The emerging massive multiuser multiple-input-multiple-output (MU-MIMO) concept is applied in IoT networks under shadow fading, enabling URLLC with pilot-assisted channel estimation (PACE) and zero-forcing (ZF) detection. Assuming users are uniformly and randomly deployed under log-normal shadow fading, the probability density function (pdf) of postprocessing signal-to-noise ratios (SNRs) is derived for the uplink (UL) of massive MU-MIMO with perfect channel state information (CSI) and imperfect CSI obtained by PACE. Then, finite blocklength (FBL) information theory is utilized to derive the error probability of accessing users with a given latency, thereby evaluating the reliability of massive MU-MIMO for short-packet transmissions. Further, the length of pilots to minimize the error probability can be decided by the golden section search method (GSSM), which can converge rapidly. Numerical results verify that massive MU-MIMO can support a large number of UL URLLC users even when users are randomly deployed under shadow fading.

Standard blind interference alignment (sBIA) suffers from noise accumulation which severely deteriorates received signal-to-noise ratio (SNR) and significantly reduces transmission rate. A noise accumulation factor is proposed to describe the loss between the user's received SNR, and the final post processing SNR which determines the performance of the decoding of the encoded data streams (EDSs). A heterogeneous semi-BIA (H-SBIA) framework where users with different noise accumulation factors can be flexibly allocated effective EDSs (E-EDSs) is constructed. Relying on the H-SBIA framework, a heuristic H-SBIA algorithm is designed for maximizing the overall E-EDSs considering both fairness and coherence time constraints. Extensive simulations demonstrate that H-SBIA produces great fairness performance improvement at a limited cost in the achievable sum rate. The Jain's fairness index is about 2.2 times greater than that for SNR-SBIA proposed in previous work, at the cost of sacrificing 10% of the achievable sum rate.

Simulation is widely used to estimate the distributions of sums of lognormal random variables because the characteristic function of the lognormal random variable is not known and numerical integration of multiple integrals is difficult. The left tail of the lognormal sum distribution is the outage probability for some wireless systems, while the right tail represents cochannel interference, both crucial design issues. Importance sampling is sometimes used but becomes less effective as the number of summands increases. A novel simulation procedure dubbed hyperspace replication is proposed and studied. The method achieves estimator variance reductions greater than 64 times in the left tail for practical values of outage probability, and 2 to 3 times in the right tail compared to traditional Monte Carlo simulation. The method can be used in cascade with importance sampling and reduces the variances of the distribution estimates by the same amounts as it does for Monte Carlo simulation.

Non-orthogonal multiple access (NOMA) has been developed as a key multi-access technique for 5G. However, secure transmission remains a challenge in NOMA. Especially, the user with weakest channel is most threatened by eavesdropping, due to its highest transmit power. In this paper, we propose a novel scheme to generate artificial jamming at the NOMA base station (BS), aiming at disrupting the potential eavesdropping without affecting the legitimate transmission. In the scheme, the transmit power of artificial jamming is maximized, with its received power at each receiver higher than that of other users. Thus, the jamming signal can be eliminated via successive interference cancellation before others, and the eavesdropping can be disrupted effectively. Due to the non-convexity of the optimization problems, we first convert it to a convex one and then provide an iterative algorithm to solve it. Simulation results are presented to show the effectiveness of the proposed scheme in guaranteeing the security of NOMA networks.

Maximal ratio combining (MRC) diversity is fundamental in wireless communication theory and widely implemented in practice. There are limited results in the theory for the probability density function (PDF) of MRC diversity on Nakagami channels when the branches have unequal powers. In addition to being restricted, the known solutions are complex and in some cases unwieldy. Novel, complete solutions for the PDF of MRC signal‐to‐noise ratio (SNR), valid for integer values of the Nakagami fading parameter m and arbitrary branch powers, are derived. In addition to being solutions for the unsolved cases, the new solutions give different and much simpler expressions for the known restricted cases than previous solutions. The effects of branch channel power imbalances on the PDF of MRC and on the outage probability are investigated quantitatively. The new solutions are used to derive asymptotic large SNR performance measures for MRC diversity with unequal branch powers, insights not obtainable from previous solutions. The new solutions are used to derive intuitive simple approximations for the densities and distributions of MRC output signal power and amplitude, as well as for the outage probability. The approximations are shown to have excellent accuracies for power imbalances 30% and good accuracies for power imbalances 60%.

We develop the optimal economical caching schemes in cache-enabled heterogeneous networks, while delivering multimedia video services with personalized viewing qualities to mobile users. By applying scalable video coding (SVC), each video file to be requested is divided into one base layer (BL) and several enhancement layers (ELs). In order to assign different transmission tasks, the serving small-cell base stations (SBSs) are grouped into $K$ clusters. The SBSs are able to cache and cooperatively transmit BL and EL contents to the user. We analytically derive expressions for successful transmission probability and ergodic service rate, and then the closed-form expression for EConomical Efficiency (ECE) is obtained. In order to enhance the ECE performance, we formulate the ECE optimization problems for two cases. In the first case, with equal cache size equipped at each SBS, the layer caching indicator is determined. Since this problem is NP-hard, after the l0-norm approximation, the discrete optimization variables are relaxed to be continuous, and this relaxed problem is convex. Next, based on the optimal solution derived from the relaxed problem, we devise a greedy-strategy based heuristic algorithm to achieve the near-optimal layer caching indicators. In the second case, the cache size for each SBS, the layer size, and the layer caching indicator are jointly optimized. This problem is a mixed integer programming problem, which is more challenging. To effectively solve this problem, the original ECE maximization problem is divided into two subproblems. These two subproblems are iteratively solved until the original optimization problem is convergent. Numerical results verify the correctness of the theoretical derivations. Additionally, compared to the most popular layer placement strategy, the performance superiority of the proposed SVC-based caching schemes is testified.

Non-orthogonal multiple access (NOMA) has been developed as a key multi-access technique for 5G. However, secure transmission remains a challenge in NOMA. Especially, the user with weakest channel is most threatened by eavesdropping, due to its highest transmit power. Two schemes are proposed to generate artificial jamming at the NOMA base station (BS), aiming at disrupting the potential eavesdropping without affecting the legitimate transmission. In the first scheme, the transmit power of artificial jamming is maximized, with its received power at each receiver higher than that of other users. Thus, the jamming signal can be eliminated via successive interference cancellation before others. When the transmit power of the BS is inadequate, the transmit jamming power is maximized with the jamming signal zero-forced at each receiver. Thus, the legitimate transmission is not affected by the jamming, and the eavesdropping can be disrupted effectively. Due to the non-convexity of these two optimization problems, we first convert them to convex ones and, then, provide an iterative algorithm to solve them. Simulation results are presented to show the effectiveness of the proposed schemes in guaranteeing the security of NOMA networks.

By suppressing repeated content deliveries, wireless caching has the potential to substantially improve the energy efficiency (EE) of the fifth-generation communication networks. In this paper, we propose two novel energy-efficient caching schemes in heterogeneous networks, namely, scalable video coding (SVC)-based fractional caching and SVC-based random caching, which can provide on-demand video services with different perceptual qualities. We derive the expressions for successful transmission probabilities and ergodic service rates. Based on the derivations and the established power consumption models, the EE maximization problems are formulated for the two proposed caching schemes. By taking logarithmic approximations of the l0-norm, the problems are efficiently solved by the standard gradient projection method. Numerical results validate the theoretical analysis and demonstrate the superiority of our proposed caching schemes, compared to three benchmark strategies.

The Beckmann distribution has a wide range of applications in radio-frequency communications, free-space optical (FSO) communications, and underwater wireless optical communications (UWOC). However, the cumulative distribution function (cdf) of the Beckmann random variable (RV) does not have a closed-form expression, which makes it challenging to derive analytical solutions for the outage probability of systems involving Beckmann RVs. In this paper, we study the generalized Beckmann distribution, which includes the Beckmann, Rayleigh, Rician, Nakagami-m, Hoyt, κ-μ, η-μ, single-sided Gaussian, and the Beaulieu-Xie distributions as special cases. Three approaches are proposed to estimate the cdf of the generalized Beckmann distribution, including closed-form upper and lower cdf bounds, single-fold integration based on the closed-form characteristic function, and a left-tail cdf approximation. We compare the three approaches in terms of the ranges of applications and the computation time complexity. Based on the new cdf estimation techniques, one can efficiently evaluate the outage probabilities of pointing-error-limited FSO systems, UWOC systems, and maximum-ratio combining over arbitrarily correlated generalized Beckmann channels.

The explosive growth of mobile data traffic and the scarcity of available licensed spectrum make resource allocation in heterogeneous networks a critical issue. A distributed resource allocation algorithm for software defined cellular networks for future 5G networks is proposed. The adoption of integrated femto-WiFi small cells is used to alleviate spectrum shortage, by permitting simultaneous access to both the licensed bands (via cellular interface) and unlicensed bands (via WiFi interface). A weighted utility maximization problem is formulated to optimize resource allocation, utilizing the software defined network controller’s global view. A fully distributed solution based on the weighted utility maximization optimizes resource allocation, keeping the interference from small cells to macrocells below predefined thresholds. The proposed algorithm considers the sDevices, which have both cellular and WiFi interfaces, and the wDevices which have WiFi-only interfaces. Numerical simulations substantiate the superiority of the proposed resource allocation algorithm, which increases significantly the average throughput and average utility of all devices, compared with the traditional and current methods. Throughput gains as large as 41.6% in spectral efficiency for the average of all sDevices and wDevices are achieved by the new designs.

A cognitive device-to-device (D2D) network with D2D transmitters (DTs) that harvest radio-frequency (RF) energy from the primary transmitters (PTs) is investigated. A novel D2D transmitter-assisted cooperative (DTAC) protocol is proposed, in which a group of DTs that have no transmission opportunity act as potential relays to improve the communications of the primary network. The primary network outage probability is characterized and used to make comparisons between the direct link and the cooperative link which adopts different combining techniques at the primary receivers. The active probability of the DTs is derived, and the D2D network throughput is maximized by seeking an optimal transmission power for the PTs. Simulation results are provided to validate the theoretical analysis.

Packet collision is a well-known severe impairment in ALOHA-based networks and, more generally, in any random access network. As a consequence, several methodologies have been considered with the aim of lowering the resulting performance degradation. A novel multiuser detection scheme exploiting channel diversity to separate collided signals is proposed here to enable multiple packet reception capability in random access schemes. The performance of this approach is analytically derived and optimized in terms of network throughput, and compared with that of different alternatives. The overall performance in terms of throughput shows the effectiveness of the proposed scheme in different operating conditions.

Determining tractable analytical expressions for the probability density functions (PDFs) of correlated Rayleigh random variables (i.e., the multivariate Rayleigh joint PDF) is a longstanding problem in wireless communications. Recent results have reported simpler forms for the 3-D and 4-D Rayleigh joint PDFs. Yet, the new solutions are still mathematically complex. New representations for the general 3-D Rayleigh and the general 4-D Rayleigh fading PDFs are derived. An advantage of the new representations is that only a single-integral computation is needed to compute the 3-D Rayleigh PDF and only double integral computation is needed for the 4-D Rayleigh PDF, where the integrals are proper and definite on [0, π) and [0, 2π), respectively. The new expressions for the 3-D and 4-D Rayleigh PDFs are used to determine several special, “best" placements in the 2-D plane for three and four antennas. Closed-form solutions are found for three antennas with two or three independent antenna pairs, and four antennas with four or five independent antenna pairs.

The maximal ratio combining (MRC) receiver has excellent performance in the uplink of massive multiple-input-multiple-output (MIMO) systems under favorable propagation, but the performance degrades very much in a harsh channel because of interference. Theoretical analysis showing this phenomenon is given for a particular class of fading channel. A novel receiver, exploiting preemphasis/deemphasis enhances the performance of MRC in the harsh channel by suppressing interference. MRC is shown to exhibit performance ceilings in a particular harsh massive MIMO channel whereas the novel receiver does not. Analytical lower bounds of the uplink achievable rate of the two methods and simulation results show the effectiveness of the proposed receiver. Monte Carlo simulation shows that the new receiver has comparable performance to minimum meansquare error (MMSE)/zero-forcing (ZF) while having much lower implementation complexity.

A max-min fairness resource allocation is studied for wideband cognitive radio under sensing-based spectrum sharing with simultaneous wireless information and power transfer. Specifically, the throughput of the worse-case secondary user is maximized by jointly optimizing the sensing time, transmit power and subchannel allocation, subject to constraints on energy harvesting, interference power and transmit power. The formulated max-min fairness resource allocation problem is a mixed integer non-convex programming. An efficient one-dimensional search algorithm based on the proposed transmit power and subchannel allocation scheme is designed to solve the formulated problem. Several tradeoffs are found, such as a tradeoff between the sensing performance and the throughput of the secondary user under a max-min fairness criterion.

A definition of least cyclostationary order (LCO) is proposed based on the inner cyclic period of single carrier and orthogonal frequency division multiplexing (OFDM) signals. The LCOs of single carrier and OFDM signals are derived. Since the LCO has a relationship with the carrier frequency offset (CFO), a blind CFO estimation scheme for single carrier and OFDM signals can be proposed. The novel scheme is entirely blind without any priori information and is proved to be the same as cumulants estimation when the LCO is known. However, the new scheme is superior to the estimation based on cumulant when the LCO is unknown. The mean‐square error of M ‐phase shift keying signals approaches the Cramér–Rao bound in additive white Gaussian noise (AWGN) channel. Simulation results are given to verify the effectiveness of the proposed blind estimation scheme in Rician fading channel and in AWGN channel.

An efficient cooperative spectrum sensing (SS) scheme based on Cholesky decomposition of the covariance matrix is proposed. The maximum eigenvalue (ME) of the matrix obtained by Cholesky decomposition is used as a test statistic. Analytical expressions for the false alarm probability and the decision threshold are derived. The effects of noise uncertainty on the ME SS algorithm and on the Cholesky ME cooperative SS scheme are assessed. It is proved that the proposed SS scheme is more robust than the conventional ME SS scheme in terms of noise uncertainty. Simulation results show that the performance of the proposed scheme is better than that of existing ME SS scheme in some conditions.

The relay-aided multicast network is considered, where an NT -antenna source multicasts confidential messages to N single-antenna legitimate users via a self-sustainable M-antenna regenerative relay. In particular, the relay is powered by the energy harvested from the radio signal of the source, and there are K unauthorized eavesdroppers wiretapping the channel. Assuming the knowledge of statistical channel state information of eavesdroppers, we aim to minimize the source transmission power via energy-efficient beamforming, subject to the signal-to-noise ratios of legitimate users/relay, the power constraint at the relay, and the outage constraints of the eavesdroppers. An efficient algorithm is developed by using the iterative first-order Taylor expansion and successive convex approximation, where the original nonconvex problem is transformed and solved.

Collaborative spectrum sensing is an effective method to improve detection rates in cognitive radio networks. However, it is vulnerable to spectrum sensing data falsification (SSDF) attacks when malicious secondary users (SUs) report fraudulent sensing data. In order to improve the robustness, numerous attack prevention schemes have been proposed to identify malicious SUs. Nevertheless, most of them neglect to incentivize SUs to send truthful reports. An incentive method based on peer-prediction is proposed to identify malicious suspects, punish attackers, and incentivize SUs to send truthful reports simultaneously for decision fusion. Moreover, continuous peer-prediction derived from the binary case is introduced, which is capable of preventing attacks in the continuous domain. Theoretical analysis and simulation results demonstrate that honest SUs are rewarded for accurate and truthful sensing results, while malicious SUs incur penalty for making falsified sensing reports. A significant improvement of detection rates is obtained by the proposed scheme when there are no more than half of malicious SUs conducting SSDF attacks.

Green communications is an inevitable trend for future communication network design, especially for a cognitive radio network. Power allocation strategies are of crucial importance for green cognitive radio networks. However, energy-efficient power allocation strategies in green cognitive radio networks have not been fully studied. Energy efficiency maximization problems are analyzed in delay-insensitive cognitive radio, delay-sensitive cognitive radio, and simultaneously delay-insensitive and delay-sensitive cognitive radio, where a secondary user coexists with a primary user and the channels are fading. Using fractional programming and convex optimization techniques, energy-efficient optimal power allocation strategies are proposed subject to constraints on the average interference power, along with the peak/average transmit power. It is shown that the secondary user can achieve energy efficiency gains under the average transmit power constraint, in contrast to the peak transmit power constraint. Simulation results show that the fading of the channel between the primary user transmitter and the secondary user receiver and the fading of the channel between the secondary user transmitter and the primary user receiver are favorable to the secondary user with respect to the energy efficiency maximization of the secondary user, whereas the fading of the channel between the secondary user transmitter and the secondary user receiver is unfavorable to the secondary user.

Collaborative spectrum sensing is an effective method to improve the detection rate in cognitive radio. However, it is vulnerable to spectrum sensing data falsification attacks. In order to improve the robustness, numerous attack prevention schemes have been proposed to identify malicious secondary users (SUs). Nevertheless, most of them neglect to incentivize SUs to send truthful reports. Therefore, an incentive method based on Private-Prior Peer-Prediction with approximate subjective priors is proposed to identify malicious suspects and punish attackers when falsifying the sensing data simultaneously. The theoretical analysis and simulation results demonstrate that honest SUs are rewarded by accurate and truthful sensing results while malicious SUs receive heavy loss for making falsified sensing results. Moreover, a significant improvement of detection rates is demonstrated when there are a large number of malicious SUs conducting cooperative attacks compared to the pure majority rule scheme.

The performance of underlay cognitive relay networks with multiple primary users and multiple proactive decode-and-forward relays is investigated. Particularly, both interference power constraints at multiple primary receivers and multiple primary transmitters' interference at secondary transmission nodes are taken into account. Considering correlations among the received signal-to- interference-plus-noise ratios, exact closed-form expressions for the outage probabilities of secondary users are derived for the cases with or without a direct secondary link over Rayleigh fading channels. A novel method is proposed to analyze the outage probability for cognitive proactive decode- and-forward relay networks in the presence of a direct secondary link. Simulation results show that the diversity gain is zero in the presence of multiple primary transmitters' interference, but the outage floor in the high SNR can be significantly decreased by an increase of the number of relays or by exploiting a direct secondary link.

For meteor burst communications (MBC), although per-survivor processing (PSP) based on joint data and channel estimation provides superior performance and robustness for meteor burst communications (MBC), great computational complexity constrains its application in practice. On this occasion, a dimension-down PSP (D- PSP) algorithm and a adaptive state reduction of PSP (ASRP) algorithm are proposed to curve this problem in this paper. On the basis of this, the adaptive state reduction using a dimension-down PSP (ADPSP) is proposed to combine the advantages of D-PSP and ASRP, which reduces the computational time and memory size for exponentially decaying meteor burst channels and makes maximum likelihood sequence detection (MLSD) possible for adaptive data transmission. Simulation results are presented to validate the theoretical analysis. It is shown that deploying the proposed ADPSP algorithm can achieve a good tradeoff between performance and computational complexity dynamically, and provide reliable data transmission for MBC systems with adaptive coding and modulation.

A unified performance analysis is presented for dual-hop amplify-and-forward (AF) relaying systems operating over non-identically distributed Rician fading channels. A general, two-parameter AF relaying model is used such as to cover various AF relaying schemes, namely, variable-gain AF relaying, fixed-gain AF relaying, and channel-assisted relaying, as well other unconventional schemes. Although, in some applications, systems operating over Rician fading links can be approximated and analyzed using equivalent systems operating over Nakagami- m fading links, we show that this is not sufficiently accurate in the case of AF relaying systems. Therefore, single-fold infinite-series expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the instantaneous end-to-end received signal-to-noise ratio (SNR) of such systems are derived, and Monte-Carlo simulations are used to verify the precision of the derived expressions. In addition, the effects of the relaying model parameters, as well as the channel fading parameters, on system performance are studied.

The outage probability of a two-hop coordinated decode-and-forward relay network is investigated. Relay coordination is performed only with the dominant interferer. Different levels of network coordination are studied and their performances are compared. Exact expressions are derived for the outage probability of a particular mobile user for each coordination scheme. Asymptotic outage probability is derived to identify the diversity and coding gains for each coordination scheme.

The performance of optimum combining (OC) in decode-and forward (DF) relaying in the presence of a Poisson field of interferers is analyzed. An approximation for the outage probability of the OC receiver is derived by considering the temporal correlation of the interference. Despite the randomness of the number and the locations of the interferers, the OC receiver suppresses the interference at the destination node and diversity gains are achieved, provided that the relay nodes are noise limited. For single-antenna relay nodes, the end-to-end performance is vulnerable to interference at the relay nodes which is not canceled, resulting in zero diversity gains.

A direct evaluation method is proposed to obtain numerical solutions for the performance metrics of dual-hop amplify-and-forward relaying systems. The proposed method accommodates any link fading distributions. The results obtained are precise while requiring less computational time than simulation, about 40 times less. The proposed solution is used to obtain precise results for the average symbol error probability, ergodic capacity and outage probability of systems operating over Nakagami-m fading links with arbitrary, non- integer fading parameter m. The new direct solution method allows the accurate assessment of the case of Nakagami-0.5 fading, the worst case fading scenario of Nakagami-m fading.

The biproduct correlation coefficient matrix structure has gained acceptance and application in wireless communications. Yet, the set of correlation matrices that has this structure has not been fully identified. It is known that the positive equicorrelated matrix satisfies the biproduct condition, but little else is known. The set of admissible correlation matrices having the special biproduct structure is investigated. Constraints on the signs of the correlation coefficients that define the admissible set are revealed. Additional constraints on the magnitudes of the correlation coefficients for admissibilty are also identified. The set of matrices satisfying the required structure is much more restricted than previously thought. The constraints are shown to become increasingly restrictive as the dimension $N$ of the correlation matrix increases. The constraints also become more restrictive as the values of the correlation coefficients increase to approach 1. Previously, only the equicorrelated matrix has been identified as having the biproduct structure. Two additional correlation matrix structures satisfying the biproduct structure are identified. Tests that exclude a correlation matrix from having the biproduct structure are derived.

An equivalent model for a multiple-input-multiple-output communication system with space-time block codes (STBCs) is proposed based on a revealed connection between STBCs and Euclidean codes. Examples of distance spectra, signal constellations, and signal coordinate diagrams of Euclidean codes equivalent to simplest orthogonal STBCs are given. A new asymptotic upper bound for the symbol error rate (SER) of STBCs, based on the distance spectra of the equivalent Euclidean codes, is derived, and new general design criteria for signal constellations of the optimal code are proposed. Some bounds relating distance properties, dimensionality, and cardinality of STBCs with constituent signals of equal energy are given, and new signal constellations with cardinalities of 8 and 16 for Alamouti's code are designed. A general methodology for performance analysis of STBCs is revisited. As an example of the application of this methodology, an exact evaluation of the SER of an orthogonal STBC is given. Namely, a new expression for the SER of Alamouti's code with binary phase shift keying signals is derived.

The outage probability of a two-hop coordinated decode-and-forward relay network is investigated. The case of two interfering cells is considered. This is analogous to the case when network coordination is performed with the dominant cochannel interfering cell. Different levels of network coordination are studied and their performances are compared. Exact expressions are derived for of the system for each coordination method. The impact of user location randomness on the outage probability is investigated.

Cooperative communication through relaying can improve the performance of communication systems under multipath fading conditions. Increasing the number of relays will also boost the performance of the system, but since relays transmit through orthogonal channels, this improvement is at the cost of bandwidth or rate of the system. A two-hop multi-relay decode-and-forward cooperative system is proposed in which selected relays transmit simultaneously in the same band, and therefore, there is no rate or bandwidth loss. To mitigate the error propagation due to incorrect decoding of symbols at the relays, we use a selection relaying method in which a relay transmits in the second hop if the channel quality between the relay and the source exceeds a minimum threshold regardless of the relay-destination link. In our proposed beamforming scheme, the phase of selected relays for transmission in the second hop is adjusted to compensate for the channel between the relay and the destination and achieve the best performance at the destination using only a simple MRC receiver. The relays use only two-bit quantized phase information of the channel gain between the relay and the destination, which can be sent to the relays by the destination. The general family of M-QAM modulation constellations is considered in the performance and diversity analysis. It is proved that the scheme achieves full diversity order, and closed-form expressions for the thresholds that achieve full diversity are found.

The performance of optimum combining (OC) in amplify-and-forward (AF) relaying systems in the presence of co-channel interference (CCI) is analyzed using a tight approximation for the signal-to-interference-plus-noise ratio (SINR) at the destination. Two types of relaying protocols are studied, all-relay transmission with OC and best-relay transmission with OC. When CCI is present only at the destination, both relaying protocols achieve diversity gains up to M when interferer powers are scaled with the source and the relay powers, where M is the number of relays. Best-relay transmission with OC maximizes the spectral efficiency as each communication consumes only two time slots.

Spatial point processes are commonly used to model the placement and the number of interferers in modern wireless networks, where the ad hoc deployment of transmitters is common. The homogeneous Poisson point process (PPP) is the most popular spatial point process used to model co-channel interference. Optimum combining (OC) is the diversity combining technique that maximizes the signal-to-interference-plus-noise ratio at the receiver. The performance of OC in cooperative relaying in an interferer field modeled by a homogeneous PPP is analyzed. Both decode-and-forward (DF) and amplify-and-forward (AF) relay protocols are studied. Multirelay transmission and relay selection techniques are considered. Accurate approximations for the outage probability are derived for DF and AF relaying when the destination is able to estimate the noise-plus-interference correlation matrix (NICM) perfectly. An approximation for the outage probability of DF relaying is obtained when the destination only estimates the channel state information of the closest interferer. Relay selection outperforms multirelay transmission in both DF and AF relaying protocols. The interference correlation at the relays significantly degrades the outage performance. Limited estimation of the NICM results in better performance than conventional maximal-ratio combining, although it fails to achieve diversity gains.

It is well known that avalanche effect errors in received noisy ciphertexts will cause severe error propagation in block-ciphered encryption systems, thus resulting in a large reduction in the achievable throughput. However, little is known about the statistical properties of the underlying error sequences in decrypted plaintexts in block-ciphered systems when channel errors are present. A rigorous study of the statistical properties of the errors in block-ciphered crypto-systems operating in cipher block chaining (CBC) mode is provided. The equivalent channel transition probability is obtained and then used to derive error statistics including both error weight probabilities and gap distributions. The validity of the theoretical analyses is confirmed by the excellent match with results obtained by simulated data encryption standard (DES)-based and advanced encryption standard (AES)-based crypto-systems operating in CBC mode. The error statistics will be valuable in the design and performance evaluation of communication protocols, as well as in error-control schemes for block-ciphered crypto-systems in the presence of erroneous ciphertexts, where errors are intentionally left to enhance security against passive eavesdroppers.

A cooperative network consisting of a source, one relay, and a destination is considered. The source and destination are both equipped with a single antenna. The relay is equipped with N antennas and operates in decode-and-forward (DF) mode. At the relay, the detected symbols are retransmitted using a novel beamforming method proposed in this paper that assumes the relay has 2-bit quantized information about the phase of all links from the relay to the destination. At the destination, the detector combines the received signals from the source and the relay in the first and second phases of transmission, respectively. An upper bound for the bit error rate (BER) performance of the detector is derived, and it is shown that the proposed beamforming and detector achieve full diversity order. The detector is extended to a multicast system with one single antenna source, one N-antenna DF relay and M single antenna destinations. It is assumed that the relay has 2-bit quantized phase information and exact signal-to-noise ratio (SNR) information at all the links from the relay to the destinations. An antenna selection algorithm based on a MAX-MIN criterion at the relay is proposed, and after beamforming, the detector is used at all destinations. By deriving a rigorous upper bound for BER performance at all destinations, it is shown that the proposed scheme achieves full diversity order at all destinations. Simulation results show that the BER performance of the proposed antenna selection algorithm outperforms the well known MAX-MIN antenna selection scheme.

Cognitive small cell networks have been envisioned as a promising technique for meeting the exponentially increasing mobile traffic demand. Recently, many technological issues pertaining to cognitive small cell networks have been studied, including resource allocation and interference mitigation, but most studies assume non-cooperative schemes or perfect channel state information (CSI). Different from the existing works, we investigate the joint uplink subchannel and power allocation problem in cognitive small cells using cooperative Nash bargaining game theory, where the cross-tier interference mitigation, minimum outage probability requirement, imperfect CSI and fairness in terms of minimum rate requirement are considered. A unified analytical framework is proposed for the optimization problem, where the near optimal cooperative bargaining resource allocation strategy is derived based on Lagrangian dual decomposition by introducing time-sharing variables and recalling the Lambert-W function. The existence, uniqueness, and fairness of the solution to this game model are proved. A cooperative Nash bargaining resource allocation algorithm is developed, and is shown to converge to a Pareto-optimal equilibrium for the cooperative game. Simulation results are provided to verify the effectiveness of the proposed cooperative game algorithm for efficient and fair resource allocation in cognitive small cell networks.

ABSTRACT Closed‐form asymptotic expressions for bit error rate and outage probability are derived for multi‐branch equal gain combining and selection combining receiver diversity over equally correlated Rician channels. Numerical results indicate that these analytical solutions can provide accurate estimation of bit error rate and outage probability in large signal‐to‐noise ratio regimes. The analytical results reveal some important insights into the performance characteristics of equal gain combining and selection combining diversity operating over equally correlated Rician fading channels. Copyright © 2013 John Wiley & Sons, Ltd.

Random wireless networks with finite number of nodes distributed uniformly in a square-shaped finite region are considered. The transmission channels are assumed to experience Nakagami-m fading. A closed-form expression for the cumulative distribution function (CDF) of the interference power imposed on two randomly-located communicating nodes is derived. In contrast to most of the existing literature, the receiving node is not necessarily required to be located at the center of the network region. Two packet traffic patterns, viz., slotted-synchronous and slotted-asynchronous are considered and closed-form expressions for the CDF of the interference is obtained for each traffic pattern. Computer simulation illustrates the validity of the theoretical analyses.

Recently, many technological issues pertaining to cognitive small cell networks have been studied, including resource allocation and interference mitigation, but most studies assume non-cooperative schemes or perfect channel state information (CSI). Different from the existing works, in this paper, we investigate the joint uplink subchannel and power allocation problem in cognitive small cells using cooperative Nash bargaining game theory, where the cross-tier interference mitigation, minimum outage probability requirement, imperfect CSI and fairness in terms of minimum rate requirement are considered. A unified analytical framework is proposed for the optimization problem, where the near optimal cooperative bargaining resource allocation strategy is derived based on Lagrangian dual decomposition by introducing time-sharing variables and Lambert-W function. Moreover, we theoretically prove the existence, uniqueness, and fairness of the solution to this game model. Accordingly, a cooperative Nash bargaining resource allocation algorithm is developed, which is shown to converge to a Pareto-optimal equilibrium for the cooperative game. Simulation results are provided to verify the effectiveness of the proposed cooperative game algorithms for efficient and fair resource allocation in cognitive small cell networks.

A generalized fading model is introduced which combines a diffuse Nakagami-m scatter and a LOS component. Solutions for the PDF of the proposed fading model are found in terms of infinite series and as a finite sum in terms of the hypergeometric functions. The behaviors of the diffuse Nakagami-m with LOS fading are investigated and are shown to be significantly different from the behaviors of Rice and Nakagami-m distributions. The bit error rate (BER) of a binary phase shift keying (BPSK) system operating in diffuse Nakagami-m with LOS fading is derived, and is compared to the BERs of BPSK systems operating in Nakagami-m and Rice fading channels.

The downlink performance of a dual-cell relay enhanced wireless network is investigated. A single relay is shared by the two base stations in the system. The relay is assumed to be placed in a region covered by both base stations. The relay station is operating in the decode-and-forward mode. Closed-form approximations which follow the exact results extremely closely are derived for the outage probability and the ergodic rate of the system.

The downlink performance of a two-cell relay enhanced wireless network is investigated. A single relay is shared by the two base stations in the system. The relay is assumed to be placed in a geographic region covered by both base stations. The relay station is operating in the decode-and-forward mode. Closed-form approximations which estimate the exact results extremely closely are derived for the outage probability and the ergodic rate of the system. The impact of finite rate channel state information feedback on the user ergodic rate is examined.

Femtocells are being considered a promising technique to improve the capacity and coverage for indoor wireless users. However, the cross-tier interference in the spectrum-sharing deployment of femtocells can degrade the system performance seriously. The resource allocation problem in both the uplink and the downlink for two-tier networks comprising spectrum-sharing femtocells and macrocells is investigated. A resource allocation scheme for cochannel femtocells is proposed, aiming to maximize the capacity for both delay-sensitive users and delay-tolerant users subject to the delay-sensitive users' quality-of-service constraint and an interference constraint imposed by the macrocell. The subchannel and power allocation problem is modeled as a mixed-integer programming problem, and then, it is transformed into a convex optimization problem by relaxing subchannel sharing; finally, it is solved by the dual decomposition method. Subsequently, an iterative subchannel and power allocation algorithm considering heterogeneous services and cross-tier interference is proposed for the problem using the subgradient update. A practical low-complexity distributed subchannel and power allocation algorithm is developed to reduce the computational cost. The complexity of the proposed algorithms is analyzed, and the effectiveness of the proposed algorithms is verified by simulations.

We define a symbol transition matrix (STM) as a matrix whose entries are the symbol transition probabilities of a relay in a decode-and-forward (DF) relaying system. Using the STM as a state transition matrix of a discrete-time Markov chain, the source-to-destination STM is shown to be the product of intermediate STMs in multihop DF relaying systems. We show that the probability of correct decision at the destination is the trace of the source-to-destination STM divided by the modulation order. The symbol error probabilities (SEPs) of multihop DF relaying systems with any modulation scheme in any independent and nonidentically distributed (ind) channels are derived using the STM. For multihop DF relaying systems in independent and identically distributed (iid) channels, the eigenvalues of the single link STM are used to simplify the calculation of the SEP for any modulation scheme. Also, the SEP of multihop DF relaying systems with 16-quadrature amplitude modulation (QAM) signals in ind Rayleigh fading channels is derived using the STM. A relay advantage criterion is derived for multihop DF relaying systems in iid Nakagami-m fading channels with both the total transmitted energy and the source-to-destination distance fixed. The relay advantage criterion can be used for deciding whether putting more relays between the source and the destination increases or decreases the SEP.

The asymptotic performances of multibranch diversity reception systems employing the popular and important combining techniques over arbitrarily correlated Rician channels are studied. Based on an integral representation of the joint probability density function of multivariate Rician random variables with arbitrary correlations, closed-form expressions for asymptotic error rate and asymptotic outage probability are derived for multibranch receiver diversity receptions. The important diversity schemes studied are maximal ratio combining, equal gain combining, selection combining, and hybrid maximal ratio combining as well as hybrid equal gain combining. Numerical results indicate that these analytical solutions can provide accurate estimation of error rate and outage probability in large-signal-to-noise-ratio regimes. The analysis provides some important theoretical and practical results concerning the performance characteristics of multibranch diversity receivers operating on arbitrarily correlated Rician fading channels.

Multiaccess interference (MAI)-plus-noise whitening for detecting impulse radio ultra-wide bandwidth (IR-UWB) signals transmitted over ideal free-space and the IEEE 802.15.3a channels is considered. IR-UWB signals are very sparse in time and, thus, MAI-plus-noise whitening cannot introduce intersymbol interference (ISI) in IR-UWB systems operating on an ideal free-space channel. In addition, ISI in UWB multipath fading channels can be eliminated by a proper choice of the frame duration. An analytical expression for the signal-to-interference-plus-noise ratio (SINR) of IR-UWB systems after MAI-plus-noise whitening is derived and the SINR improvement due to whitening is investigated. It is shown that whitening can improve the performance of a variety of the well-known IR-UWB receivers, viz., soft-limiting, P-order metric, optimal, and the conventional matched filter receivers. It is also observed that MAI-plus-noise whitening can improve the overall SINR of the system and, thus, decrease the complexity of Rake receivers through reducing the number of their processing branches.

In order to mitigate the problem of crowded radio spectrum, dynamic spectrum access (DSA) has become the solution and a research focal point. The number of works in wideband spectrum sensing is dramatically increasing recently due to its importance in cognitive radio (CR) networks. Most works assume that secondary users (SUs) are synchronous with the primary users' (PUs) network. However, in many practical systems the SUs will have no information about the PUs' communication protocols. Furthermore, it is also possible that communications among PUs are not based on synchronous operation. In order to address such problems, a contention-based wideband DSA algorithm with asynchronous cooperative spectrum sensing (CSS), called the DySac, is proposed. In this scheme, the SUs need not maintain synchronism with the PUs, and the SUs who intend to access the primary network compete among each other for available channels. Performance analysis and simulations are conducted to evaluate the proposed DySac.

Closed-form expression for the outage probability of dual-hop amplify-and-forward (AF) systems with relay selection from N independent and non-identically (i.ni.d.) distributed dual-hop branches is obtained. Closed-form expression for the probability density function of the end-to-end signal-to-noise ratio (SNR) is also obtained for such systems, and is used to obtain the exact average symbol error probability for systems operating over i.ni.d. Nakagami-m fading links. It is found that the limiting slopes of the outage probability and the average symbol error probability curves are proportional to the sum of the minimums of the fading parameters of the source-to-relay and relay-to-destination links of each branch. The modified generalized transformed characteristic function (M-GTCF) is used to obtain exact, integral solutions for the outage probability and the average symbol error probability of multihop AF relaying systems operating over N i.ni.d. Nakagami-m fading links. It is found that the limiting slopes of the performance metrics curves are proportional to the minimum of the fading parameters of the individual links. Dual-hop AF systems with relay selection from N available relays are compared to multihop AF systems with N intermediate relays. It is found that dual-hop AF systems can significantly outperform multihop AF systems. The findings are used to propose multiple criteria for practical design of wireless cooperative systems.

The diversity gains of cooperative relay networks are degraded in the presence of co-channel interference (CCI), which is the principal limiting factor in a properly planned cellular network. Optimum combining (OC) can be used to mitigate the adverse effects of CCI, which enables achieving diversity gains when CCI is present. The performance of OC in a channel state information (CSI) assisted amplify-and-forward (AF) relay network is analyzed when the destination node is affected by CCI, with the aid of a tight approximation for the signal-to-interference-plus-noise-ratio (SINR) at the destination node. Closed-form expressions are derived for the outage probability and the moment generating function for the approximated SINR. It is proved that OC results in a diversity gain of M, where M is the number of relay nodes. OC shows significant performance improvements over maximal-ratio combining (MRC), which reaches error floors at low-to-medium power levels.

Cooperative spectrum sensing is a promising technology for spectrum sensing with superior performance. Previous work has assumed that secondary users (SUs) are synchronous with the primary users' (PUs) network. However, on one hand, the SUs may have no information about the PUs' communication protocols. On the other hand, in some cases communications among PUs are not based on synchronous operation. In order to address such problems, an asynchronous cooperative sensing scheme is proposed. In this scheme, the SUs need not synchronize with the PUs when dynamically sensing and accessing primary channels. The channel-usage pattern is modeled as an ON-OFF process and the SUs' average throughput of each asynchronous case is analyzed based on the detection and false alarm probability. The optimal sensing period for the sensing scheme is achieved by maximizing the SUs' average throughput. Simulation results evaluate the performance of the scheme.

Cooperative relaying achieves a wide range of advantages including diversity gain, coverage extension and mitigation of shadowing. Nevertheless, the performance advantages of cooperative relaying diminish considerably if co-channel interference is present. Optimum combining (OC) can be used to mitigate the adverse effects of co-channel interference in wireless communications. The performance of optimum combining in a decode-and-forward relay network with N equal-power interferers is analyzed. The probability density function of the output signal-to-interference-plus-noise ratio is obtained and a closed-form expression for the exact outage probability is derived for N ≥M+1 where M is the number of relay nodes. An approximation for the symbol error rate (SER) is presented. The performance results and closed-form expressions for outage probability and for SER suggest that the asymptotic diversity gain of OC is equal to M, which is a significant improvement over maximal-ratio combining, whose asymptotic diversity gain is equal to zero when operating in co-channel interference.

One nontrivial special value of the bivariate Gaussian distribution is well known. Two unreported nontrivial special values are derived.

Estimation of the location parameter of the generalized Gaussian distribution with shape parameterp= 5 is studied and a novel closed-form approximate maximum likelihood estimator is proposed. The new estimator outperforms all other closed-form estimators forp=5 .

A novel generalized framework for performance analysis of selection combining diversity in Rayleigh fading channels is derived. It is shown that the performance of arbitrary systems used with selection combining diversity can be expressed in terms of only the performance of the system on a single branch Rayleigh fading channel. The results are valid for coded and uncoded transmission as well as for balanced (equal power) diversity branches and unbalanced (unequal power) diversity branches. The generalized framework encompasses both general noise and general interference, and allows correlated noise and correlated interference sources. Applications of the generalized framework to analytical, semi-analytical and simulation based performance evaluation of digital modulation schemes are discussed.

The performance of opportunistic relaying in a dual-hop amplify-and-forward relay network where the relaying nodes are distributed according to a homogeneous two-dimensional Poisson point process with fixed density is analyzed. Largely ignored in the literature, this assumption leads to more realistic results, as in a typical practical scenario neither the number of relays nor their distances from the source and destination are known. An exact expression for the outage probability of this cooperative system for general fading environments and different types of relaying is derived. The expression is then {simplified under an assumption that the radius of the relay deployment region is sufficiently large}, and specialized to additive white Gaussian noise (no fading), Rayleigh fading and severe (half-Gaussian) fading environments. Simple and tight upper and lower bounds on the outage probability are also derived. Simulation results validate the theoretical analyses and verify the accuracies of the proposed bounds.

The outage probability of a multiuser two-hop amplify-and-forward relaying system employing opportunistic scheduling is investigated. A practically important case where there are cochannel interference signals present at the network is considered for the analysis. Exact expressions and closed-form lower bounds are derived for the outage probability. Exact closed-form expressions are derived for the system outage probability when interference signals are present at the relay and at the destination separately. A closed-form lower bound is derived for the outage probability when the relay and the destination nodes are affected by interference simultaneously. The effects of channel state information feedback delay are investigated for special cases. In addition, asymptotic outage probability results are derived to obtain useful insights on the effects of interference and feedback delay. The novel expressions can be used by practicing engineers to obtain reliable and realistic performance estimates for dual-hop multiuser relay networks. The results are useful for understanding the capabilities of the feedback channel required in this system.

The optimization of pilot symbol parameters can improve the spectral efficiency of adaptive modulation for orthogonal frequency division multiplexing (OFDM) systems, since pilot symbols impose an overhead on the system consuming power and bandwidth. An optimal pilot symbol assisted adaptive modulation (PSAAM) scheme for OFDM systems is proposed that maximizes spectral efficiency by adapting the power and constellation size of each subcarrier based on employing imperfect channel state information (CSI) at the transmitter. The pilot symbol power and spacing is also optimized in this scheme. A suboptimum scheme that decreases computational complexity without perceivable loss in performance is also presented. The optimality of minimum mean square error (MMSE) channel prediction for OFDM systems expressed in terms of a lower bound on spectral efficiency is approached. It is proved that the rectangular pilot pattern with equi-spaced and equal power pilot tones achieves the minimum MSE of the channel prediction in addition to having the advantage of simplifying PSAAM design. Numerical results show the importance of optimal pilot parameter adjustment for rapidly fading channels.

Ultra-wide bandwidth communication systems are known to suffer from non-Gaussian interference. In general, wireless ad-hoc networks, due to the lack of perfect power control and the random placement of nodes, are very likely to experience non-Gaussian multiple access interference. In systems with additive non-Gaussian noise, non-Gaussian signal detection and nonlinear signal processing can play important roles, especially in suppressing the multiple access interference. Practical ultra-wide bandwidth receiver designs based on the α-stable non-Gaussian additive impairment model are proposed and evaluated. It is demonstrated that the α-stable model together with a fractile based parameter estimation technique constitute a robust technique for adaptive receiver designs. The proposed receivers based on the α-stable model suppress multiple access interference, adapt to the noise and the interference in the environment, and are robust to estimation errors in the receiver parameters. The proposed receivers provide much better bit error rates than linear detectors and previously known nonlinear detectors.

ABSTRACT The channel capacity and the bit error rate of ultra‐wide bandwidth transmitted‐reference systems are optimized with respect to time delay between the reference and the adjacent data pulses. Approximate and theoretical expressions for the signal‐to‐interference‐plus‐noise ratio are derived. Numerical results show that optimizing the receiver can provide a significant capacity improvement of up to 2.2 bits/s/GHz and a bit error rate performance gain of up to 2 dB in effective signal‐to‐noise ratio. Copyright © 2011 John Wiley & Sons, Ltd.

The outage probability of a multiuser amplify-and-forward relaying protocol is investigated. The practical case where there are co-channel interference signals present at the network is considered for the analysis. Exact expressions and closed-form lower bounds are derived for the outage probability. Three network configurations are analyzed based on the presence of co-channel interference in the system.

An adaptive resource allocation scheme is designed for OFDM that maximizes the average transmission rate by adapting the power of the data symbols while optimizing the pilot symbol spacing and power. Assuming imperfect channel state information (CSI) at the transmitter, the exact solution obtained for optimum power loading across data subcarriers can not be expressed in terms of elementary functions. A useful approximation, that has the simple form of a water-filling function, is derived for determining the optimum power loading function that is based on imperfect CSI. The merits of the proposed adaptive resource allocation schemes are corroborated by numerical results.

Computation of the lognormal characteristic function (CF) is required in analysis of many wireless communication systems. No closed-form expression exists for the lognormal CF. In this paper, two approximations to the lognormal CF are derived. The approximations are accurate over specified ranges of parameters. The first approximation is in terms of elementary mathematical functions and is useful for parameters typical in optical communication applications. The second approximation is a finite series in terms of the generalized hypergeometric functions and can be used to evaluate the lognormal CF with parameters motivated by both optical and wireless communication applications. Theoretical results are corroborated by computer simulations.

An exact expression for the outage probability of opportunistic relaying in a dual-hop amplify-and-forward relay network is derived for general fading environments and the case where the source and destination nodes make use of directional antennas. The relaying nodes are assumed to be distributed according to a homogeneous two-dimensional Poisson point process with fixed density. This assumption is of great practical importance as in a typical practical scenario, the number of relays as well as their distances from the source and destination are random. It is observed that under some circumstances, a directional antenna at the source may permit more efficient deployment of the relay network than the case where an omnidirectional antenna is used.

Novel expressions for the symbol error probability (SEP) of maximal ratio combining (MRC) diversity detection are derived. The case of independent and identically distributed Nakagami-m fading channels is considered. It is shown that expressions for the SEPs of MRC diversity operating in Nakagami-m fading channels can be obtained by both replacing the diversity order, L, with mL and replacing the average signal-to-noise ratio (SNR) per bit, γ̅ with γ̅/m in expressions for the SEPs of MRC diversity in Rayleigh fading channels. An identity which states that the bit error probability (BEP) of L-branch soft-decision MRC detection equals that of (2L - 1)-branch hard-decision detection with majority logic combining, both in independent Rayleigh fading channels and with equal branch SNRs, is recalled. The identity is used to derive new expressions for the SEP of MRC diversity in Nakagami-m fading channels. It is also shown that outage probability and average level-crossing rate for MRC reception in Nakagami-m fading channels can be obtained from corresponding outage probability and average level-crossing rate for MRC reception in Rayleigh fading channels. The relationships established will find application both in deriving solutions to unsolved problems and, where past solutions exist, in finding simpler solutions.

The problem of determining the distribution of sums of (weighted) log-gamma random variables occurs in spectrum sensing for cognitive radio. An infinite series is derived for the characteristic function of log-gamma random variables. Some special cases are identified for which the infinite series can be represented in terms of some well-known functions, greatly improving computational simplicity and robustness. The derived characteristic function representations are used to calculate the PDF of sums of log-gamma random variables. The results are extended to the case of weighted sums of log-gamma random variables. Examples indicate that a Gaussian approximation to a log-gamma sum density can be very inaccurate for smaller numbers of summands. The application of the results to a spectrum sensing problem in cognitive radio is explained.

New, exact closed-form expressions are derived for the probability density function (PDF) and the cumulative distribution function (CDF) of the instantaneous end-to-end signal-to-noise ratio (SNR) of amplify-and-forward (AF) relaying systems with “full” selection diversity. The direct path, from the source to the destination, as well as multiple dual-hop paths, through intermediate relays, are considered in the selection set. The selection process follows a maximum SNR policy, such that the path of the maximum end-to-end SNR is used as the communication link, whether this path is the direct path or one of the dual-hop paths. The derived expressions are used to obtain the first exact results for the average error probability and the outage probability of such AF relaying systems. The results are verified through simulations for identically distributed as well as non-identically distributed Nakagami-m fading links. The system performance is compared to that of conventional wireless systems which use only the direct link between the source and the destination for communication. The system performance is compared also to that of an opportunistic dual-hop AF system with maximum end-to-end SNR relay selection that excludes the direct path from the selection set. Results show that the full selection system performance is superior to those in the comparison. For example, in the case of Nakagami-m fading links with m = 4 and N = 2 candidate intermediate relays, an average error probability of 2×10-4in the case of AF relaying with full selection, occurs at 4.06 dB less than it occurs in the case of only direct transmission and at 0.95 dB less than it occurs in the case of maximum end-to-end SNR relay selection that excludes the direct path from selection. Results show also that the system provides diversity gain, proportional to the selection set size, N +1.

The potential benefits of deploying Matrix C in mobile WiMAX applications are investigated for improving quality of service (QoS). Also, it is shown that Matrix C in the IEEE 802.16e standard is not a Golden code, as previously thought, but a threaded algebraic space-time (TAST) code.

A new transform method, the generalized transformed characteristic function (GTCF), gives an exact, integral solution for the probability density function of the end-to-end received signal-to-noise ratio (SNR) of multihop amplify-and-forward (AF) relaying systems. The results are precise for any number of hops and can accommodate any channel fading distribution. The theory provides the first exact theoretical solutions when the number of hops N >; 2. Both cases of identically and non-identically distributed links are investigated. The case of dissimilar links, in which the link fadings follow different distributions, is also studied. The effect of the number of hops, N, on the performance metrics is studied.

The outage probability of a recently proposed relay network with multiple antennas at the relay is analyzed. The relay uses maximal ratio combining to combine the received signals, while it uses maximal ratio transmission for the transmission. It is assumed that the reception at the relay and the destination are corrupted by multiple co-channel interfering signals. Closed-form outage probability expressions are derived when the relay is operated in the amplify-and-forward mode with fixed gain. Both cases of equal power and unequal power interferers are considered.

We examine the decoding of Matrix C in the 802.16e WiMAX standard. An exhaustive search and zero-forcing (ES-ZF) decoder and an exhaustive search and nulling canceling (ES-NC) decoder are proposed for uncoded systems. The computational complexity of Matrix C decoding using the ES-ZF decoder is shown to be the same as the complexity of the ZF decoder for Matrix B decoding with twice the number of receive antennas times the complexity of the maximum likelihood (ML) decoder for Matrix B decoding with twice the number of receive antennas. Matrix C can be implemented in a $2 × 2$ multiple-input multiple-output (MIMO) system using the ES-NC decoder with reduced complexity compared to ML decoding with no performance loss. For coded systems, double pruned trees using a zero-forcing (DPT-ZF) algorithm or nulling canceling (DPT-NC) algorithm are proposed. The DPT-NC decoder can be implemented in a $2 × 2$ MIMO coded system with reduced complexity compared to the Max-Log decoding with no performance loss.

Novel exact closed-form expressions are derived for the probability density function (PDF) and the cumulative distribution function (CDF) of the instantaneous received end-to-end signal-to-noise ratio (SNR) of dual-hop amplify-and-forward (AF) relaying systems operating over Rayleigh, Nakagami-m and Rician fading channels. New exact closed-form expressions are also obtained for opportunistic dual-hop AF relaying systems, with maximum relay-to- destination SNR relay selection. The average symbol error probability, ergodic capacity and outage probability are calculated using the derived PDF and CDF expressions. It is found that the opportunistic dual-hop AF system, with relay selection pool size M = 2, has at least 2.84 dB power advantage over the dual-hop AF system without relay selection for average error probabilities less than 10^-2 in the case of Rayleigh fading links. It is shown that although the performance of a dual-hop AF system with maximum relay-to-destination SNR relay selection is improved by increasing the selection pool size, the improvement has diminishing returns and a relay selection pool of more than 6 relays is not of practical benefit.

Recent work has reported a lognormal limit theorem for sums of identically distributed equicorrelated lognormal random variables. An extended lognormal limit theorem for sums of nonidentically distributed correlated lognormal random variables having a particular correlation structure is derived.

A new theoretical method, the generalized transformed characteristic function (GTCF) approach gives an exact, integral solution for the probability density function of the end-to-end received signal-to-noise ratio in multihop amplify-and-forward relaying systems. In turn, the GTCF approach is used to obtain exact integral solutions for the ergodic capacity, outage probability and average symbol error probability of multihop amplify-and-forward relaying systems. The results are precise for any number of hops and can accommodate any channel fading distribution. The theory provides the first exact theoretical solutions for numbers of hops larger than 2.

A novel single-integral representation for the bivariate Rician distribution was presented in a recent letter in this Transactions (ibid., vol. 59, no. 11. pp. 2951-2954, Nov. 2011). The expression given for the bivariate Rician probability density function (PDF) [1, eq. (12a)] contains a typographical error. The correct expression for the bivariate Rician PDF is presented here.

Weighted sums of Rayleigh random variables occur in diverse problems in wireless, and particularly in interference systems. Previous work has reported upper bounds on the cumulative distribution function of weighted Rayleigh sums. New lower bounds to the cumulative distribution function of weighted Rayleigh sums are derived. The new lower bounds to the cumulative distribution function are used as an intermediate result in deriving a new upper bound on the ratio of a Rayleigh random variable to a weighted sum of Rayleigh random variables shifted by a nonnegative constant. Special cases of this ratio occur in the context of cognitive radio systems and synchronization components. Novel approximations, that are tighter than any known bounds, to the cumulative distribution function of weighted Rayleigh sums are also presented.

Two optimal frameworks for multichannel spectrum sensing in cognitive radio networks are presented. Both frameworks search for multiple secondary transmission opportunities over a number of narrowband channels, enhancing the secondary network performance while respecting the primary network integrity and keeping the interference limited. Considering a sequential periodic sensing scheme with non-uniform channel sensing durations, the original sensing problems are formulated as optimization problems to maximize the throughput capacity of the secondary network subject to some bounds/limits on the interference to the primary network. The first framework, referred to as sequential multichannel joint detection, considers the aggregate (weighted) interference on the primary network as the constraint. The second framework, known as decoupled sequential multichannel joint detection, assumes that interference is limited in each channel separately (i.e. independently). The non-convex sensing problems are transformed into convex optimization problems under certain practical conditions. Simulation results demonstrate the effectiveness of both the proposed frameworks and attest to their superior performances compared to contemporary strategies.

New, exact closed-form expressions are derived for the probability density function and the cumulative distribution function of the end-to-end signal-to-noise ratio (SNR) of opportunistic dual-hop amplify-and-forward (AF) relaying systems with relay selection. The expressions are used to obtain the first exact integral solutions for the ergodic capacity and average symbol error probability, and the first exact closed-form solution for outage probability of an opportunistic AF relaying system where the best node is selected from a number of candidate intermediate nodes to relay the data signal between the source and the destination. The selection follows a maximum end-to-end SNR policy, based on the available channel state information. The results are precise for any number of candidate relays and Rayleigh, Nakagami-m or Rician fading distributions. The effects of different channel fading parameters and the number of relays in the relay selection pool are studied. The system performance is compared to that of dual-hop AF systems without relay selection and to dual-hop AF relaying systems with maximum relay-to-destination SNR relay selection. The adopted selection method provides diversity gain over dual-hop AF relaying systems without relay selection and over maximum relay-to-destination SNR relay selection. The diversity gain is proportional to the relay selection pool size.

In opportunistic relaying systems, only the relay with best channel condition among K relays is selected to take part in cooperation. This setup efficiently achieves diversity gain. However, the high switching rate of such systems may be undesirable due to practical implementation issues, for example, the corruption of the data signal by receiver switching transients, channel estimation and synchronization failures due to excessive switching as well as network control switching overheads which increase with increased switching. Recently, switch-and-examine relaying whose main advantage is its low switching rate, was proposed as a low complexity suboptimal alternative to opportunistic relaying. Meanwhile, comparisons of the switching rates of opportunistic and switch-and-examine schemes have been undertaken only for the case of Rayleigh fading. The switching rates of opportunistic relaying and switch-and-examine relaying systems with two or more relays operating under Rician and Nakagami-m fading are obtained in closed-form or single integral expressions. Results for independent and identically distributed fading links are obtained for the case of multiple relays and additionally for independent but not identically distributed fading links for the two relays case. The closed-form solutions explicitly depend on the Doppler frequency of the fading.

In many communication channels, the ambient disturbance is known through experimental evidence as well as theoretical considerations to deviate strongly from the Gaussian model. In order to evaluate the performance of digital signaling in such channels, the non-Gaussian noise must be properly modeled. The Laplace distribution is used here to model the non-Gaussian noise and study the performance of communication systems employing block data transmission in the presence of impulsive noise. Analytical expressions for assessing codeword error probability and bit error probability are derived for hard-decision decoders, soft-decision decoders and optimum maximum likelihood detectors in both nonfading and quasi-static Rayleigh fading scenarios. Numerical results are presented for different codes, block sizes and error rate levels. The characteristics of error performance are discussed for both nonfading and quasi-static Rayleigh fading channels.

An amplify-and-forward (AF) multihop relaying system employing constant-power rate-adaptive M-QAM transmission is investigated. Accurate expressions for performance evaluation in Nakagami-m fading of adaptive continuous rate (ACR) and adaptive discrete rate (ADR) M-QAM are obtained. The analysis is based on a new approximation for the instantaneous end-to-end received SNR in the form of a scaled version of the harmonic mean of the individual per-hop SNRs. The scaling factor is determined based on the average link SNRs. Performance results evaluated using the proposed approximation are more accurate than the performance bounds obtained using the conventional harmonic- mean-based upper bound on the instantaneous received SNR, even though they are obtained with the same computational complexity. Numerical results show that the approximate performance results are very close to the exact results especially in small SNR regimes and for larger values of the Nakagami parameter. It is shown that the ACR QAM achieves an average spectral efficiency within a certain distance of the Shannon limit. The ADR QAM achieves smaller bit error rates than the target bit error rate but at the expense of an additional penalty on the average spectral efficiency, especially for smaller numbers of region boundaries.

A new multihop relaying scheme based on repetition transmission is developed. The performance in Rayleigh fading of the proposed system with amplify-and-forward (AF) and decode-and-forward (DF) relaying is studied. In AF relaying systems, the source re-transmits the same signal in every three time slots, each relay simply amplifies and forwards the received signal, and the destination employs maximal ratio combining (MRC). In DF relaying systems, the source re-transmits the same signal in subsequent time slots, each relay detects the received signal based on square-law selection combining and then forwards the estimated signal, and the destination employs MRC or square-law combining. Using simple closed-form bounds on the average error probability, it is shown that the proposed repetition-based multihop transmission systems with AF relaying and DF relaying achieve diversity order equal to the number of repetitions. Numerical results are provided to assess the tightness of the proposed bounds. It is shown that repetition-based DF relaying systems achieve better symbol error rate performance than repetition-based AF relaying systems in medium to large SNRs. It is also shown that DF relaying systems with balanced links employing square-law combining at the destination achieve almost the same performance as those employing MRC. In addition, the throughputs of various multihop transmission systems are obtained. It is seen that multihop transmission systems employing a DF relaying scheme achieve higher throughput than multihop transmission systems employing an AF relaying scheme.

A direct sequence design is proposed for impulse radio ultra-wide bandwidth systems to suppress the mutual interference between ultra-wide bandwidth wireless and coexisting narrowband services. Notch frequencies are created in the ultra-wide bandwidth signal spectrum at bands where narrowband services operate. The direct sequence design has low computational complexity and can be easily implemented in practical systems. Numerical results are provided to show that the direct sequence design can significantly suppress the mutual interference between ultra-wide bandwidth and narrowband services and highly enhance the integrity of both ultra-wide bandwidth and narrowband systems.

In opportunistic relaying systems, only the best relay among $K$ available relays is selected to participate in cooperation. This setup efficiently achieves diversity gain. However, the switching rate of such systems are of great importance due to practical implementation issues, for example, the corruption of the data signal by the switching transient, channel estimation failure due to excessive switches as well as switching overheads which increase with increased switching. The switching rates of opportunistic relaying systems with two or more relays operating under Rician and Nakagami-\textit{m} fading are obtained in closed- form or single integral expressions. The closed-form solutions have an explicit dependence on the Doppler frequency of the fading.

The problem of joint routing and power allocation optimization is addressed for decode-and-forward (DF) and amplify-and-forward (AF) multihop TDMA wireless networks. A distributed solution is proposed for power-optimized routing with desired end-to-end capacity constraint based on the local instantaneous channel state information measurement at the nodes of the network. The proposed distributed routing algorithm is optimal in DF networks and performs close to optimal in AF networks.

A new repetition-based multi-hop transmission with non-coherent detection is proposed. The symbol error probability (SEP) of this system is derived for both amplify-and-forward (AF) and decode-and-forward (DF) relaying schemes. It is shown that the repetition-based non-coherent AF relaying achieves diversity order equal to the number of repetitions, while the repetition-based non-coherent DF relaying does not achieve diversity order. In addition, throughput of the proposed systems is evaluated. Repetition does not enhance the throughput of the DF relaying systems, whereas it improves the throughput of the AF relaying systems for small and moderate values of signal-to-noise ratio.

An optimal multichannel spectrum sensing framework which searches for multiple secondary transmission opportunities over a number of narrowband channels is presented. The framework, referred to as sequential multichannel joint detection, enhances the secondary network performance while respecting the primary network integrity and keeping the interference limited. Considering a sequential periodic sensing scheme with nonuniform channel sensing durations, the sensing problem is formulated as an optimization problem to maximize the throughput capacity of the secondary network given a bound on the aggregate (weighted) interference on the primary network. Despite its nonconvexity property, the original problem is transformed into a convex optimization problem under certain practical conditions. Simulation results demonstrate the effectiveness of the proposed framework and attest to its superior performance compared to contemporary strategies.

Impulse radio ultra-wide bandwidth wireless is a fast emerging technology where its applications underlay coexisting narrowband services over a huge bandwidth. Therefore, the coexistence problem between ultra-wide bandwidth and narrowband systems warrants investigation. A time-hopping sequence design is proposed for impulse radio ultra-wide bandwidth systems to suppress the mutual interference between ultra-wide bandwidth wireless and coexisting narrowband service. This sequence design has low computation complexities and can be easily implemented in practical systems. Numerical results are provided to show that the time-hopping sequence design can significantly suppress the mutual interference between ultra-wide bandwidth and narrowband services, hence, the integrity of both ultra-wide bandwidth and narrowband systems can be greatly enhanced.

A novel approach is introduced for the analysis of energy detection of unknown deterministic signals, where the energy detector uses dual diversity reception. The energy detector is assumed to employ a low complexity diversity technique, namely square-law combining. A general case where the two diversity branches are correlated is treated by the analysis. Detection and false alarm probabilities for the energy detector are derived for correlated Rayleigh and Rician fading channels.

An efficient and low-complexity algorithm for implementing a newly proposed wideband spectrum sensing framework in cognitive radio systems is presented. The framework which is known as multiband joint detection identifies suitable secondary transmission opportunities while protecting the primary network from harmful interference imposed by the secondary network. It has previously been demonstrated that the optimization problem obtained from the framework can be made convex if certain practical constraints are applied. In order to have a more insightful view of the optimization process and make the implementation of the framework more time- and cost-effective, an efficient algorithm which searches for the optimal solution with much lower complexity compared to other commonly used numerical algorithms is proposed. It is established that the iteration-complexity and the complexity-per-iteration of the proposed algorithm increases linearly with the number of optimization variables (i.e. the number of narrowband channels). The proposed algorithm is evaluated via simulation and is shown to obtain the optimal solution quickly and efficiently.

A new approximation to the average symbol error rate of amplify-and-forward diversity is derived for independent and non-identically distributed Nakagami-m fading channels. The new approximation has low computational complexity. Numerical results show that it is almost identical to the exact average symbol error rate in all the cases considered.

Novel representations for the multivariate probability density function (PDF) and cumulative distribution function (CDF) of the equi-correlated non-central chi-square (χ2) distribution are derived. The new representations are given as single integral solutions in terms of well known mathematical functions which are available in common mathematical software packages. The advantage of the new representations is that only a single integral computation is needed to evaluate the PDF and CDF for an arbitrary number of dimensions. The new representations are used to numerically evaluate the outage probability of a single user multiple input multiple output system with receiver antenna selection diversity, operating in correlated Rician fading channels. The well known constant (equal) correlation model, which is considered to be a useful model for a closely placed set of antennas, is used for the analysis in this paper. A novel single-integral representation for the joint characteristic function of the equi-correlated non-central χ2distribution is also given.

The exact average capacities of rate adaptive single-relay selection decode-and-forward dual-hop relaying for block Rayleigh fading with two cooperation schemes, called parallel channel cooperation and repetition-based cooperation (RC), are obtained. General, dissimilar fading channels and the effect of the source-destination link are considered. Accurate approximations to the average capacity in the RC case are derived for large and small signal-to-noise ratio (SNR) regimes. The approximations characterize the cooperative power gain of the system, and show that the power gain almost increases with half the logarithm of the number of relays, and that the capacity is logarithmic in SNR in both large and small SNR scenarios. In the scenarios with the SD link, the power gain in dB is always positive. In the scenarios without the SD link, the gain is positive only for more than 3 to 5 relays. The small SNR power gain is greater than the large SNR power gain for any number of relays.

The problem of optimizing the placement of the antennas for an optimum combining receiver equipped with a linear antenna array of fixed length is addressed. A Rayleigh fading model is considered where the complex channel gains of both the desired user and the interfering users are assumed to be correlated due to the mutual proximity of the antennas. The average output signal-to-interference-plus-noise ratio is adopted as a measure of the system's performance and is maximized over the number and the arrangement of the antennas in the array. The optimization problem is formulated as a quadratic convex optimization problem in an infinite dimensional space where finite dimensional approximations of the problem are numerically solved using a convex optimization method. For the special case of an exponential correlation function the optimal arrangement is also derived analytically. It is shown for an exponential correlation model that the optimal number of antennas is infinite meaning that adding more antennas is always beneficial. Perhaps unexpectedly, the best arrangement of antennas in this case is not uniform, in general. On the contrary, it is shown through numerical results that for a two dimensional omnidirectional scattering correlation model the optimal number of antennas is a finite number and the optimum placement is uniform.

Novel single-integral representations for the bivariate probability density function and cumulative distribution function of two correlated Rician random variables are derived. The solutions are expressed in terms of well known functions which are available in common mathematical software. The two random variables are not necessarily identically distributed as required by some past solutions. The new form of the bivariate Rician cumulative distribution function is applied to give a new expression for the outage probability of dual selection combining diversity operating in correlated Rician fading.

The Nakagami-0.5 distribution is an important special case of the Nakagami distribution as it represents a worst case fading scenario. This scenario is of particular significance for wireless applications with high quality of service requirements. The bit error probability (BEP) performances of three basic diversity combining schemes in Nakagami-0.5 fading are considered. It is shown that the error rate performances of dual branch equal gain and selection combining (SC) diversity are identical regardless of modulation format. It is also shown that L-branch maximal ratio combining diversity in Nakagami-0.5 fading has the same BEP performance as single branch reception in Nakagami-L/2 fading with L times the transmission power of each branch. A useful upper bound for the BEP of L-branch SC diversity in Nakagami-0.5 fading is also derived. The performance degradation for the worst case Nakagami-0.5 fading relative to Rayleigh fading can be as much as 24.6 dB for a dual-diversity receiver at target BEP of 10-6. The additional resources required to restore a specified performance level, as increased channel signal-to-noise ratio and as number of additional diversity branches, are quantified. It is concluded that worst case Nakagami channels can result in dramatically poorer performance than Rayleigh channels, making proper system design and evaluation essential to achieve a required transmission quality.

Two effects of a single interference on the performance of an automatic frequency control (AFC) loop are explained, and two measures, average switching rate and mean time to loss of lock, are presented to capture the impact of each effect. These measures are derived in closed-form expressions and single integral formulas in dissimilar fading channels with Rayleigh, Rician, and Nakagami-m distributions. The general case of modulated carriers as well as different special cases are considered. Numerical examples are provided to illustrate the effects of different fading scenarios on the performance of an AFC. The effect of maximum Doppler frequency on the performance of the AFC is also investigated.

Novel representations for the multivariate probability density function and cumulative distribution function of the non-central chi-square distribution are derived. The solutions are expressed in terms of well known functions which are available in common mathematical software. When the number of degrees of freedom, m, is even, the new representation has the advantage that only a single-integral computation is needed to compute a N-dimensional distribution. The new representations are used to numerically evaluate the outage probability of multiple input multiple output systems with receiver antenna selection, operating in correlated Rician fading. The well known equal correlation model, which is considered to be a useful model for a closely placed set of antennas, is used for the analysis.

Novel single-integral representations for the multivariate probability density functions (PDFs) and cumulative distribution functions (CDFs) of the Gaussian class Weibull distribution are derived. The solutions are expressed in terms of familiar mathematical functions which are available in common mathematical software. The well known equal (constant) correlation model is considered. A special linear transformation of independent Gaussian random variables is used to generate correlated Weibull random variables. The advantage of the new representation is that only a single integral computation is needed to compute a N-dimensional distribution. The new representation of the CDF is used for the performance evaluation of a selection diversity combiner operating in equally correlated Weibull fading channels. The new PDF representation is also used for an analysis of the moments of the output signal-to-noise ratio of an equal-gain diversity combiner operating in equally correlated Weibull fading channels.

Investigation into the characteristics and behaviours of Laplace noise is of crucial importance for evaluating the performance of communication systems operating in impulsive noise, as well as for ultra-wideband wireless systems operating in the presence of multi-user interference. The bit error rate performances of a binary data communication system operating in the presence of additive bandlimited white Laplace noise is analyzed theoretically. A theoretical expression for the average bit error rate is derived using the Beaulieu series for the optimal soft-limiting detector and the matched-filter detector when arbitrary pulse shapes are used. The bit error rate performance of a reduced complexity version of the optimal detector, the hard-limiting detector, and a reduced complexity version of the matched-filter detector, the sum-of-samples detector, are also analyzed. The analytical expressions for the bit error rate are validated by numerical examples.

Binary weightbooks for multiple-input multiple-output (MIMO) beamforming systems using quantized feedback are designed based on the Grassmannian beamforming criterion. It is shown that the Grassmannian criterion for binary weightbook design is to maximize the minimum Hamming distance of the corresponding block code. Thus, block codes that have large minimum Hamming distance can be used for binary weightbook design for MIMO beamforming systems using quantized feedback. The optimum binary weightbooks when the number of transmit antennas has value from two to six are tabulated.

A signal-plus-noise (S+N) energy selection diversity combining (S+N-ESC) scheme for M-ary phase shift keying (MPSK) in Rayleigh fading channels is mathematically analyzed. Also, the S+N-ESC scheme for MPSK and 16-quadrature amplitude modulation (16-QAM) signaling in Nakagami-m and Rician fading channels is studied by computer simulations. The S+N-ESC selects the branch with the maximum S+N energy for detection. The advantage of the S+N-ESC scheme is that it requires no explicit channel estimation for diversity branch selection. We show that the symbol error probability (SEP) of the S+N-ESC is the same as that of classical selection combining (SC) for MPSK signaling in independent and identically distributed (i.i.d.) Rayleigh fading channels. Also, we show that the SEP of a weighted S+N-ESC scheme is the same as that of classical SC for MPSK signaling in independent and nonidentically distributed (i.n.d.) Rayleigh fading channels. It is shown by computer simulations that the S+N-ESC scheme provides a smaller SEP than classical SC for MPSK signaling in nondispersive fading channels such as Nakagami-m fading channels with Nakagami parameter m >; 1 and Rician fading channels with Rician parameter K >; 0. On the other hand, the S+N-ESC scheme is shown by computer simulations to have a larger SEP than classical SC for 16-QAM signaling in Nakagami-m and Rician fading channels.

The exact average bit error probability (BEP) performance of decode-and-forward (DF) cooperative systems for binary phase shift keying (BPSK) signals in Nakagami-m fading channels for integer values of m is analyzed. Two types of receivers, a λ-maximal ratio combining (λ-MRC) receiver and a piecewise linear (PL) receiver are examined. Closed-form, integral-free, expressions for the BEPs of the λ-MRC receiver and the PL receiver are obtained.

Multiple-symbol differential detection (MSDD) of differentially encoded phase-shift keying (PSK) signals in the presence of random frequency variation and additive white Gaussian noise is studied. It is shown that frequency variation distorts the transmitted signal through attenuating its amplitude and introducing a time-varying phase shift to the information symbols. A double differential PSK (DDPSK) modulation scheme is then introduced and a MSDD for detecting DDPSK signals in the presence of frequency offset is proposed. It is shown that the proposed receiver is robust to the distortions caused by the random frequency variation. A lower bound on the error probability of the proposed MSDD receiver is also derived and compared to that of an autocorrelation demodulator for the case where the observation interval approaches infinity.

Direct sequence and time-hopping sequence designs are proposed for impulse radio ultra-wide bandwidth systems to suppress the mutual interference between ultra-wide bandwidth wireless and coexisting narrowband services. Notch frequencies are created in the ultra-wide bandwidth signal spectrum at bands where narrowband services operate. The direct sequence and the time-hopping sequence designs have low computational complexities and can be easily implemented in practical systems. When combined with the cognitive radio technique, these designs can adapt to channel conditions according to the spectral occupancy information provided by cognitive radio. Numerical results are provided to show that these designs can significantly suppress the mutual interference between ultra-wide bandwidth and narrowband services. Therefore, the integrity of both ultra-wide bandwidth and narrowband systems can be highly enhanced.

Novel single-integral representations for the multivariate probability density functions and cumulative distribution functions of Gaussian class distributions (Rayleigh, Rician, Weibull, Nakagami-m, and generalized Rician) are derived. The solutions are expressed in terms of well-known functions which are available in common mathematical software. The marginal random variables are not necessarily identically distributed as is the case for some past solutions. A generalized correlation structure based on a special linear transformation of independent Gaussian random variables is used in this study. The advantage of the new representation is that only a single-integral computation is needed to compute anN-dimensional distribution.

The instantaneous end-to-end received signal-to-noise ratio (SNR) in K-hop amplify-and-forward (AF) relaying systems is commonly upper bounded by 1/k of the harmonic mean of the individual per-hop instantaneous SNRs. It is shown that performance results in Nakagami-m fading of AF multihop relaying systems obtained based on this upper bound are not tight for small values of SNR or for larger values of the Nakagami parameter and, depending on certain channel conditions, these bounds may become looser as the number of hops increases. A new approximation to the instantaneous end-to-end received SNR is introduced in the form of a scaled version of the harmonic mean of the individual per-hop SNRs. The scaling factor is determined based on the average link SNRs. Performance results evaluated using the proposed approximation are more accurate than all performance bounds previously reported in the literature, even though they are obtained with the same computational complexity. Numerical results show that the approximate performance results are very close to the exact results especially in small SNR regimes or for larger values of the Nakagami parameter.

Coherent modulation is more effective than differential modulation for orthogonal frequency division multiplexing (OFDM) systems requiring high data rate and spectral efficiency. Channel estimation is therefore an integral part of the receiver design. Two iterative maximum likelihood (ML) based channel estimation algorithms are proposed for OFDM uplinks in dispersive time-varying channels. The uplink multipath fading channel is modeled such that the channel state can be determined by estimating the unknown channel parameters. A second-order Taylor series expansion is adopted to simplify the channel estimation problem. Based on the system model, an iterative ML-based algorithm is first proposed to estimate the discrete-time channel parameters. The mean square error performance of the proposed algorithm is analyzed using a small perturbation technique. Based on a convergence rate analysis, an improved iterative ML channel estimation algorithm is presented using a successive overrelaxation method. Numerical experiments are performed to confirm the theoretical analyses and show the improvement in convergence rate of the improved algorithm.

The decoding of Matrix C in the WiMAX standard is investigated. We propose an exhaustive search and zero-forcing (ES-ZF) decoder and an exhaustive search and nulling canceling (ES-NC) decoder for uncoded systems. The computational complexity of the ES-ZF decoder for Matrix C decoding is shown to be the same as the complexity of the ZF decoder for Matrix B decoding with twice the number of receive antennas times the complexity of the maximum likelihood (ML) decoder for Matrix B decoding with twice the number of receive antennas. Matrix C can be implemented in a 2 x 2 multiple-input multiple-output (MIMO) system using the ES-NC decoder with reduced complexity compared to ML decoding with no performance loss. For coded systems, double pruned trees using a zero-forcing (DPT-ZF) algorithm or nulling canceling (DPT-NC) algorithm are proposed. The DPT-NC decoder is shown to be implemented in a 2 x 2 MIMO coded system with reduced complexity compared to the Max-Log decoding, with no performance loss, by computer simulations.

Three low complexity, single-parameter, selection cooperation protocols, called P-n, P-γ, and P-t, are introduced for dual-hop relaying networks. The protocols are based on information accumulation, and can potentially be implemented using rateless codes. The expected transmission time is analyzed for the three protocols for block fading channels. As a baseline for performance comparison, a rate optimal protocol, called P-o, is proposed. In the single-relay case, all the protocols, if used with their optimized parameter which is trivially obtained, coincide with P-o. Large signal-to-noise ratio (SNR) approximations to the optimal parameters in the multirelay case, which have good accuracy in large SNR regimes, and satisfactory accuracy for smaller values of SNR, are derived. The dependence of the optimal parameters on the network parameters is numerically studied for Rayleigh fading. The average rate and average source transmission time (ASTT) of the schemes are compared with one another and other comparable previous relaying schemes through numerical examples. It is observed that the suboptimal schemes exhibit near-optimal rate and ASTT performances. As a general rule, P-o and P-γ have the best performances. The P-n scheme has a larger rate, but a larger or smaller ASTT, compared to P-t. Increasing the number of relays ultimately causes diminishing returns in the average rate and ASTT.

Employing channel state information at the network layer, an effective routing metric is obtained that minimizes the end-to-end outage probability in amplify-and-forward multihop wireless networks. A disadvantage of the routing metric obtained is that it cannot be optimized in distributed manner, i.e., it does not converge onto optimal routes. The disadvantage cannot be remedied by exhaustive search because an exhaustive search is not feasible owing to the factorial growth of the search space with the number of nodes in the network. Therefore, a new composite metric and a packet forwarding algorithm are introduced which satisfy the optimality and consistency requirements for distributed implementation. It is proved that the proposed distributed algorithm converges onto optimal paths in any network topology.

A unified theory for selection combining diversity in Rayleigh fading channels is derived. It is shown that the performance of arbitrary systems used with selection combining diversity can be expressed in terms of only the performance of the system on a single branch Rayleigh fading channel. The results are valid for coded and uncoded transmission as well as for balanced (equal power) diversity branches and unbalanced (unequal power) diversity branches. The unified theory encompasses both general noise and general interference.

The performance in fading of two dual signal-plus-noise (S+N) selection combining (SC) diversity structures employing different filtering is examined. The proposed structure includes either a minimum mean square error filter or a lowpass filter designed to reduce the noise in the signal used for determining the antenna switching times. The switching rate and the bit error rate of the proposed structures are compared to a receiver in which no filtering is used for switching rate reduction.

Novel single integral representations for the multivariate probability density function and cumulative distribution function of Rayleigh and Rician distributions are derived. A generalized correlation structure is used in this analysis. The derived novel representations are used to evaluate the outage probability of N-branch selection diversity operating in correlated Rayleigh and Rician fading channels modeled by the generalized correlation model.

Estimation of the received signal amplitude is critical to the optimization of the performance of detectors for data communication systems operating in the presence of impulse-like interference. A binary data communication system in the presence of Laplace noise is considered. Maximum likelihood estimators are derived for both data-aided and non- data-aided cases. A ML-based non-data-aided absolute median estimator with simpler implementation is also proposed. The performances of the proposed estimators are examined and compared to the well-known mean estimator and absolute moment estimator in terms of their mean- squared errors. Numerical results quantify the superiority of the optimal ML estimators over the conventional estimators.

Novel single integral representations for the multivariate probability density function (PDF) and cumulative distribution function (CDF) of Gaussian class Weibull distributions are derived. A special linear transformation of independent Gaussian random variables is used to generate correlated Weibull random variables. The solutions are expressed in terms of familiar functions which are available in common mathematical software. The well known equal (constant) correlation model is used in this paper. The advantage of the new representation is that only a single integral computation is needed to compute a L-dimensional distribution. Some applications of the new distribution representations are also given.

Adaptive modulation exhibits the advantage of great spectral efficiency for high data rate wireless transmission, where the transmission power and rate of subchannels in orthogonal frequency division multiplexing (OFDM) systems are matched to the channel state information (CSI). CSI can be acquired at the receiver by MMSE channel estimation based on pilot symbol assisted modulation (PSAM), which is a widely used technique, and fed back to the transmitter. While more accurate channel estimation will result in more reliable transmission, pilot symbols don''t carry information and they impose an overhead on the system consuming power and bandwidth. An optimal adaptive PSAM scheme, that maximizes spectral efficiency by optimizing pilot power and spacing simultaneously is proposed. A rectangular pilot pattern is adopted to simplify the adaptive scheme.

The coding performance of impulse radio ultra-wide bandwidth systems in the presence of multi-user interference is studied. Analytical expressions for assessing the codeword error probability and bit error probability are derived for soft-decision decoders in lognormal multipath fading UWB channels where the Rake receiver is used for signal detection. Numerical results are presented for different codes and error rate levels, and corresponding discussions of the coding performance characteristics in ultra-wide bandwidth systems are also provided.

New combining schemes for partial decisions using one-bit and two-bit information of the received samples are derived for Rayleigh fading channels with diversity. Compared to previous partial decision combining schemes, these new schemes have either better performances, or simpler structures, or both. Simulation results show that some of the new schemes can achieve considerable performance gains over the conventional partial decision combiner in Rayleigh fading or lognormal shadowed Rayleigh fading, while their structures are much simpler than the conventional partial decision combiner. This confirms the advantages of the newly designed combining schemes.

A decentralized power allocation scheme for amplify-and-forward (AF) multi-hop relaying systems is proposed. The scheme maximizes a harmonic mean-based approximate expression for the instantaneous received signal-to-noise ratio (SNR). The outage probability in Rayleigh fading of the proposed power-optimized system is evaluated. Numerical results show the superior performance of AF multi-hop relaying systems employing the proposed power allocation scheme over those with uniform power allocation. The asymptotic outage behavior for sufficiently large values of SNR is also studied and it is demonstrated that AF multi-hop relaying systems employing the proposed power allocation scheme achieve diversity order 2.

Distributed coherent receivers, that require no instantaneous channel amplitude information, are developed for amplify-and-forward (AF) cooperative diversity systems. According to the availability of phase information at the relays and the destination, repetition-based and spectral-efficient distributed equal gain combining (DEGC) schemes are obtained. In the former scheme, relays transmit over separate orthogonal subchannels, whereas in the latter scheme all relays transmit simultaneously. An expression for evaluation of the symbol error probability is derived and it is demonstrated that these schemes achieve full spatial diversity. It is also shown that the spectral-efficient DEGC scheme outperforms the repetition-based DEGC scheme especially by increasing the number of relays.

An optimal wideband spectrum sensing algorithm which jointly detects the primary activities over multiple narrowband channels is presented. The algorithm enhances then overall secondary user performance while protecting the primary network at a desired level. The problem is formulated as an optimization problem to maximize the available secondary throughput capacity given a bound on the imposed aggregate interference. It is demonstrated that the problem can be solved as a convex optimization if certain practical constraints are applied. Simulation results attest that the proposed algorithm achieves a superior performance compared to contemporary algorithms.

The problem of transmitter pulse-shaping design for suppressing multiple access interference in bandlimited multiaccess communication systems is considered. The design is laid out in such a way that the transmitter-receiver (T-R) combination maximizes the signal-to-interference-plus-noise ratio (SINR). It is shown that the optimum transmitter filter is composed of a sum of two sinc functions with different gains and bandwidths. An exact expression for the output SINR of the proposed T-R combinations is derived and compared to that of the conventional matched filter (CMF) receiver with a root raised-cosine transmitter filter. The SINRs of the proposed T-R pairs and the CMF receiver in the presence of timing error are also analyzed and accurate expressions for them are derived.

It has been reported that impulsive noise, which can be well modeled by the Laplace distribution, is present in both indoor and outdoor radio environments. The performance of communication systems employing block data transmission in the presence of impulsive Laplacian noise is studied, where analytical expressions for evaluating the block error probability are derived for both hard-decision and soft-decision decoders. Both unfaded and quasi-static Rayleigh fading channels are considered. Computations of the block error probability are also presented for different block sizes and error levels, and the characteristics of block error probabilities are compared for both nonfading and fading scenarios.

Efficient routing protocols for equal power and optimal power allocation in a multi-hop decode-and-forward network in fading are proposed. The end-to-end outage probability from source to destination is used as the optimization criterion. The problem of finding the optimal route is investigated when either the mean channel state information (CSI) or the instantaneous CSI for all the links of the network is known at a central controller. The analysis shows that the proposed routing strategy achieves full diversity, equal to the total number of nodes in the network excluding the destination, only when instantaneous CSI is known and used. The average number of hops and the performances of the proposed schemes are examined for several numbers of nodes in the network and different values of path loss exponent.

Novel simple forms for the probability density function (PDF) and the cumulative distribution function (CDF) of two correlated Rician random variables (RVs) are derived. The new representations for the bivariate Rician PDF and CDF are given in the form of single integral solutions in terms of well known functions that are available in common mathematical software packages. The general case of non-identically distributed Rician RVs is considered in this analysis. The new form of the bivariate Rician cumulative distribution function is applied to give a new expression for the outage probability of dual selection combining diversity operating in correlated Rician fading.

Novel single integral representations for the multivariate probability density function (PDF) and cumulative distribution function (CDF) of the Nakagami-m distribution with integer and identical fading severity parameter m are derived. A generalized correlation structure is used in this model. The single integral solutions for the PDF and the CDF are given in terms of well known mathematical functions which are available in common mathematical software packages. The novel representation derived for multivariate CDF is used to evaluate the outage probability of N-branch selection diversity combining operating in correlated Nakagami-m fading modeled by the generalized correlation model.

We design binary weightbooks for multiple-input multiple-output (MIMO) beamforming systems using quantized feedback based on the Grassmannian beamforming criterion. We show that the Grassmannian criterion for binary weightbook design is to maximize the minimum Hamming distance of the corresponding block code. Thus, a block code that has a large minimum Hamming distance can be used for binary weightbook design for MIMO beamforming systems using quantized feedback. The optimum binary weightbooks when the number of transmit antennas has value from two to five are tabulated.

A signal-plus-noise (S + N) energy selection diversity combining (S + N-ESC) scheme for M-ary phase shift keying (MPSK) and 16-quadrature amplitude modulation (16-QAM) signaling in Nakagami-m and Rician fading channels is studied. The S + N-ESC selects the branch with the maximum S + N energy for detection. The advantage of the S + NESC scheme is that it requires no explicit channel estimation for diversity branch selection. We show that the symbol error probability (SEP) of the S + N-ESC is the same as that of classical selection combining (SC) for MPSK signaling in independent and identically distributed (i.i.d.) Rayleigh fading channels. Also, we show that the SEP of a weighted S + N-ESC scheme is the same as that of classical SC for MPSK signaling in independent and nonidentically distributed (i.n.d.) Rayleigh fading channels. It is shown that the S + N-ESC scheme provides a smaller SEP than classical SC for MPSK signaling in nondispersive fading channels such as Nakagami-m fading channels with Nakagami parameter m > 1 and Rician fading channels with Rician parameter K > 0. On the other hand, the S + N-ESC scheme is shown to have a larger SEP than classical SC for 16-QAM signaling in Nakagamim and Rician fading channels.

Wireless communication systems operating in the presence of additive Gaussian noise have been well studied in the literature. The additive thermal and ambient noise in the system can be modeled by a Gaussian distribution. This model makes the analysis tractable due to the desirable analytic properties of the Gaussian distribution. However, in many situations the additive noise contains another impulsive noise component which cannot be modeled by a Gaussian approximation. The Laplacian distribution is one of the widely used distributions for modeling non-Gaussian and impulsive noise. The performance of linear diversity combining schemes corrupted by additive Gaussian-plus-Laplacian noise in a Rayleigh fading channel is analyzed.

New and improved energy detectors for cognitive radios are derived by considering the effect of the primary user traffic on spectrum sensing. The new energy detectors are designed based on the assumption that the primary user randomly arrives or departs during the sensing period. Numerical results show that the new energy detector outperforms the conventional energy detector in all the cases examined. The performance gain depends on the operating signal-to-noise ratio as well as the sample size used.

The signal-to-noise ratio (SNR) and signal-to-interference ratio (SIR) for multiuser time-hopping binary phase shift keying ultra-wide bandwidth impulse radio systems are jointly estimated using the moment-based method. Both additive white Gaussian noise channels and multipath fading channels are considered. Numerical results show that the new SNR and SIR estimators have normalized root-mean-squared errors of less than 0.2 in most cases considered.

The estimation of signal amplitude for a binary data communication system in the presence of Laplace noise is considered. Maximum likelihood estimators are derived for both data-aided and non-data-aided cases. An absolute median estimator with a simple implementation is also proposed. The performances of the proposed estimators are examined and compared to well-known previous estimators in terms of mean-squared error. Numerical results quantify the superiority of the proposed estimators over the conventional estimators.

A more appropriate statistical model for the multiple access interference than the generally used Gaussian approximation is proposed to reflect the heavy-tailed nature of the multiple access interference in ultra-wide bandwidth systems. Novel receiver structures which surpass the performance of the conventional matched filter receiver are studied for ultrawide bandwidth multiple access communications in both AWGN and fading multipath channels. A proposed Rake receiver is advantageous over the conventional Rake receiver when multiuser interference dominates ambient Gaussian noise and originates from a small to moderate number of interferers. Explanation is provided for the inaccuracy of a Gaussian approximation with regard to the multiple access interference, and the heavy-tailed nature of the probability density function of the multiple access interference is also discussed.

Novel non-data-aided near-maximum-likelihood estimators for the delays and the attenuations in an ultra-wide bandwidth channel are proposed by using an approximation to the maximum likelihood equation. Numerical results show that these new estimators outperform previous approximate non-data-aided maximum likelihood channel estimators reported in the literature. Moreover, in some cases, the performances of the new non-data-aided estimators approach those of the data-aided estimators, enabling a reduction in the overhead expense of pilot symbols.

Bandwidth efficient signaling requires using pulse-shaping that inherently has intersymbol interference (ISI) except when the timing is perfect. Several lower bounds to the mean-square-error (MSE) of non-data-aided bit-synchronizers are derived for this case. The optimal lower bound is derived using the maximum likelihood (ML) criterion for a sequence of binary pulse amplitude modulated pulses in the presence of ISI and Gaussian noise. This lower bound is used as a benchmark to evaluate the performance of other synchronizers in a practical scenario. It is shown that a previous lower bound based on the ISI-free ML synchronizer cannot be used to lower bound the MSE of bit-synchronizers. A detection theory bound (DTB) (also called Ziv-Zakai bound) is applied to the symbol timing recovery problem in the presence of ISI and it is shown that this bound is a tight lower bound on the MSE of the ML synchronizer. A simple lower bound on this DTB is derived and it is shown that the simple bound is almost as tight as the well known modified Cramer-Rao bound (MCRB) at moderate values of SNR, while it does not suffer from the shortcomings of the MCRB at small values of SNR.

The performance of an automatic frequency control (AFC) loop is investigated using two measures, the mean time to loss of lock and the average switching rate. The AFC is considered to operate in fading while a single interferer is also present at its input. Channels are modeled using independent non-identically distributed Rayleigh, Rician and Nakagami-{m} fading while the special case of independent identically distributed channels is also considered. Closed-form expressions and integral form formulas are derived for the general case of modulated signals as well as important special cases of similar modulations and unmodulated signals. The considered scenarios include previous results from the literature as special cases. Corresponding numerical examples are provided and discussed to illustrate the performance of an AFC in such scenarios.

The capacity of amplify-and-forward multi-hop relaying systems under different adaptive transmission schemes over Nakagami-m fading channels is considered. Accurate theoretical approximations for the capacity of these systems are derived in terms of the characteristic function of the reciprocal of the instantaneous received signal-to-noise ratio. An accurate theoretical approximation for the probability of outage is also obtained. The accuracy of the expressions obtained is verified by Monte Carlo simulation. It is shown that a system with optimal power and rate adaptation outperforms the system with truncated channel inversion adaptive technique. Systems employing optimal rate adaptation with constant power achieve almost the same capacity as those with optimal rate and power adaptation at large values of signal-to-noise ratio. However, the capacity performance of a system with the truncated channel inversion adaptive technique is better than the corresponding system employing optimal rate adaptation with constant power for small values of signal-to-noise ratio.

The performance of multi-hop diversity transmission systems in Rayleigh fading is studied. Simple closed-form approximations for the outage and bit error probabilities of multi-hop diversity systems employing fixed amplify-and-forward relaying are derived. An exact closed-form expression for calculating the outage probability of a multi-hop diversity transmission scheme employing fixed decode-and-forward relaying is obtained. In addition, a selective relaying protocol for multi-hop diversity transmission systems, which adapts transmissions at the source and relays based on the instantaneous received signal-to-noise ratio at each relay, is developed and analyzed in terms of outage probability and bit error rate. The mathematical analyses show that multi-hop diversity transmission systems with fixed decode-and-forward relaying offer no diversity order gain, while those employing the other relaying schemes achieve diversity order equal to the number of hops. It is also shown that multi-hop diversity transmission systems employing fixed amplify-and-forward relaying attain the best outage probability and bit error rate performances, despite the noise amplification at the relays.

A maximum energy selection (MES) receiver scheme is proposed for noncoherent amplify-and-forward (AF) cooperative diversity systems. An expression for the symbol error probability of this system when deployed with M-ary frequency shift keying (FSK) modulation is derived. It is shown that a noncoherent AF system employing the proposed MES scheme achieves full spatial diversity, while requiring neither instantaneous nor statistical channel gain information at the destination, but only knowledge of the average source-relay link signal-to-noise ratio (SNR) at the corresponding relay. The average source-relay link SNR information can be locally obtained at each relay using conventional practical estimation techniques, which in turn allows fully distributed implementation of the proposed scheme.

Low complexity receivers for coherent amplify-and-forward (AF) cooperative diversity systems are developed. According to the availability of phase information at the relays and the destination, repetition-based and spectral-efficient distributed equal gain combining (DEGC) schemes are developed. In the former scheme, relays transmit over separate orthogonal subchannels, whereas in the latter scheme all relays transmit simultaneously. Analytical expressions for evaluation of the average output signal-to-noise ratio (SNR) and symbol error probability are derived and it is demonstrated that these schemes achieve full spatial diversity. In addition, upper and lower bounds on the ergodic capacity are obtained. The upper bound is tight in small-SNR regions whereas the lower bound is accurate for sufficiently large values of SNR. It is shown that the spectral-efficient DEGC scheme outperforms the repetition-based DEGC scheme especially by increasing the number of relays. The impact of combining loss on the performance of the proposed schemes is also studied. The average output SNR expression can be used as a simple theoretical tool for choosing the best number of relays that avoids the combining loss.

A signal-plus-noise (S + N) energy selection combining (S + N-ESC) scheme and a weighted S + N-ESC scheme for binary phase shift keying (BPSK) signaling are studied. The S + N-ESC selects the branch with the maximum S + N energy for detection. The advantage of the S+N-ESC and the weighted S+N-ESC is that they require no explicit channel estimation for diversity branch selection. The bit error rate (BER) performances of the S + AT-ESC and the weighted S + N-ESC are analyzed for BPSK signaling in independent and nonidentically distributed (i.n.d.) Rayleigh fading channels. We show that the average error rate performance of the S +N-ESC is the same as classical signal-to-noise ratio selection combining (SNR-SC), which requires the estimation of fading amplitudes for branch selection, in independent and identically distributed (i.i.d.) Rayleigh fading channels. We also show that the weighted S + N-ESC has the same BER performance as the classical SNR-SC for i.n.d. Rayleigh fading channels.

We propose the Hadamard matrix as a codebook for multiple-input multiple-output (MIMO) beamforming systems, and show that a quantized equal gain transmission (QEGT) scheme using the Hadamard codebook has the same symbol error probability performance as a receiver selection diversity combining scheme operating in independent generalized Rayleigh fading channels. We show that a MIMO beamforming system using quantized feedback over Rician fading channels can be analyzed by considering a corresponding receiver selection combining scheme operating in single-input multiple-output (SIMO) systems over correlated generalized Rician fading channels. Also, we propose a greedy cophasing scheme for MIMO beamforming systems using quantized feedback. The greedy cophasing scheme provides 3.2 dB power gain over an orthogonal space-time block code when the number of transmit antennas is four, the number of receive antennas is one, and the number of feedback bits is three.

A new symbol error probability (SEP) formula for selection combining (SC) with M-ary phase shift keying (MPSK) signals in i.i.d. Nakagami-m fading channels is derived.

Asymptotic error rate expressions are derived for multi-branch equal gain combining and selection combining operating on arbitrarily correlated Rayleigh fading channels. These closed-form solutions are used to provide rapid and accurate estimation of the error rates in large signal-to-noise ratio regions. More importantly, they reveal additional insights into the transmission characteristics of linear diversity combining schemes operating on correlated Rayleigh fading channels. It is shown that the asymptotic error rates over correlated branches can be obtained by scaling the asymptotic error rates over independent branches with a factor, det(M), where det(M) is the determinant of the normalized channel correlation matrix. This relationship is valid for both coherent and noncoherent signalings. A similar relationship is also established for the outage probabilities of fading wireless systems employing multi-branch diversity reception.

An analytical expression is derived for the average output signal-to-interference-plus-noise ratio of optimum combining for a spatially correlated array of antennas in the presence of a single interferer and Rayleigh fading. Using the derived expression and based on an asymptotic analysis of the eigenvalues of dense correlation matrices, the asymptotic performance of optimum combining is evaluated as the number of the antennas increases while the total physical size of the array is fixed. Two different scenarios are considered, namely, fixed average received power per antenna and fixed total average received power. It is shown that in the former scenario, the average output signal-to-interference-plus-noise ratio is asymptotically a linear function of the number of the antennas while in the latter scenario it eventually saturates at a certain value. The slope of the asymptotic line in the former scenario as well as the value of the saturation limit in the latter scenario are derived in terms of the point spectrum of the underlying array correlation function. The case of multiple interferers is examined by simulation and is shown to exhibit similar asymptotic behaviour to the case of one interferer.

The bit error rate performance of Rake reception of impulse radio ultra-wide bandwidth signals over the IEEE 802.15.3a channel models is evaluated. Instead of using Gaussian approximation for the probability density function of the total disturbance which includes the multi-user interference and the background additive white Gaussian noise, two new models dubbed the "composite lognormal-Gaussian" and the "composite lognormal-Laplacian" are proposed for modeling the multi-user interference and shadowing in ultra-wide bandwidth multipath fading channels. Tractable formulae for bit error rate evaluation of Rake reception in ultra-wide bandwidth multipath channels are derived for both models. Numerical results indicate that these formulae predict the bit error rate performance with good accuracy, and can be rapidly and easily evaluated using commonplace computer resources.

Employing channel state information at the network layer, efficient routing protocols for equal-power and optimal-power allocation in a multihop network in fading are proposed. The end-to-end outage probability from source to destination is used as the optimization criterion. The problem of finding the optimal route is investigated under either known mean channel state information (CSI) or known instantaneous CSI. The analysis shows that the proposed routing strategy achieves full diversity order, equal to the total number of nodes in the network excluding the destination, only when instantaneous CSI is known and used. The optimal routing algorithm requires a centralized exhaustive search which leads to an exponential complexity, which is infeasible for large networks. An algorithm of polynomial complexity for a centralized environment is developed by reducing the search space. A distributed approach based on the Bellman-Ford routing algorithm is proposed which achieves a good implementation complexity-performance trade-off.

A new approximation to the average symbol error rate of cooperative diversity is derived for independent and non-identically distributed Nakagami-m fading channels. The new approximation has the same computational complexity as previous lower bounds in the literature, while it is much more accurate than the lower bounds, especially when the signal-to-noise ratio is small to medium. Numerical results show that the new approximation is almost graphically identical to the exact average symbol error rate for moderate values of the signal-to-noise ratio.

A l-Bayesian erasure test (BET) based on order statistics with diversity reception for noncoherent M-ary frequency shift keying (FSK) signaling is examined. In the l-BET, the M-ary FSK symbol is erased whenever the a posteriori probability of correct decision, which is a function of the l-largest sums of energy detector outputs, is less than a threshold. For binary FSK signaling in Rayleigh flat fading channels, the 2-BET is found to be the same as the difference threshold test (DTT), which declares an erasure whenever the difference between the largest and the second largest sums of energy detector outputs is less than a threshold. The output threshold test (OTT), which declares an erasure whenever the largest sum of energy detector outputs is less than a threshold, is proved equivalent to the 1-BET for the Rayleigh flat fading channel. Closed-form expressions for the probabilities of correct decision and symbol error for the DTT, Viterbi's ratio threshold test (RTT), and the OTT are derived when square-law combining (SLC) diversity is used. Several erasure tests including the Z-BET, the RTT, the OTT, and the DTT are compared in terms of probability of codeword error. The 2-BET provides almost the same performance as the BET that requires all the sums of energy detector outputs. The 2-BET provides power gains of 0.9 dB and 0.7 dB over the RTT for (7, 3) and (15, 7) Reed-Solomon (RS) codes, respectively, when the probability of codeword error is 10-3and the diversity order is one.

The maximum likelihood optimal combiner for signal detection in alpha-stable noise is not known in general, except for some special values of the characteristic exponent ?. A linear Rake combiner receiver is simple and easy to realize. The optimal linear Rake receiver, in the sense of minimizing the bit error rate, for the detection of signals contaminated by symmetric alpha stable noise is derived for values of ?, 0 < ? ? 1. Interestingly, for this range of ?, the optimal combiner is found to be a selection combiner which selects the channel (finger) with the largest signal amplitude and suppresses all other channels (fingers). This interesting result is valid over the range 0 < ? ? 1 and allows one to implement effective signal detection without having to know the actual value of the parameter ?. Therefore, the result yields a very simple form of diversity combiner for signal detection in symmetric alpha-stable noise for 0 < ? ? 1. Comparisons with the widely used maximal ratio combining and equal gain combining schemes are made in terms of signal-to-noise ratio advantage defined in the bit error rate sense.

The switching rate of a correlated dual branch selection diversity combiner in Rayleigh and Rician fading is derived in noise-free conditions. Balanced and unbalanced branches are considered. Numerical results are presented for a space-diversity system with horizontally spaced omnidirectional antennas at a mobile station.

Generalized ultra-wide bandwidth (UWB) transmitted reference (TR) receivers proposed previously in the literature are improved with respect to the energy allocation in the data packet and the integration interval length in the correlator. The improvement refers to a best-effort technique to reduce the receiver bit error rate. Simulation results show that the improvement can provide a performance gain of up to 4.2 dB in signal-to-noise ratio. These results give useful guidance on the design of generalized UWB TR receivers.

The maximum likelihood (ML) criterion for symbol timing estimation is derived for a sequence of pulse amplitude modulated pulses in the presence of intersymbol interference (ISI) and Gaussian noise. The performance of this synchronizer is used as a benchmark to evaluate the performance of other synchronizers in a practical scenario. It is shown that a previous lower bound based on the ISI-free ML synchronizer cannot be used to lower bound the mean square error (MSE) of bit-synchronizers. A detection theory bound (DTB) is applied to the symbol timing recovery problem in an ISI channel and it is shown that this bound is a tight lower bound on the MSE of the ML synchronizer. A simple lower bound on this DTB is derived and it is shown that the simple bound is almost as tight as the well known modified Cramer-Rao bound (MCRB) at moderate values of SNR while it does not suffer from the shortcomings of the MCRB at small values of SNR.

The capacity of rate adaptive, power nonadaptive, multibranch, multihop, decode-and-forward relaying networks is analyzed for ergodically fading channels. Different cases of superimposed, selection, and orthogonal relaying are investigated. Parallel channel coding and repetition coding are considered for each case. Closed-form expressions for the maximum instantaneous achievable rates are obtained for each case. The distribution functions of the maximum instantaneous achievable rates for a source-relay-symmetric (S-R-sym.), relay-destination-symmetric (R-D-sym.) case are evaluated. The ergodic capacity of rate adaptive, power nonadaptive, multibranch, dual-hop networks in the S-R-sym., R-D-sym. case with no-source-destination-link assumption is derived for Rayleigh fading. It is observed that parallel channel coding gain can attain as much as 1 bit improvement for the examples considered. Increasing the number of branches deteriorates the performance of the orthogonal relaying scheme, but improves the performances of the other schemes albeit with diminishing returns. The performances of all schemes degrade rapidly as the number of hops per branch increases, such that no scheme is more energy efficient than direct transmission for more than three hops per branch.

Exact statistics of the local signal-to-noise ratios (SNRs) of the best relay in decode-and-forward (DF) opportunistic relaying (ORe) are derived. It is observed that although the different links are assumed to suffer independent fadings, the best-relay local SNRs are dependent. Both joint and marginal statistics are determined for the general case of nonidentical SNR distributions, and a source-relay-symmetric (S-R-sym.), relay-destination-symmetric (R-D-sym.) case. Both general fading and Rayleigh fading cases are considered. Using the statistics derived, exact, closed-form expressions for the outage probability and ergodic capacity of DF ORe are calculated in the S-R-sym., RD-sym., Rayleigh fading case. The exact results for the outage probability show almost linearly increasing diversity order with the number of relays. The exact results for the ergodic capacity show a multiplexing gain almost equaling one half and a power gain increasing with the number of relays that exhibits diminishing returns.

Using an asymptotic analysis of the eigenvalues of dense correlation matrices, the asymptotic average output signal-to-interference-plus-noise ratio performance of optimum combining is evaluated as the number of the antennas in the receiver array increases while the total physical size of the array is fixed. As a result of the constraint imposed on the total physical dimensions of the array, the array output signals become more and more spatially correlated as more antennas are introduced to the array. A Rayleigh fading channel model is considered and the desired signal is assumed to be corrupted by a single cochannel interferer and thermal noise. Two different scenarios are investigated, namely, fixed average received power per antenna and fixed total average received power. It is shown that in the former scenario, the average output signal-to-interference-plus-noise ratio is asymptotically a linear function of the number of the antennas, while in the latter scenario it eventually saturates at a certain value. The slope of the asymptote in the former scenario and the value of the saturation limit in the latter scenario are derived in terms of the point spectrum of the underlying array correlation function. The case of multiple interferers is examined by simulation and is shown to exhibit similar asymptotic behavior to the case of one interferer for both power constraint scenarios. Numerical examples show that the receiver exhibits its asymptotic behavior for a practically small number of antennas.

The problem of allocating power over a non-ergodic Gaussian block fading channel is addressed for delay constrained applications, where transmission takes place over a limited number of time slots. We propose an algorithm in which the transmission power is determined at each time slot based on the channel condition at the current and future time slots, where a Markov model is used to capture the correlation between channel coefficients in different time slots. The problem is formulated in the framework of finite-horizon dynamic programming, where the optimal transmission strategy is assigned based on the relative importance of power and the quality of service (QoS). Depending on the importance of meeting the QoS constraint compared to the cost of power, the best power level is dynamically assigned by the algorithm, taking into account the channel state and the chance of meeting the QoS constraint. The performance of the proposed dynamic power allocation algorithm is evaluated for different channel states and QoS constraints. We compare the performance of the algorithm with schemes having strict constraints on power. Simulation results show that due to the flexibility given to the algorithm by removing the strict power constraint, the dynamic power allocation algorithm outperforms the optimal power constrained algorithm. Also, the results indicate that increasing the cost of power at the transmitter changes the system dynamics in a way that keeps the balance between QoS and power consumption.

A transmission scheduling algorithm is proposed for wireless sensor networks with high node densities, where a mobile sink is responsible for collecting the information from the sensor nodes with similar observations as well as determining the best transmission strategy. The proposed optimal algorithm and the reduced complexity algorithm are based on the well known tradeoff between the energy consumption and the probability of successful packet arrival at the sink, when the sensor nodes need to share a single transmission channel at each time slot. When the algorithm is used for transmission scheduling, it is advantageous in terms of power consumption and successful packet transmission rate for networks with higher node densities. Moreover, the effect of the cost of transmission power at the sink is studied for different node densities. It is shown that as we increase the cost of power at the sink, the transmission power at the nodes is dynamically adjusted in a way that keeps the average number of transmitted packets high.

Switching transients generated by a selection diversity combiner corrupt receiver filters and increase the system outage as well as corrupting channel estimation. In order to produce an accurate (transient-free) channel estimate and reduce the internal outage, one prefers small switching rates. Therefore, knowledge of the switching rate provides useful information for system engineers in the design of selection diversity receivers. Yet, few results regarding the switching rates of select diversity receivers operating in noisy fading channels have been published. The switching rate of L-fold selection diversity combining in a noisy environment is studied. A closed-form expression for the switching rate is derived for independent and identically distributed (i.i.d.) Rayleigh fading channels in the presence of noise using order statistics. Simulation results are also provided to validate the theoretical results. Our results show that in order to produce an accurate channel estimate and reduce the internal outage, one prefers small switching rates, which can be realized by employing adaptive receiver filters to avoid excessive deleterious switching transients.

Novel non-data-aided maximum likelihood estimators for the delays and the attenuations in an ultra-wide bandwidth channel are proposed. Numerical results show that these new estimators outperform the previous non-data-aided maximum likelihood channel estimators derived in the literature. Moreover, in some cases, the performances of the new non-data-aided estimators approach those of the data-aided estimators, enabling us to reduce the overhead expense of pilot symbols.

The performance of an automatic frequency control (AFC) loop in a noisy fading channel when an interference signal is present at the input of the AFC is studied. Independent non-identically distributed (i.n.d.) channels with Rayleigh and Rician fading are considered. The received signals are assumed to be narrowband and linearly modulated while the analysis is applicable to the unmodulated scenario as well. Closed-form expressions and integral form formulas are derived for the mean time to loss of lock (MTLL) and the average switching rate (ASR) of an AFC. Numerical examples are provided to illustrate the effects of noise and slow fading on the performance of an AFC in the presence of an interferer. It is shown that in some scenarios, an AFC has a better performance if the desired signal is corrupted by more noise.

Multiple access interference (MAI) in time hopping (TH) ultra-wideband (UWB) systems is known to be non-Gaussian. Much previous research in TH-UWB receiver design has attempted to propose better single-user UWB detectors by introducing more accurate models for the distribution of the MAI. Recently, it was shown that some of the single-user receivers track closely the optimum achievable single-user performance. Although, these receivers are simple, all suffer from error rate floors, and hence limited user capacity. Multiuser detection (MUD) is considered for offering high performance at the cost of complexity that grows exponentially with the number of users. Thought to be too complex for low-cost UWB receivers, MUD applied in TH-UWB systems benefits from the low duty cycle implying that the number of effective interfering users is small compared to the number of active users. A novel low-complexity multisampling multiuser detector inspired by the inferiority of single-user receivers and the small number of effective interfering users in TH-UWB systems is proposed. Simulation results show that this detector achieves the performance of the conventional matched filter receiver operating in a single-user system.

We propose the Hadamard matrix as a codebook for multiple-input multiple-output (MIMO) beamforming systems, and show that a quantized equal gain transmission (QEGT) scheme using the Hadamard codebook has the same symbol error probability performance as a receiver selection diversity combining scheme operating in independent generalized Rayleigh fading channels. Also, we propose a greedy cophasing scheme for MIMO beamforming systems using quantized feedback. The greedy cophasing scheme provides 3.2 dB power gain over an orthogonal space-time block code when the number of transmit antennas is four, the number of receive antennas is one, and the number of feedback bits is three.

Asymptotic error rate expressions are derived for multi-branch equal gain combining and selection combining operating on arbitrarily correlated Rayleigh fading channels. These closed-form solutions are used to provide rapid and accurate estimation of the error rates in large signal-to-noise ratio regions. More importantly, it is shown that the asymptotic error rates over correlated branches can be obtained by scaling the asymptotic error rates over independent branches with a factor, det(M), where det(M) is the determinant of the normalized channel correlation matrix.

Optimal component and system design requires knowledge of the statistics underlying the system. To date, the determination of the probability distributions characterizing the multiple access interference in ultra-wide bandwidth wireless systems is an unsolved problem. The statistical characteristics of the multiple access interference in ultra-wide bandwidth wireless systems are studied. Expressions for the probability density functions of the distribution due to asynchronous multiple access interference and additive white Gaussian noise are derived for both additive white Gaussian noise and multipath fading ultra-wide bandwidth environments. The accuracies of the derived expressions for the probability density functions are assessed and confirmed by simulation results.

The mean time to loss of lock and the average switching rate of an automatic frequency control (AFC) loop are derived in this paper for the case of two received signals in dissimilar fading channels. The general case of modulated carriers is considered while the results are also applicable to unmodulated carriers. The channels are assumed to have Rayleigh, Rician and Nakagami-m distributions. Numerical examples are provided to illustrate the effect of these fading scenarios on the performance of an AFC in the presence of cochannel interference.

An optimal power allocation algorithm for delay-limited energy-constrained data transmission in block-fading channels, where blocks are separated in time, is proposed in this paper. Using this algorithm together with a discrete predictive model for the channel, an optimal power allocation strategy is obtained which minimizes the information outage probability based on the current channel state as well as a probabilistic knowledge of the future channel states. It is shown that for schemes with various orders of predictability of the channel, this algorithm outperforms equal power allocation in terms of the outage probability and the average maximum achievable rate.

The performance of collaborative spectrum sensing for cognitive radio in a lognormal shadowing and Rayleigh fading channel is investigated. Unlike previous works that assume perfect knowledge of the average channel signal-to-noise ratio, this paper considers the realistic case where estimation of the average channel signal-to-noise ratio has error. Furthermore, while previous works have designed and examined estimators based on assuming that the channel samples used in the average signal-to-noise ratio estimators are noiseless, the present work assumes that the channel samples are noisy, as is the case in practical systems. Numerical results show that the probability of missed opportunity decreases as the estimation error decreases, as expected. Perhaps unexpectedly, the results also show that in the presence of noise, there exists a threshold phenomenon for the noise level. Below a particular threshold, the probability of missed opportunity increases as the noise level increases. Yet above this threshold, the probability of missed opportunity decreases as the noise level increases.

Maximum-likelihood based channel estimation is considered for orthogonal frequency division multiplexing systems in dispersive time-varying channels. A successive overrelaxation approach is adopted to analyze the convergence rate of an iterative channel estimation algorithm. Based on the analysis, an improved fast converging iterative channel estimation algorithm is proposed. Numerical tests are performed to show the improvement of the proposed algorithm over a recently proposed channel estimation algorithm.

The mean time to loss of lock and the average switching rate of an automatic frequency control loop operating in fading in the presence of a single interferer are derived. Closed-form expressions and integral form formulas are derived for the general case of modulated carriers as well as important special cases of similar modulations and unmodulated carriers. The general results include, as special cases, some previous more restricted results. Fading channels are assumed to be independent non-identically distributed (i.n.d.) with Rayleigh, Rician and Nakagami-m distributions while the special case of independent identically distributed (i.i.d.) channels is also considered. Corresponding numerical examples are provided and discussed to illustrate the results.

The multiple access interference (MAI) in a time-hopping (TH) ultra-wideband (UWB) system is known to be non-Gaussian even when the system has a moderately large number of active users. Therefore, the conventional matched filter (CMF) receiver, the optimal structure for Gaussian noise which maximizes the signal-to-noise ratio (SNR) and minimizes the probability of detection error in the absence of non-Gaussian interference, is not necessarily optimal. We express and prove a stronger claim that even the outputs of the matched filters in the conventional UWB receiver can not provide a sufficient decision statistic for detecting the information bits transmitted by the desired user. Further, a novel TH-UWB receiver is introduced which uses a similar methodology to the optimal multiuser detection (MUD) algorithm for detecting the information bits. However, the complexity of this new receiver is much less than that of the optimal MUD algorithm. It employs only one matched filter instead of a bank of matched filters resulting in a simple and low-cost TH-UWB receiver. Simulation results show that the new receiver outperforms previous single-user TH-UWB receivers and achieves essentially the performance of the CMF receiver operating in a single-user system.

A transmission scheduling algorithm is proposed for wireless sensor networks with energy limited mobile sinks. The algorithm is primarily based on the well known tradeoff between the expected number of data packets that are successfully received by the sink and the transmission power consumed in the system. The likelihood of having new packets generated at the sensor node during the transmission as well as the possibility of erroneous reception of acknowledge packets at the sensor node are accounted for in the algorithm. The behavior of the system is studied in terms of power consumption and packet reception for different packet generation rates as well as different costs of transmission power at the sink.

Switching rate is an important parameter in selection diversity receiver design because the switching transients increase the system outage. An exact closed-form solution for the switching rate of dual selection diversity in kappa-mu and alpha-mu distributed fadings is derived. Independent and identically distributed (i.i.d.) kappa-mu and alpha-mu fading channels are considered. The switching rate for dual i.i.d. kappa-mu distributed fading includes the switching rate for dual i.i.d. Rayleigh, Rician and Nakagami-m fading channels as special cases. Similarly, the switching rate for dual alpha-mu fading channels also includes special cases such as Rayleigh, Nakagami-m and Weibull fading channels.

The multiple-user interference (MUI) in time-hopped impulse-radio ultrawide bandwidth (UWB) systems is impulse-like and poorly approximated by a Gaussian distribution. Therefore, conventional matched filter receiver designs, which are optimal for Gaussian noise, are not fully efficient for UWB applications. Several alternative distributions for approximating the MUI process and the MUI-plus-noise process in UWB systems are motivated and compared. These distributions have in common that they are more impulsive than the Gaussian approximation, with a greater area in the tails of the probability density function (pdf) compared to a Gaussian pdf. The improved MUI and MUI-plus-noise models are utilized to derive new receiver designs for UWB applications, which are shown to be superior to the conventional matched filter receiver. Multipath propagation is abundant in UWB channels and is exploited by a Rake receiver. A Rake receiver uses multiple fingers to comb the multipath rays with a conventional matched filter implemented in each finger. Rake structures utilizing the new receiver designs that are suitable for reception of UWB signals in multipath fading channels are provided. An optimal performance benchmark, based on an accurate theoretical model for the interference that fully explains the features of the MUI pdf, is also presented. Analysis and simulation results are shown for the novel receivers, which demonstrate that the new designs have superior performance compared to the conventional linear receiver when MUI is significant. Several adaptive receivers are shown to always match or exceed the performance of the conventional linear receiver in all MUI-plus-noise environments. Parameter estimation for the new receivers also is discussed.

Statistical moments of the inter-path interference, the inter-chip interference and the intersymbol interference in a direct-sequence binary phase shift keying ultra-wide bandwidth (UWB) system are analyzed for the IEEE UWB channel models. Exact expressions for the first- and second-order moments are derived. The effects of the duration of the monocycle pulse, the spreading gain, and the number of interfering symbols on the average powers of the interferences are examined.

Maximum likelihood (ML) receivers for space-time coded multiple-input multiple-output (MIMO) systems with Gaussian channel estimation errors are proposed. Two different cases are considered. In the first case, the conditional probability density function (PDF) of the channel estimate is assumed Gaussian and known. In the second case, the joint PDF of the channel estimate and the true channel gain is assumed Gaussian and known. In addition to ML signal detection for space-time coded MIMO with ML and minimum mean-squared-error channel estimation, ML signal detection without channel estimation is also studied. Two suboptimal structures are derived. The Alamouti space-time codes are used to examine the performances of the new receivers. Simulation results show that the new receivers can reduce the gap between the conventional receiver with channel estimation errors and the receiver with perfect channel knowledge at least by half in some cases.

The performance of collaborative spectrum sensing for cognitive radio in a lognormal shadowing and Rayleigh fading channel is investigated. Unlike previous works that assume perfect knowledge of the average channel signal-to-noise ratio, this paper considers the realistic case where estimation of the average channel signal-to-noise ratio has error. Furthermore, while previous works have designed and examined estimators based on assuming that the channel samples used in the average signal-to-noise ratio estimators are noiseless, the present work assumes that the channel samples are noisy, as is the case in practical systems. Numerical results show that the probability of missed opportunity decreases as the estimation error decreases, as expected. Perhaps unexpectedly, the results also show that in the presence of noise, there exists a threshold phenomenon for the noise level. Below a particular threshold, the probability of missed opportunity increases as the noise level increases. Yet above this threshold, the probability of missed opportunity decreases as the noise level increases.

The performance of a dual-branch decorrelator receiver operating in correlated Rayleigh and Rician fading channels in conjunction with selection combining (SC) and switch-and-stay combining (SSC) is analyzed and compared to the performance of a conventional SC and SSC receiver. For each combining scheme, analytical expressions for the average bit error rate (BER) of several modulation techniques of practical interest, the mean output signal-to-noise ratio (SNR) and the outage probability are derived. It is shown that the decorrelator receiver has superior performance over the conventional receiver by as much as 2.83 dB in average SNR. The effects of modulation order, correlation coefficient and the severity of fading on the performance of the decorrelator receiver are studied.

The performance of non-data-aided feedback-loop symbol timing synchronization operating with the raised-cosine (RC) and the "better than" raised-cosine (BTRC) pulses is investigated. The individual effects of additive channel noise, self noise, and their product on the variance of the jitter are studied for the two pulses. The BTRC pulse is shown to have better synchronization performance than the conventional RC pulse, except when the signal-to-noise ratio is very large and the excess bandwidth is large. Furthermore, in the case where a prefilter removing self-noise is employed, the BTRC pulse always has a performance gain over the RC pulse. The gain is, for example, as much as 1.4 dB for excess bandwidth of 0.35 without a prefilter and is larger when the excess bandwidth is smaller or a prefilter is employed.

Analytical results for the symbol error rate (SER) of M-ary phase shift keying (MPSK) in a slow, flat Rayleigh fading channel for a multiple-input multiple-output (MIMO) system using an Alamouti transmission scheme and generalized selection combining (GSC) scheme are given. Two new receiver selection schemes, generalized space-time sum-of-squares (GSTSoS) selection diversity and generalized space-time sum-of-magnitudes (GSTSoM) selection diversity are proposed. The first provides the same performance as conventional GSC, and the second provides slightly poorer performance, but neither requires channel state information and both have much simpler implementations. The SER of MPSK in Rayleigh fading using these two selection schemes is studied and compared to that of conventional GSC. The effects of channel estimation errors on each selection scheme are examined.

The average bit-error rate performance of one-stage and two-stage diversity combining schemes operating over correlated fading channels is investigated. Two channel models that can significantly simplify the performance analysis are considered. In particular, a linear correlation channel model having equal branch variances can be decorrelated at the receiver, so that the branches become independent. It is shown that, in general, employing diversity combining schemes for decorrelated or orthogonalized branches can recover some of the diversity gain lost due to the branch correlations. This is observed, for example, for the case of hybrid selection/maximum ratio combining operating over decorrelated and orthogonalized non-zero mean Gaussian fading channels. Furthermore, a fading amplitude channel model is proposed assuming vector norm superposition of the impinging plane waves. This channel model is well-suited for the performance analysis of maximum ratio and equal gain combining schemes operating over correlated fading channels. Finally, the average bit error rates of several diversity combining schemes are evaluated analytically using the Prony approximation method as well as using computer simulation.

A framework for analyzing the performance of coded OSTBC-OFDM systems over arbitrary correlated generalized Ricean fading channels is established. The moment generating function of the signal-to-noise ratio at the input to the channel decoder is derived assuming correlated transmitter and receiver antennas and correlated paths in frequency selective channels. The probability of outage, the pairwise error probability, and the bit error rate are then evaluated. Bit-interleaved and iteratively decoded turbo product codes, Gray encoded M-ary quadrature amplitude modulation, and other parameters of the IEEE 802.16 Standard are used to illustrate numerical results.

Selection amplify-and-forward (SAF) relaying, which has been shown to be optimal under the constraints of localized channel information at the relays and a constant relay power allocation (PA) template, is shown to be globally strictly suboptimal. A necessary condition for the outage optimality of the SAF PA, and an exponentially vanishing upper bound on the probability of the SAF optimality are derived.

An integrated cross-noise component frequently arises in communications and in signal processing. One typical example is the autocorrelation receiver. Integrated cross-noise generally appears when a noisy signal is recovered (detected) using correlation techniques with a noisy signal as the reference. The statistics of the integrated cross-noise component are analyzed in general for both the cases of uncorrelated and correlated noise terms in the integrand. The exact 2ndorder statistics of the integrated cross-noise are derived, and new improved expressions are derived for an approximate probability density function. Accurate computer simulations are performed to evaluate the actual probability density function of the integrated cross-noise component and these results are compared with the approximations. The convergence of the approximation to a Gaussian distribution is also discussed.

The optimal linear Rake receiver for the detection of signals contaminated by symmetric alpha stable noise is derived for 1 < ¿ ¿ 2. Although this structure is suboptimal, it is optimal among the class of linear Rake receivers in the sense of minimizing the bit error rate. The proposed receiver is a very simple form of diversity combiner for signal detection in symmetric alpha-stable noise. The bit error rate improvements of the optimal linear Rake receiver over the maximal ratio combiner and the equal gain combiner are also derived in the form of signal-to-noise ratio advantage.

Exact closed-form expressions are derived for the bit error rate of binary phase shift keying in Rayleigh fading channels with maximal ratio combining diversity in the presence of cochannel interference and additive white Gaussian noise. The desired signal and the interferer signals are subject to correlated Rayleigh fading and binary phase shift keying modulation is used by all users.

A novel ultra-wide bandwidth receiver structure dubbed the "zonal" receiver is based on the qualitative nature of the probability density function of the multiple access interference. It is proposed for time-hopping ultra-wide bandwidth wireless signal detection in multiple access interference channels. In ideal free-propagation channels, the zonal receiver always meets or outperforms the conventional matched filter UWB receiver, the recently proposed soft-limiting UWB receiver and its enhanced version, the adaptive threshold soft-limiting UWB receiver. A new Rake receiver design based on the zonal receiver is proposed for signal detection in multipath fading channels. Simulation results and analysis show that this new Rake receiver can achieve larger signal-to-interference-plus-noise ratio than the standard matched filter Rake receiver when multipath components are resolvable in UWB channels.

The effect of noise on the switching rate of a dual branch selection diversity combiner in noisy fading channels is examined. A closed-form solution is derived for independent and identically distributed (i.i.d.) and independent and nonidentically distributed (i.n.d.) fading channels. The switching rate in noisy fading channels is compared to that in noise-free conditions.

Accurate approximations to the bit error rates of equal gain combining and maximal ratio combining diversity are obtained for pulse-amplitude-and-position-modulation operating in IEEE ultra-wide bandwidth (UWB) channel models. Numerical results are presented to show the accuracy of the approximations for the IEEE CM1 and CM3 UWB channel models. Results for pulse amplitude modulation and pulse position modulation are obtained as special cases of the more general results. Precise estimates of the loss of equal gain combining relative to maximal ratio combining are obtained for both line-of-sight CM1 and non-line-of-sight CM3 channels. Noteworthy, while the performance loss of equal gain combining with respect to maximal ratio combining is less than 0.4 dB for the non-line-of-sight channel, it can be as much as 2 dB for the line-of-sight channel.

The ergodic capacity in Rayleigh fading of multi- hop wireless transmission systems employing either amplify- and-forward relaying or decode-and-forward relaying is studied, assuming channel state information is only known at the receiving terminals. Two upper bounds based on Jensen's inequality and the harmonic-geometric means inequality as well as an infinite series representation for the ergodic capacity of an amplify-and- forward multi-hop transmission system are derived. Numerical results are provided to examine the tightness of the upper bounds as well as to show the high accuracy of the infinite series approach. In addition, the ergodic capacity of a decode- and-forward multi-hop transmission system is obtained. It is shown that multi-hop transmission systems employing a decode- and-forward relaying scheme achieve higher ergodic capacities than multi-hop transmission systems with amplify-and-forward relaying schemes.

Optimal power allocation schemes that maximize the instantaneous received signal-to-noise ratio in an amplify-and- forward multi-hop transmission system under short-term (ST) and long-term (LT) power constraints are presented. The optimal power allocation strategy under a ST power constraint requires a centralized architecture for implementation. However, the power allocation solutions to the LT power constraints can be implemented in a decentralized manner. Theoretical expressions for evaluation of the outage probability of the proposed power-optimized multi-hop relaying systems over Rayleigh fading channels are obtained. Numerical results show the superior performance of amplify-and-forward multi-hop relaying systems with the power allocation scheme over those with uniform power allocation. It is shown that at sufficiently large values of signal-to-noise ratio (SNR), an amplify-and-forward K-hop relaying system employing the optimal power allocation scheme under ST power constraint achieves K times better outage performance than that of the corresponding system employing uniform power allocation. It is also shown that the optimal power allocation schemes under LT power constraints provide substantial performance gain at both small and large values of SNR and achieve diversity gain.

It is well known that the Gaussian distribution is not an accurate model for approximating the probability density function (PDF) of the multiple access interference (MAI) in timehopping UWB (TH-UWB) systems. An exact theoretical model which explains the key features of the PDF of the MAI in THUWB systems is discussed. These features, which can be precisely anticipated by the proposed model include impulses, singularities, and the tail behaviour in the distribution of the MAI. The model reveals in quantitative terms why a Gaussian approximation for the MAI in TH-UWB systems is highly imprecise even in an environment with a large number of independent interferers. Based on the model obtained for the PDF of the MAI and exploiting the maximum a posteriori (MAP) receiver design rule, the optimal attainable BER performance of binary TH-UWB receivers in additive white Gaussian noise channels is numerically determined. The performances of some recently proposed UWB receivers are benchmarked against the optimal performance showing that some of them achieve near-optimal performance.

The problem of cochannel interference (CCI) suppression using a noise-plus-interference whitening matched filter (WMF) is addressed. Binary phase-shift keying modulated transmission over a Nakagami-m fading channel is considered in a bandlimited microcellular wireless system. It is shown that the signal-to-interference-plus-noise ratio (SINR) of the WMF can not exceed that of the conventional matched filter (CMF) receiver for synchronous CCI, but in the asynchronous channel, CCI whitening can be used to improve receiver performance. The SINR-maximizing filter (SINRMF) in an asynchronous channel is derived and shown to be composed of a WMF followed by a discrete time filter. The SINRs of the WMF and SINRMF receivers are analytically evaluated for a standard raised-cosine (RC) and a Beaulieu-Tan-Damen pulse. It is shown that for the RC pulse, the WMF can achieve a SINR gain as large as 1.76 dB over the CMF receiver provided that the transmission is free of intersymbol interference (ISI). The SINR of the ISI-impaired system is also evaluated and the conditions under which this system can achieve close to ISI-free SINR are studied. The SINR is evaluated for the SINRMF and it is shown that this filter can restore much of the SINR loss incurred due to ISI introduced by the WMF.

An analytical expression for the switching rate of a dual branch selection diversity combiner in kappa-mu and alpha-mu distributed fadings is derived. Independent and identically distributed (i.i.d.) kappa-mu as well as alpha-mu fading channels are considered. The switching rates for dual i.i.d. Rayleigh, Rician and Nakagami-m fading channels are special cases of the switching rate for dual i.i.d. kappa-mu fading channels. Similarly, the general switching rates for dual alpha-mu fading channels also include special cases such as Rayleigh, Nakagami-m, and Weibull fading channels.

The ergodic capacity in Rayleigh fading of multi- hop wireless transmission systems employing either amplify-and-forward relaying or decode-and-forward relaying is studied, assuming channel state information is only known at the receiving terminals. Two upper bounds based on Jensen's inequality and the harmonic-geometric means inequality as well as an infinite series representation for the ergodic capacity of an amplify-and- forward multi-hop transmission system are derived. Numerical results indicate the upper bound obtained based on Jensen's inequality is tight. This upper bound is tighter than the upper bound based on harmonic and geometric means for larger numbers of hops and especially for systems in non-identical fading. Numerical results are provided to show the high accuracy of the infinite series approach. In addition, the ergodic capacity of a decode-and-forward multi-hop transmission system is obtained. It is shown that multi-hop transmission systems employing a decode-and-forward relaying scheme achieve higher ergodic capacities than multi-hop transmission systems with amplify-and- forward relaying schemes.

An exact mathematical model which explains the important characteristics of the probability density function (PDF) of the multiple access interference (MAI) in time-hopping UWB (TH-UWB) systems is discussed. The proposed model accurately foresees impulses, singularities, and heavy tails found in the distribution of the MAI. Also, it discloses precisely why a Gaussian approximation for the MAI in TH-UWB systems is highly inaccurate even in the presence of a large number of interferers. Then, using the maximum a posteriori (MAP) receiver rule and based on the obtained model for the PDF of the MAI, the optimal achievable BER performance of binary TH-UWB receivers is numerically determined. Finally, the performances of some recently proposed UWB receivers are benchmarked against the optimal performance.

Selection cooperation is proposed for rateless coded relaying by developing a novel low-complexity protocol that exploits all source-destination, source-relay, and relay-destination link qualities for relay selection. The source or any decoding relay having a link to the destination with a gain greater than a preset threshold is a candidate for collaboration. When the number of candidates reaches a preset value, the best of them is selected for passing the source data to the destination. The source and relays are informed of the selected node by a broadcast feedback from the destination. Limited feedback is required only between the destination and the other nodes and merely for declaring success in decoding or selecting the next transmitting node. The system power and complexity are independent of the system parameters. Also, the system dispenses with internode synchronization at carrier or symbol levels, multireception combining, multiaccess interference, and multiuser detection. Assuming independent fading on different links, a general performance analysis of the new system is presented valid for any individual link fading model. It is shown through numerical results that the novel scheme is considerably more energy efficient, for diverse input conditions, than a more complex commensurate scheme previously proposed. Also, the energy efficiency is enhanced as the number of relays increases, such that despite an increase in the capacity, the energy expenditure diminishes.

An amplify-and-forward relaying network where the source is orthogonal to all the relays but the relays are nonorthogonal (SORNAF) is studied. The problem of relay power optimization in a SORNAF relaying scheme is formulated as a nonconcave fractional program. Selection amplify-and-forward (SAF) relaying is a possible power allocation strategy previously proposed for the SORNAF scheme. A necessary condition for the optimality of the SAF power allocation is derived in terms of instantaneous channel coefficients, based on which, an upper bound on the SAF optimality probability is calculated. The upper bound approaches zero almost exponentially as the number of relays increases, showing that SAF relaying is asymptotically strictly suboptimal. A suboptimal power allocation, which is significantly superior to the SAF algorithm in terms of outage performance, is also proposed for SORNAF relaying.

The problem of cochannel interference mitigation using interference-plus-noise whitening receiver design in the presence of intersymbol interference (ISI) is considered. The effect of ISI on the signal-to-interference-plus-noise ratio (SINR) of the interference whitening receiver is examined. Then, two methods are proposed to maximize the SINR without introducing ISI. In the first method, the transmitter and receiver filters are designed to maximize the SINR while their overall spectrum maintains a given Nyquist spectrum to avoid ISI. In the second method, the transmitter filter is assumed to be fixed and only the receiver filter is designed to achieve maximum SINR without introducing ISI. The SINR of the ISI-free SINR-maximizing filter is then analytically compared with that of the conventional matched filter receiver and the interference whitening receiver. Numerical results are presented for the cases when standard raised-cosine and Beaulieu-Tan-Damen pulses are used in the system.

The switching rates of dual-branch selection combining diversity and switch-and-stay combining diversity in Rayleigh, Rician and Nakagami-m (m half-integer or integer) fading are derived. The switching rate of selection combining is compared to that of switch-and-stay combining for the cases of balanced channels and unbalanced channels. The closed-form solutions have an explicit dependence on the Doppler frequency of the fading.

The performances of two recently proposed receiver antenna selection schemes based on maximum sum-of- squares and maximum sum-of-amplitudes are investigated for the Alamouti space-time block coded multiple-input multiple-output system with correlated receiver antennas and M-ary signals. These schemes require neither channel estimation nor channel quality ordering. Their performances are compared with the conventional diversity selection scheme based on maximum signal- to-noise ratio, which does require channel quality information. Unlike the independent antenna case, where the performances of the new selection schemes are very close to that of the conventional scheme, the performance differences between the new schemes and the conventional scheme is significant in some cases when the receiver antennas are correlated.

A quadrature Markov chain model of the Rayleigh fading channel is examined. The model is defined by formulating a Markov chain model of the underlying Gaussian fading process, using a state-space that consists of both the amplitude and rate-of-change of the Gaussian fading, then transforming that model into a Markov chain model of the Rayleigh fading process. Power margin quality measures are used to determine the most suitable number of states for the model. It is shown that the proposed model is an improvement over previous amplitude-based models, and that, in some instances, it is also an improvement over previous amplitude/rate models.

Novel maximum likelihood (ML) receivers for multiple-input and multiple-output systems with imperfect channel estimation are proposed. Two different cases are considered. In the first case, the conditional probablity density function (PDF) of the channel estimate is assumed Gaussian and known. In the second case, the joint PDF of the channel estimate and the true channel gain is assumed Gaussian and known. In addition to optimal signal detection with channel estimation, optimal signal detection without channel estimation is also studied. To reduce the implementation cost of optimal receivers, two suboptimal structures are derived. As an example, the Alamouti space-time codes are used to examine the performances of the new receivers. Simulation results show that the new receivers can reduce the gap between the conventional receiver with channel estimation errors and the receiver with perfect channel knowledge at least by half in some cases.

Five new receivers for generalized transmitted- reference ultra-wide bandwidth systems are proposed. Three of these receivers are derived by optimally combining the channel estimates using the reference symbols, the data decisions and the data symbols. Two of these receivers are derived by using iterative algorithms. These receivers have very simple structures. Simulation results show that they outperform previous receivers.

The ergodic capacities in Rayleigh fading of various wireless relaying systems with an arbitrary number of half- duplex relays are analyzed, assuming channel state information is only known at the receivers. Closed-form analytical expressions for calculation of the ergodic capacities of wireless relaying systems with regenerative relays and nonregenerative relays employing decode-and-forward relaying and amplify-and-forward relaying, respectively, are derived. It is shown that systems with regenerative relays employing decode-and-forward relaying offer higher ergodic capacities than systems with nonregenerative relays employing amplify-and-forward relaying.

Simple, closed-form expressions for the outage probability and bit error rate of multi-hop diversity transmission systems employing either fixed or selective amplify-and-forward relaying are derived. Numerical results show the accuracy of the obtained analytical results for sufficiently large values of signal- to-noise ratio. In addition, it is shown that a multi-hop diversity transmission system employing fixed amplify-and-forward relaying outperforms the corresponding systems employing fixed decode-and-forward, selective decode-and-forward or selective amplify-and-forward relaying, despite the noise amplification at all relays.

Multi-hop and multi-branch wireless transmission systems with nonregenerative fixed gain relays employing amplify-and-forward relaying are studied. Simple closed-form expressions for the outage and bit error probabilities of these systems are derived. The analysis is valid for an arbitrary number of hops, arbitrary number of branches and any fading channel model whose signal power probability density function has nonzero value at the origin. It is shown that while a multi-hop transmission system does not offer diversity gain, it can perform better than a single hop system if its average individual link SNRs satisfy a certain condition. In addition, the analysis clearly shows the diversity gains achieved by multi-branch systems for any fading channel model.

The performance of a dual-branch decorrelator receiver operating in correlated Rayleigh and Rician fading channels in conjunction with selection combining (SC), square- law combining (SLC) and equal gain combining (EGC) diversity is analyzed and compared to the performance of a conventional SC, SLC and EGC diversity receiver. Analytical expressions for the average symbol error rate (SER) and the average bit error rate (BER) of several modulation techniques of practical interest, the mean output signal-to-noise ratio (SNR) and the outage probability are derived. It is shown that the decorrelator receiver has superior performance over the conventional receiver by as much as 2.1 dB in average SNR when SC is employed. Interestingly, it is also shown that the mean output SNR of the decorrelator SC receiver improves with increasing the correlation coefficient while that of the conventional SC receiver degrades with increasing the correlation coefficient. In Rician fading, the results indicate that the outage probability of the decorrelator receiver is much less than the outage probability of the conventional receiver and the gap between the two increases as the channels become less faded.

A new receiver for convolutional coded information, which performs both the equalization and decoding in a joint scheme, based on the Viterbi algorithm is proposed. This method is based on creating a trellis for the joint system assuming some virtual auxiliary registers in the structure of the coder. In this way, the state space of the convolutional coder extends to support different states of the channel, enabling the receiver to include different states of the channel directly during the process of recovering the source information. Simulations indicate that the capability of taking the channel states into account during the decoding increases the performance of the overall receiver in the case of channels with memory. Also, the proposed method has lower complexity than a separated equalizer and hard decoder structure. A similar receiver for a memoryless channel can outperform conventional receivers. Simulation results for channels with and without memory are discussed.

Cooperative diversity, where multiple communication nodes collaborate to exploit independent signal replicas that are combined at the destination has been proposed. Practical diversity receivers often employ simple combining techniques especially if comparable performance to more complex optimum combining can be achieved. The performances of cooperative diversity systems that use selection combining are investigated. In particular, we consider decode-and-forward and amplify- and-forward relaying protocols. Closed-form expressions for the outage probability of systems with an arbitrary number of relay nodes are derived. By comparing the performance of a system that uses selection combining to one that uses optimum maximal ratio combining, the trade-off between performance and receiver complexity is determined.

A signal-plus-noise (S + JV) energy selection combining (S+JV-ESC) scheme for binary phase shift keying (BPSK) signaling is proposed. The S + JV-ESC selects the branch with the maximum S + JV energy for detection. The advantage of the S + JV-ESC is that it requires no channel estimation for diversity branch selection. The bit error rate (BER) performance of the S +JV-ESC is analyzed for BPSK signaling in independent and identically distributed (i.i.d.) Rayleigh fading channels. We show that the performance of the S + JV-ESC is the same as conventional signal-to-noise ratio selection combining (SNR-SC), which requires estimation of the fading amplitudes for branch selection.

A Z-Bayesian erasure test (BET) based on order statistics with diversity reception for noncoherent M-ary frequency shift keying (FSK) signaling is examined. In the Z-BET, the M-ary FSK symbol is erased whenever the a posteriori probability of correct decision, which is a function of the Z-largest sums of energy detector outputs, is less than a threshold. For binary FSK signaling in Rayleigh flat fading channels, the 2-BET is found to be the same as the difference threshold test (DTT), which declares an erasure whenever the difference between the largest and the second largest sums of energy detector outputs is less than a threshold. The output threshold test (OTT), which declares an erasure whenever the largest sum of energy detector outputs is less than a threshold, is proved equivalent to the 1-BET for the Rayleigh flat fading channel. Closed-form expressions for the probabilities of correct decision and symbol error for the DTT, Viterbi's ratio threshold test (RTT), and the OTT are derived when square-law combining (SLC) diversity is used. Several erasure tests including the Z-BET, the RTT, the OTT, and the DTT are compared in terms of probability of codeword error. The 2-BET provides almost the same performance as the BET that requires all the sums of energy detector outputs. The 2-BET provides power gains of 0.9 dB and 0.7 dB over the RTT for (7,3) and (15,7) Reed-Solomon (RS) codes, respectively, when the probability of codeword error is 10 3 and the diversity order is one. Higher-order diversity has reduced gains.

Asymptotic bit-error rate expressions are derived for binary phase shift keying with multi-branch equal gain combining (EGC) and selection combining (SC) on equally correlated Rician channels. Numerical results indicate that these analytical error rate expressions can provide accurate error rate estimation at large signal-to-noise ratio (SNR). Furthermore, these analytical results can be used to reveal some important insights into the performance characteristics of EGC and SC operating on equally correlated Rician fading channels.

Further results on a Prony approximation for efficient evaluation of the average probability of error over fading channels are presented. A generic definition of the average probability of error for a communication system is given. The Prony approximation method is shown to be an extension of the Chernoff bound and the MGF method. An improved algorithm for obtaining the parameters of the Prony approximation is developed. New, simple and highly accurate Prony approximations for the conditional probability of bit-error of M-ary modulations assuming parameter quantization to only 3 significant figures are presented. Furthermore, the rank and determinant design criteria for space-time block codes in Gaussian channels are shown to be valid for the exact pairwise error probability. Numerical results indicate that the relative approximation error using the Prony approximation method is less than 5% of the exact average probability of error for all practical values of the signal-to-noise ratio.

Hypergeometry of objects in K dimensions is used to determine the optimum dimension of signal-to-noise ratio adaptive receivers. Previously, it is shown that the volume and surface area of many A'-dimensional objects are maximized for a particular dimension. In this paper, this observation is used to conjecture that the average performance measures of signal-to- noise ratio adaptive receivers reach a maximum for a particular dimension. The performance analysis is obtained assuming a generic two-stage diversity combining structure at the receiver front-end. Although the diversity combining schemes increase the output channel amplitude by adding more receiver antennas for any branch fading statistics, the subsequent signal-to-noise ratio adaptive signal processing creates an optimum in the number of receiver antennas. This is confirmed by numerical examples assuming a bank of detectors operating over erasure subchannels. The optimum dimension of the receiver has significant impact on the overall receiver complexity.

The achievable rates of three decode-and-forward half-duplex (DFHD) and two decode-and-forward full-duplex (DFFD) protocols are studied under a peak power constraint (PPC) and an average power constraint (APC). Two of the DFHD and one of the DFFD protocols are known. One new, much simpler, DFHD protocol, and one new DFFD protocol are proposed. The fairness in comparing the protocols in terms of energy cost is formulated, and the protocols are compared to each other in a power-fair regime. The two previously proposed DFHD protocols, one of which is superior to the other under the PPC, are found to have almost the same performances when compared power-fairly. The proposed protocols are built upon the water filling principle and power optimization such that, although inferior to their predecessors in a PPC regime, they can slightly surpass them under the APC. The protocols considered here take advantage of the previously proposed opportunistic relaying (ORe) concept. The original ORe is not directly applicable to the rateless schemes. However, it is shown that the ORe, after a novel modification, is compatible with, and implementable in the rateless protocols. The ORe brings about practical benefits and economical use of network resources in relaying systems.

UWB multiple access interference is known to be non-Gaussian. Work has attempted to design better UWB detectors by approximating the distribution of the multiple access interference by a non-Gaussian noise model. In this paper, a non-linear detector is proposed, which is inspired by the empirical finding that the UWB multiple access interference can be better modeled by a symmetric-alpha-stable distribution than the Laplacian, generalized Gaussian, Cauchy and Gaussian distributions. The new detector which is adaptive to the current interference-plus-noise condition is found to outperform many other non-Gaussian (non-linear) detectors proposed for UWB multiuser communication.

The optimal linear Rake receiver for the detection of binary signals contaminated by symmetric alpha-stable noise is derived for 1 < alpha les 2. The bit error rate improvements of the optimal linear Rake receiver over the maximal ratio combiner and the equal gain combiner are also derived in the form of signal-to-noise ratio advantage. The proposed receiver is a very simple form of diversity combiner for signal detection in alpha- stable noise.

Two multiuser combining receiver structures for space diversity reception of a signal distorted by cochannel interference and additive white Gaussian noise are derived. The desired and interfering signals are assumed to be binary phase- shift keying modulated and Rayleigh-faded. The first receiver concurrently minimizes the error probability for all users and is composed of a bank of maximal ratio combiners (MRC's) followed by a maximum-likelihood detector. In the second receiver, the error probability is minimized only for the desired user and it is shown that the receiver comprises an MRC bank followed by a likelihood ratio tester that picks the globally best hypothesis. Simulation results illustrate the superiority of the proposed detection strategies over a receiver which makes use of optimum combining, especially for small values of signal-to- interference power ratios.

Exact closed-form expressions are derived for the bit error rate of binary phase shift keying in Rayleigh fading channels with maximal ratio combining diversity in the presence of cochannel interference and additive white Gaussian noise. The desired signal and the interferer signals are subject to correlated Rayleigh fading and binary phase shift keying modulation is used by all users. Using the derived expressions, it is shown through some numerical examples that for a fixed number of antennas, there is a best radius for a uniform circular array at which the array performance is almost as if all antennas in the array were uncorrelated. Counterintuitively, at this radius, the adjacent antennas in the array are not uncorrelated.

In this paper, the bit error rate performance of the Rake reception of binary signals over the IEEE 802.15.3a ultra- wide bandwidth channel model is evaluated. Instead of using Gaussian approximation for the PDF of the total disturbance, a more accurate method is introduced by using the characteristic function of the interference and the additive white Gaussian noise. A formula for the evaluation of the bit error rate performance of ultra-wide bandwidth systems is thus derived, which can be rapidly calculated by using Gaussian Hermite quadrature with excellent accuracy.

Four hybrid selection maximum ratio combining (HS/MRC) diversity schemes over correlated Ricean fading channels are investigated. In particular, the correlated diversity branches are either decorrelated or orthogonalized prior to diversity combining. The optimum time-invariant selection of diversity branches prior to MRC as well as conventional HS/MRC are also considered. The average bit error rate (BER) performance of these four diversity combining schemes is obtained using the Prony approximation method and using computer simulations. Numerical results indicate that decorrelation and orthogonalization of the correlated branches prior to diversity combining can restore some of the diversity gain lost due to the correlation between branches. This is observed especially for the case of a strong line-of-sight fading component, and for small numbers of selected branches in HS/MRC diversity where the signal-to-noise ratio (SNR) improvement can be as large as 2 dB.

The performance of a dual-branch decorrelator receiver operating in correlated Rayleigh and Rician fading channels in conjunction with switch-and-stay combining (SSC) is analyzed and compared to the performance of a conventional SSC receiver. Analytical expressions for the average bit error rate (BER) of several modulation techniques of practical interest, the mean output signal-to-noise ratio (SNR) and the outage probability are derived. It is shown that the decorrelator receiver has superior performance over the conventional receiver by as much as 2.83 dB in average SNR. The effects of modulation order, correlation coefficient and the severity of fading on the performance of the decorrelator receiver are studied.

A new ultra-wide bandwidth communication system using both a time-hopping (TH) sequence and a direct spreading sequence, called direct-sequence impulse radio (DS-IR), has recently been proposed. An exact analysis to evaluate the bit error rate (BER) performance of this new scheme in multi-user interference (MUI) is provided. On the basis of this new analysis, ultra-wideband communication systems employing TH, direct-sequence and the newly proposed DS-IR schemes operating in MUI are accurately compared in terms of the BER. Our results indicate that DS-IR outperforms the TH binary phase-shift keying (BPSK) system. However, its performance is poorer than the performance of the conventional full-duty direct sequence BPSK system. Compared with the low-duty direct sequence BPSK system, DS-IR achieves a better error rate performance for medium and large signal-to-noise power-ratio values.

Abstract Security is of ultimate importance to the global communication and information networks. Both academia and industry have seen the importance of the R&D activities in security and communication networks, and a great deal of resources has been invested by both governments and private sectors around the world to enhance the security of global information and communication networks, which virtually cover all regions of the world. Therefore, the timely launch of Security and Communications Networks is of great interest to the world community. In this inaugural issue, worldwide experts contribute their papers, covering various important research areas in security. Copyright © 2008 John Wiley & Sons, Ltd.

Abstract The ever‐increasing demand for the services of wired and wireless data networks has led to network security being a prerequisite for all successful data transactions. This has accelerated research activities in academia, private sectors, and governments to respond to the challenges of providing complete solutions for secure communications and networks. Security and Communication Networks provides a distinctive global platform to explore the research advances in the communications network security from academia, industry, and governments. In this second issue, six thought provoking papers discussing various element of security research in communications and networks are presented. Copyright © 2008 John Wiley & Sons, Ltd.

No closed-form expression is known for the lognormal characteristic function. Computation of the characteristic function using numerical integration is time consuming and often converges poorly. Alternative published numerical methods for its evaluation are complex and often valid only for particular values of the dB-spread. A novel definite integral form of the lognormal characteristic function is derived. This form lends itself to rapid and convenient computation of the lognormal characteristic function using simple, common methods of numerical integration.

The switching rates of dual selection combining diversity and dual switch-and-stay combining diversity in Rayleigh, Rician and Nakagami-m (m half-integer or integer) fading are derived. Closed-form or single integral expressions are obtained for both the cases of balanced channels and unbalanced channels.

The generalized Gaussian probability density function is shown to better approximate the probability density function of the multiple access interference in ultra-wide bandwidth systems than the Gaussian approximation and the Laplacian density approximation. Two ultra-wide bandwidth receiver structures based on this new approximation using a p-order metric receiver decision statistic are investigated for the detection of time-hopping ultra-wide bandwidth wireless signals in multiple access interference channels. The first receiver outperforms both the conventional matched filter ultra-wide bandwidth receiver and the soft-limiting ultra-wide bandwidth receiver when only multiple access interference is present in UWB channels. The second new receiver with adaptive limiting threshold outperforms the conventional matched filter ultra-wide bandwidth receiver, the soft-limiting ultra-wide bandwidth receiver, and the adaptive threshold soft limiting ultra-wide bandwidth receiver in all multiple access interference-plus-noise environments. In multipath channels, a new Rake receiver based on the porder metric receiver is proposed for signal detection. Mathematical analysis and numerical results show that this new Rake receiver can achieve larger signal-to-interference-plus-noise ratio than the standard matched filter Rake receiver when multipath components are resolvable in UWB channels.

Asymptotic error rate expressions are derived for equal gain combining and selection combining on dual-branch correlated Rician channels. The asymptotic error rate performances of three popular diversity combining techniques are compared and some insights are obtained. The impacts of various channel parameters on the asymptotic performances of these diversity combining techniques are studied comprehensively. Some previous observations on diversity performances on correlated Rician channels are unified and further extended.

Optimum selection combining using the maximum energy (OSC-ME) criterion for M-ary noncoherent frequency shift keying signaling in independent and nonidentically distributed fading channels is examined. A weighted maximum energy selection combining (WMESC) scheme is proposed and found to provide virtually the same symbol error probability as OSC-ME in Rician fading channels. The WMESC always provides power gain over the classical selection combining regardless of diversity order and signal-to-noise ratio.

It is known that the "better than" raised-cosine pulse has several advantages over the conventional raised-cosine pulse. In addition to the advantages previously reported, this letter reports that the "better than" raised-cosine pulse enables better performance of symbol timing estimation than the raised-cosine pulse. Both Cramer-Rao lower bounds and simulations of practical synchronizers show the superiority of the new pulse. The performance gain can be as much as 3.4 dB for a practical system.

A characteristic function-based method is used to derive closed-form bit error probability (BEP) expressions for orthogonal frequency-division multiplexing (OFDM) systems in the presence of channel estimation error over frequency-selective Rayleigh fading channels and frequency-selective Ricean fading channels. Both single channel reception and diversity reception with maximal ratio combining (MRC) are examined. The BEP expressions are shown to be sums of several conditional probability functions which can be calculated by using proper complex Gaussian random variable theory and a characteristic function method. The closed-form BEP expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models. The performances of two interpolation methods, a sine interpolator with Hamming windowing and a Wiener interpolator, are compared.

Pulse design is examined for multiple access ultrawideband communication systems with consideration of the transmitter pulse-shaping and the receiver filter at the same time, subject to a transmitter power constraint. It is shown that an appropriate sinc pulse not only conforms to required spectral emission constraints, but also optimizes the signal-to-noise-plus interference ratio of the ultra-wideband system when corrupted by multiple access interference. Compared with previously proposed pulse shapes, the sinc pulse proposed here achieves better error rate performance in multiple access environments without adding any implementation complexity. The design of ideal ultrawideband pulses is clarified in terms of properties of the spectral emission mask.

Three new receivers for generalized transmitted-reference ultra-wide bandwidth systems are proposed. The receivers are derived by optimally combining the channel estimates using the reference symbols, the data decisions and the data symbols. The structures are very simple. Simulation results show that they outperform previous receivers.

Multi-hop, multi-branch, and multi-branch multi- hop wireless transmission systems with nonregenerative fixed gain relays employing amplify-and-forward relaying are considered. Simple closed-form expressions for the outage and bit error probabilities of these systems are derived. It is shown that while a multi-hop transmission system does not offer diversity gain, it can perform better than a single hop system if its average individual link SNRs satisfy a certain condition. In addition, the analysis clearly shows the diversity gains achieved by multi- branch and multi-branch multi-hop systems. A design criterion is also presented which guarantees better outage and bit error performances for a multi-branch multi-hop system compared to a multi-branch system with the same number of branches.

The ergodic capacities in Rayleigh fading of various wireless relaying systems with an arbitrary number of half duplex relays are analyzed, assuming channel state information is only known at the receivers. Closed-form analytical expressions for calculation of the ergodic capacities of these systems are derived. It is shown that systems with nonregenerative fixed gain relays achieve higher ergodic capacities than the corresponding systems with nonregenerative variable gain relays. A modified fixed gain relay, which incorporates the power constraint at the relays, is proposed. It is shown that systems with modified fixed gain relays slightly outperform the corresponding systems with nonregenerative variable gain relays and fixed gain relays at small signal-to-noise ratios, but attain almost the same ergodic capacities as systems with nonregenerative variable gain relays as the signal-to-noise ratio increases. In addition, the ergodic capacity of a hybrid system with both regenerative and nonregenerative relays is studied. Systems with regenerative relays employing decode-and-forward relaying offer higher ergodic capacities than the corresponding systems with any classes of nonregenerative relays or hybrid relays.

The performances of two signal-plus-noise (S + N) selection diversity receivers employing noncoherent M-ary frequency shift keying (MFSK) in slow, flat, correlated Rayleigh and Rician fading channels are examined. The branches are assumed to be equally correlated for Rician fading. The correlation model for Rayleigh fading is more general than the equally correlated scenario and includes it as a special case. Analytical expressions are derived for the average symbol error rate (SER) and the average bit error rate (BER) of each receiver structure. Extensive Monte Carlo simulation results are presented to validate the analytical expressions. The performances of the S + N SC receivers are compared to the performance of the classical SC receiver. The effects of correlation, average fading power imbalance and diversity order on the performances of the S + N SC receivers are examined.

A new optimal pulse is derived considering both the symbol timing estimation performance and the mean squared error of intersymbol interference corrupted data recovered in timing error. The new pulse design minimizes the mean squared error of the recovered data averaged over the timing error, accounting for the fact that the distribution of the timing error is also affected by the pulse shape. The new pulse resembles the Franks' double-jump pulse, but has different slope than the Franks' double-jump pulse in the spectral rolloff region. Although the new pulse has greater mean squared error than the Franks' pulse for a fixed small timing error, it has better symbol timing estimation performance and better overall performance as measured by the Cramer Rao lower bound and by the mean square error of the recovered data accounting for both timing recovery effects and data recovery distortion, respectively. An optimal pulse that minimizes the mean squared error of intersymbol interference corrupted data recovered in the presence of fixed but arbitrary timing error is derived as an intermediate result.

In the first part of the paper, the capacity of a general multiuser code division multiple access (CDMA) jamming channel was analyzed for noncooperative and cooperative users in uplink and downlink static and Nakagami fading channels when the receiver has or lacks jammer state information. The results were applied to a unified channel model encompassing a variety of multiuser spread spectrum systems contaminated by jamming. It was found that the jammer should spread its energy evenly over all degrees of freedom in order to minimize the average capacity. In the second part of the paper, using a standard orthogonal frequency division multiplexing (OFDM) model, the performance of a coded version of a multicarrier frequency-hopping (MC-FH) CDMA system in static and Rayleigh fading jamming uplink channels is analyzed. The MC-FH system under study is a hybrid of the OFDM and frequency hopping concepts, and is also a practical example of the model developed in the first part. It is demonstrated that in the cases where the receiver knows the jammer state and the receiver lacks the jammer state, spreading and contracting the jamming power over the system bandwidth, respectively, will give rise to the worst performance for the communicators. Optimal decorrelator weights for the receiver soft outputs in different channels, valuable for practical system design, are also obtained.

The capacity of a general multiuser CDMA jamming channel is analyzed when the receiver has or lacks jammer state information. Analyses are carried out for noncooperative and cooperative users in uplink and downlink static and Nakagami fading channels. The results are applied to a versatile multiaccess channel model which is based on the time-bandwidth dimensionality and is considered for the user capacity analysis of a variety of multiuser spread spectrum systems contaminated by jamming. In this model, different users are distinguished by signatures of either direct sequence or hopping type. It is found that the jammer should spread its energy evenly over all degrees of freedom in order to minimize the average capacity. Also, the capacity behavior appears to be dominated more by knowledge of jammer state information than by the effects of fading. The capacity of downlink channels in cooperative schemes is found to be more sensitive to changes in fading severity, compared with the capacity of other kinds of channels.

The average throughput of three decode-and-forward (DF) half-duplex (DFHD) and two DF full-duplex (DFFD) rateless coded relaying schemes are studied under a peak power constraint (PPC) and an average power constraint (APC). Two of the DFHD and one of the DFFD protocols are known. One new, much simpler, DFHD protocol, and one new DFFD protocol are proposed. The fairness in comparing the protocols in terms of energy cost is formulated, and the protocols are compared to each other in a power-fair regime. The two previously proposed DFHD protocols, one of which is superior to the other under the PPC, are found to have almost the same performances when compared power-fairly. The proposed protocols are built upon opportunistic communication and power optimization such that, although inferior to their predecessors in a PPC regime, they can slightly surpass them under the APC.

A new analytical method for evaluating the bit error rate performance of a transmitted reference ultra-wide bandwidth system with an arbitrary front-end filter is derived. The method is based on expanding the received signal using the Karhunen-Loeve expansion and then evaluating the characteristic function of the receiver decision metric. This new method puts no restriction on the front-end filter type, is suitable for any arbitrary value of receiver time-bandwidth product and is highly accurate for evaluating bit error rates as small as 10-9 in both additive white Gaussian noise and fading multipath channels. The method is also extended to the case of correlated message and reference noises. The results indicate that the effect of this cross-correlation is not negligible in evaluating the bit error rate. It is found that differences in the front-end filter can lead to significant differences in the system bit error rate.

Pulse design is examined for multiple access ultra- wideband communication systems with consideration of the transmitter pulse-shaping and the receiver filter at the same time, subject to a transmitter power constraint. It is shown that an appropriate sine pulse not only conforms to required spectral emission constraints, but also optimizes the signal-to-noise-plus- interference ratio of the ultra-wideband system when corrupted by multiple access interference. Compared with previously proposed pulse shapes, the sine pulse proposed here achieves better error rate performance in multiple access environments without adding any implementation complexity. The design of ideal ultra- wideband pulses is clarified in terms of properties of the spectral emission mask.

The multivariate Rayleigh distribution is intractable, a fact which has motivated research into modeling Rayleigh fading using Markov chains. Previous work has focused on amplitude-based Markov chains, but has had limited success in accurately modeling the autocorrelation of the fading channel. A different state-space definition, one that involves both the amplitude and rate-of-change of the envelope of the fading signal is analyzed. The expanded state-space definition is used as the basis for first- and second-order Markov chain models. This expanded state-space improves upon previous models with regard to the shape of the autocorrelation.

Infinite integrals involving the products of two, three and four Gaussian Q-functions of different arguments are solved in closed-form or in single integral form with finite upper and lower limits. These solutions provide novel expressions in the error rate analyses of signals such as general rectangular quadrature amplitude modulation, differentially encoded quaternay phase shift keying and new solutions for the error rate of the repetition code. As an example, closed-form expressions for the average symbol error rates of general rectangular quadrature amplitude modulation and the repetition code are obtained for a Nakagami-m fading channel.

Statistical moments of the inter-path interference, the inter-chip interference and the intersymbol interference in a direct-sequence binary phase shift keying ultra-wide bandwidth (UWB) system are analyzed for the IEEE UWB channel models. Exact expressions for the first- and second-order moments are derived. Using these expressions, the effects of the channel model parameters and the duration of the monocycle pulse are examined. For comparison, the first- and second-order moments of the signal component are also obtained. An approximation to the probability density function of the signal component is presented, and its accuracy is verified by calculating the bit error rate of a maximal ratio combining Rake receiver.

A selective decode-and-forward relaying protocol for serial multi-hop diversity schemes, which adapts transmissions at the source and relays based on the instantaneous received signal-to-noise ratio at each relay, is developed and analyzed. Based on the proposed selective protocol, if the received signal- to-noise ratio at each relay exceeds a certain threshold, that relay combines, decodes, and re-encodes its received signals and then re-transmits. Otherwise, the source repeats its signal. It is shown that employing the proposed method significantly improves the system performance by achieving diversity order equal to the number of hops while maintaining the same maximum normalized spectral efficiency compared to a multi-hop transmission system employing a fixed decode-and-forward relaying scheme. An exact closed-form expression for calculating the outage probability of a serial multi-hop diversity scheme employing fixed decode-and-forward relaying strategy is also obtained. A rigorous mathematical analysis showing that the serial multi-hop diversity scheme offers no diversity gain is given.

The performances of non-data-aided feedback-loop symbol timing synchronization operating with the raised-cosine and the "better than" raised-cosine pulses are investigated. In terms of the jitter variance, modified Cramer-Rao bounds are compared and the individual effects of additive channel noise, self-noise, and their product on jitter variance are also investigated for the two pulses. The better than raised-cosine pulse is shown to have better synchronization performance than the conventional raised-cosine pulse. The gain is, for example, as much as 1.4 dB for excess bandwidth of 0.35 without a prefilter and is larger when the excess bandwidth is smaller or a prefilter is employed.

A new optimal pulse is derived considering both the symbol timing estimation performance and the mean squared error of intersymbol interference corrupted data recovered in timing error. The new pulse resembles the Franks' double-jump pulse, but has different slope than the Franks' double-jump pulse in the spectral rolloff region. Although the new pulse has greater mean squared error than the Franks' pulse for a fixed small timing error, it has better symbol timing estimation performance and better overall performance as measured by the Cramer Rao lower bound and by the mean square error of the recovered data accounting for both timing recovery effects and data recovery distortion, respectively. An optimal pulse that minimizes the mean squared error of intersymbol interference corrupted data recovered in the presence of fixed but arbitrary timing error is derived as an intermediate result.

Two ultra-wide bandwidth receiver structures based on a p-order metric receiver decision statistic are investigated for the detection of time-hopping ultra-wide bandwidth wireless signals in multiple access interference channels. A receiver with adaptive metric order outperforms both the conventional matched Alter and the soft-limiting ultra-wide bandwidth receiver in multiple access interference. The second new receiver with adaptive metric order and adaptive limiting threshold achieves the best known performance of any ultra-wide bandwidth receivers employing a repetition code in all operating conditions. A new Rake receiver design based on the p-order metric receiver is proposed for signal detection in multipath channels. Mathematical analysis shows that this new Rake receiver can achieve larger signal-to-interference-plus-noise ratio than the standard matched filter Rake receiver when multipath components are resolvable in UWB channels.

A novel ultra-wide bandwidth receiver structure is proposed for time-hopping ultra-wide bandwidth wireless signal detection in multiple access interference channels. In ideal free-propagation channels, the zonal receiver always meets or outperforms the conventional matched filter UWB receiver, the recently proposed soft-limiting UWB receiver and its enhanced version, the adaptive threshold soft-limiting ultra-wide bandwidth receiver. A new Rake receiver design based on the zonal receiver is proposed for signal detection in multipath channels. Simulation results and analysis show that this new Rake receiver can achieve larger signal-to-interference-plus-noise ratio than the standard matched filter Rake receiver when multipath components are resolvable in UWB channels.

Two novel receiver structures which surpass the performance of the conventional matched filter receiver are proposed for ultra-wide bandwidth multiple access communications. The proposed receiver structures are derived based on a more appropriate statistical model for the multiple access interference than the generally used Gaussian approximation. Reasons are provided for the slow convergence of a central limit theorem with regard to the multiple access interference, and the heavy tailed nature of the probability density function of the multiple access interference is also discussed.

Recent published work suggests that correlative coding can improve OFDM performance by several dB. This work, however, does not consider fully a symbol error rate performance measure for the OFDM systems. Exploiting an equivalence between correlative coding and partial-response signaling, a bit error rate performance measure is employed to assess the performance of OFDM systems using correlative coding. It is shown that although partial-response pulse-shaping or correlative coding can reduce intercarrier interference due to carrier frequency offset, they do not necessarily improve the system bit error rate performance because of the introduction of multilevel signaling with associated reduced receiver decision distance. It is observed that bit error rate performance improvement for symbol-by-symbol detection can be achieved only in some cases of large frequency offset. In the case of smaller, practical, values of frequency offset the bit error rate is increased by correlative coding or partial-response pulse-shaping.

The effect of noise on the maximum useful number of receiver antennas that can be deployed in a cochannel interference diversity system is examined. The long term signal- power-to-interference-plus-noise-power ratio (SINRP), the long term signal amplitude to the square root of interference plus noise power ratio (SAINPR), the average instantaneous signal-to- interference-plus-noise ratio (AISINR), and the average bit error rate (BER) of a maximal ratio combining (MRC) diversity system in the presence of multiple cochannel interferers and additive white Gaussian noise (AWGN) are evaluated when the desired user signal and the interfering user signals are independent, and each of them experiences correlated Ricean fading at the receiver antennas. The results show that a previous design rule which states that the performance of a fixed-size antenna array containing the maximum number of independent antennas cannot be significantly improved by adding more than one additional antenna, still applies when the interference dominates the noise. It is shown that the SINRP and SAINPR measures exhibit asymptotic limits as the number of correlated antennas increases. Simple expressions for these limits are derived and it is shown that these asymptotic limits are unchanged when noise is neglected.

The performance ofM-ary frequency shift keying (MFSK) with dual-branch postdetection switch-and-stay combining (SSC) in correlated Rayleigh and Rician fading is studied. Closed-form expressions are derived for the average bit error rate (BER) of MFSK with postdetection SSC in correlated Rayleigh and Rician fading. Optimum switching thresholds that minimize the average BER are obtained. Extensive Monte Carlo simulations are presented to test the validity of the analytical results. The performance of MFSK with dual-branch postdetection SSC is compared to the performance of MFSK with dual-branch predetection SSC. The effects of correlation, fading parameter, fading power imbalance and switching threshold on the relative performance of the postdetection SSC compared to predetection SSC are examined.

User cooperation protocols, where mobile stations relay signals to the final destination, have been proposed for wireless networks. A general mathematical probability model is developed to study the performance of the decode-and-forward relaying protocol. Practical systems may employ relay channels that experience statistically different signal fadings. The performance of decode-and-forward relaying in channels with dissimilar fading parameters is investigated. In particular, closed-form expressions for the outage and error probabilities of a system with an arbitrary number of relays are derived.

A three stage network protocol that can achieve coded and cooperative diversity to improve network coverage is investigated. In Stage 1, a cyclic redundancy check code is used to detect erroneous packets. Binary repetition codes and single parity check product codes are used in Stage 2 to achieve forward diversity. The transmitter powers for binary repetition codes are optimized to improve the packet error rate. "N" Node cooperation in Stage 3 is implemented using random single parity check codes distributed across the nodes. The network coverage is shown to be improved in all three stages. The cooperation gains are found to be strongly dependent on the particular network realization and less on the number of cooperating nodes.

The sampling expansion approach for computing the performance of TR UWB systems has restricted validity and is very inaccurate in some cases. A new analytical method to evaluate the BER performance of a TR UWB system is derived. The method is based on expanding the received signal using the Karhunen-Loeve expansion and then evaluating the characteristic function of the receiver decision metric. This new method puts no restriction on the front-end filter type and is accurate for any arbitrary value of receiver time-bandwidth product. The analytical results are validated with simulation results, and it is found that the method is highly accurate and can evaluate BER rates down to 10-9.

The detection of a binary phase-shift keying signal distorted by like-modulated cochannel interference and noise using a noise-plus-interference whitening matched filter (WMF) is considered. The interfering signals are assumed to be independent and Rayleigh-faded. It is shown that in a synchronous channel, the signal-to-interference-plus-noise ratio (SINR) at the output of a WMF can not exceed that of the conventional matched filter (CMF) receiver. It is observed that in a synchronous channel, an interference WMF degrades the performance both through decreasing the SINR and introducing intersymbol interference (ISI). In contrast, in an asynchronous channel an optimal WMF can improve the SINR relative to the CMF receiver. It is shown that for a standard raised-cosine pulse the maximum achievable SINR gain over the CMF receiver is 1.76 dB. The SINR of the WMF receiver in asynchronous CCI is also evaluated for the case when a linear equalizer is used to mitigate the ISI caused by the WMF.

This paper provides a power-margin-based measure of the quality of computer-generated random variates having a distribution that derives from the multivariate Gaussian distribution. The measure is designed to be simple to compute, and to provide assessments which are meaningful and intuitive in communication system simulation applications. For example, the measure can be used to assess and compare the qualities of different methods of generating Rayleigh fading samples for simulation.

An exact and closed-form expression for the average bit error rate (BER) of coherent binary phase-shift keying (BPSK) using maximal ratio combining (MRC) in the presence of multiple cochannel interfering users is derived for correlated Rayleigh fading. Under the assumption that the branch gains of the desired user signal and interfering signals experience correlated Rayleigh fading with the same correlation eigenvector matrix, as is the case for receiver diversity in an omnidirectional scattering environment, this BER expression is valid for arbitrary correlation structure such as 2-D and 3-D channel correlation models, and applys for an arbitrary number of interfering users and an arbitrary number of receiver antennas.

The performances of two signal-plus-noise (S + N) selection diversity receivers employing M-ary noncoherent frequency shift keying (NCFSK) in slow, flat, correlated Rayleigh fading channels are examined. The correlation model is more general than the equally correlated scenario and includes it as a special case. Analytical expressions are derived for the average symbol error rate (SER) and the average bit error rate (BER) of each receiver structure. Extensive Monte Carlo simulation results are presented to validate the analytical expressions. The performances of the S + N SC receivers are compared to the performance of the classical SC receiver. The effects of correlation, average fading power imbalance and diversity order on the performances of the S + N SC receivers are examined.

It is known that the "better than" raised-cosine pulse has several advantages over the conventional raised-cosine pulse. In addition to the advantages previously reported, this paper reports that the "better than" raised-cosine pulse enables better performance of symbol timing estimation than the raised- cosine pulse. Both Cramer-Rao lower bounds and simulations of practical synchronizers show the superiority of the new pulse. The performance gain can be as much as 3.4 dB for a practical system.

Cyclic shifts of the binary codewords in multiple dimensions are used to construct a novel class of multidimensional binary block repetition codes. This construction is well suited as an inner encoding scheme for concatenated one-dimensional outer codewords to increase their minimum Hamming distance without increasing the transmission bandwidth. Two design criteria for multidimensional binary repetition codes are given, and an efficient algorithm to search for good codes is presented. The construction is illustrated using examples of the proposed codes in two and three dimensions. The union bound on the bit-error rate is used to optimize the transmission energy distribution over the codewords to improve the transmission reliability.

The capacity of a general multiuser CDMA jamming channel is analyzed when the receiver has or lacks jammer state information. Analyses are carried out for noncooperative and cooperative users in uplink and downlink static and Nakagami fading channels. The results are applied to a versatile multiple access channel model introduced in Nikjah and Beaulieu (2006). The model is based on the time-bandwidth dimensionality and is considered for the user capacity analysis of a variety of multiuser spread spectrum systems contaminated by jamming. It is found that the jammer should spread its energy evenly over all degrees of freedom in order to minimize the average capacity. Also, the capacity behavior appears to be dominated more by knowledge of jammer state information than by the effects of fading. The capacity of downlink channels in cooperative schemes is found to be more sensitive to changes in fading severity, compared with the capacity of other kinds of channels.

It is proved that the intercarrier interference matrix in orthogonal frequency division multiplexing systems is unitary for an arbitrary value of frequency offset and any number of subcarriers. The benefit of a recently published precoding scheme in practical applications is thereby established.

A precise analysis is derived for calculating the bit error probability of a direct-sequence ultra-wideband system accounting for the multiuser interference on additive white Gaussian noise (non-frequency selective) channels. The exact solution is validated by simulation and used to determine the accuracy of a recently published approximation based on a simplified receiver decision statistic, as well as to assess the inaccuracy of the Gaussian approximation. It is established that the Gaussian approximation may only be accurate for an impractically large number of simultaneous users.

Optimum detectors for pilot symbol assisted modulation (PSAM) signals in Rayleigh and Rician fading channels are derived. Conventional PSAM as used on Rayleigh fading channels is also employed on Rician fading channels. It is shown that the conventional PSAM receiver is optimal for binary phase shift keying in Rayleigh fading but suboptimal for Rician fading and suboptimal for 16-ary quadrature amplitude modulation in Rayleigh fading. The optimum PSAM signal detector uses knowledge of the specular component and also jointly processes the pilot symbols and the data symbol. The performance of the optimum detector is analyzed and compared with that of the conventional detector. It is concluded that substantial gains can be achieved by exploiting knowledge of the specular component while joint processing of the data symbol with the pilot symbols may offer small benefits.

The bit error rate of a binary phase shift keying (BPSK) signal in Ricean-faded cochannel interference is studied. A precise bit error rate expression is derived for a bandlimited BPSK signal corrupted by an arbitrary number of asynchronous Ricean-faded interfering signals. An error rate estimation based on a saddlepoint approximation is also provided. It is shown that this approximation is highly accurate. For the special case, when there is one synchronous Ricean-faded interfering signal in an interference-limited environment, an asymptotic error rate analysis based on the saddle point approximation reveals that fading in the cochannel interfering signal can have different impacts on the desired user's error rate performance. Our study shows that when the signal-to-interference ratio (SIR) is sufficiently large, the error floor of the desired user signal decreases with an increase of the Rice factor in the interfering user's fading channel. However, the opposite phenomenon can happen when the SIR is small.

The performance of binary frequency-shift keying (BFSK) and M-ary frequency shift keying (MFSK) with dual-branch postdetection switch-and-stay combining (SSC) in correlated Rayleigh and Rician fading is studied. Two postdetection SSC receivers are considered and the performances of noncoherent BFSK and MFSK are analyzed. Closed-form expressions are derived for the average bit-error rate (BER) of BFSK and MFSK with postdetection SSC in correlated Rayleigh and Rician fading. Optimum switching thresholds that minimize the average BER are obtained. Extensive Monte Carlo simulations are presented to test the validity of the analytical results. The performance of dual-branch postdetection SSC is compared with the performance of dual-branch predetection SSC. The effects of correlation, fading parameter, average fading power imbalance, and switching threshold on the performances of postdetection SSC receivers are examined

An analytical expression for the bit-error rate (BER) of an individually optimal receiver in a two-user synchronous channel is derived. The desired signal is a binary phase-shift keying (BPSK) signal corrupted by a like-modulated interference and additive white Gaussian noise (AWGN). The BER expression decomposes into the probability of error of BPSK in AWGN plus an interference term which tends to zero when either the interferer power or the interferer signal correlation with the desired signal approaches zero

Precise outage probability performance analysis of a micro- cellular system with selection and switched diversities is considered. The micro-cellular system is assumed to follow a flat slow Nakgami/Raleigh fading model wherein the fading channels from the desired transmitter to all the receiver antennas are independent and identically distributed Nakagami channels, and all the fading channels for the interfering signals are independent, identically distributed Rayleigh channels. Three selection and switching criteria, namely, desired signal power, signal-to-interference power ratio and total output power are considered. Unlike previous results, the system model under investigation takes into account the pulse shaping and the random delays and phase offsets of the interfering users. Two Nyquist pulse shapes, spectrum-raised-cosine and Beaulieu–Tan–Damen pulse shapes are considered. Analytical outage probability expressions derived for an arbitrary number of interferers, arbitrary diversity order and arbitrary value of desired user fading parameter. The outage performance of the selection criteria are compared. The optimum switching thresholds for different switching criteria are formulated.

Precise outage probability performance analysis of a microcellular system with selection and switched diversities is considered. The microcellular system is assumed to follow a flat, slow Nakagami/Rayleigh fading model wherein the fading channels from the desired transmitter to all the receiver antennas are independent and identically distributed Nakagami channels, and all the fading channels for the interfering signals are independent, identically distributed Rayleigh channels. Three selection and switching criteria, namely, desired signal power, signal-to-interference power ratio, and total output power are considered. Unlike previous results, the system model under investigation takes into account the pulse shaping, the random delays, and the phase offsets of the interfering users. Two Nyquist pulse shapes, spectrum-raised-cosine and Beaulieu-Tan-Damen pulse shapes, are considered. Analytical outage probability expressions are derived for an arbitrary number of interferers, arbitrary diversity order, and arbitrary value of desired user fading parameter. The outage performances of the selection criteria are compared. The optimum switching thresholds for different switching criteria are formulated.

An exact closed-form expression for the average bit error rate (BER) of coherent BPSK using maximal ratio combining (MRC) with correlated branches in the presence of cochannel interference (CCI) and noise is derived. This expression is valid for an arbitrary correlation structure under the assumption that the branch gains of the desired user signal and interfering signals experience correlated Rayleigh fading with the same correlation eigenvector matrix.

The symbol-error rate (SER) of a quadrature subbranch hybrid selection/maximal-ratio combining (QBHS/MRC) scheme for 1-D modulations in Rayleigh fading is examined. At the receiver, N diversity branches are split into 2N in-phase and quadrature subbranches. Traditional hybrid selection/maximal-ratio combining (H-S/MRC) is then applied over the 2N subbranches. M-ary pulse amplitude modulation, including coherent binary phase-shift keying, with QBHS/MRC is studied. The SER performances of QBHS/MRC and H-S/MRC are compared. Results show that QBHS/MRC systems outperform traditional H-S/MRC systems

The outage probability of maximal ratio combining diversity with an arbitrary number of antennas in the presence of an arbitrary number of cochannel interferers and thermal noise is derived when the branch gains of the desired user signal and interfering signals experience Rayleigh fading and have the same correlation matrix. Two special cases, when the correlation matrix is equicorrelated and when the correlation matrix has different eigenvalues, are considered for both the equal-power cochannel interference case and the unequal-power cochannel interference case. Further, the average bit-error rate of a coherent binary phase-shift keying (BPSK)-modulated cellular system using maximal ratio combining diversity in cochannel interference and correlated Rayleigh fading is derived. The effects of the average signal-to-noise ratio (SNR) and the average signal-power-to-interference-power ratio on the system performance are examined.

A maximum a posteriori (MAP) estimator for the Nakagami m parameter in an ultra-wide bandwidth (UWB) indoor channel is proposed. Previous work exclusively studies maximum likelihood (ML) estimation and moment method (MM) estimation of the Nakagami m parameter. This letter derives the MAP estimator for the Nakagami m parameter by using the a priori probabilities of the Nakagami fading parameters in an indoor UWB channel. The performance of the MAP estimator is examined and compared with those of the ML estimator and the MM estimator. Numerical results demonstrate that the new MAP estimator is superior to the ML estimator and the MM estimator in an indoor UWB channel, especially when the sample size in the estimation is small

An exact bit error rate (BER) expression for an OFDM system with windowing reception is derived. The effects of several Nyquist windows, including the raised-cosine window, the "better than" raised-cosine (BTRC) window, the second order continuity window (SOCW), the Franks window, and the double-jump window on the performance of the system are examined based on both BER measure and signal-to-interference (SIR) measure. It is found that the SIR comparison is not necessarily consistent with the BER comparison. The BTRC windowing gives the smallest BER among the five windowing functions considered for small to medium values of pulse roll-off factor. However, the Franks windowing or SOCW windowing shows better BER performance when the roll-off factor approaches one

The problem of estimating two measures of signal-to-noise ratio (SNR) is investigated, both for static and slowly fading channels without memory. Maximum likelihood SNR estimators that use digitally modulated signals are derived for sampled signal processing receivers as well as continuous time signal processing receivers. The performances of the estimators are examined analytically in terms of biases and root-mean-squared errors. Numerical results are presented to show their good performances

The problem of estimating the K parameter and the local average signal-to-noise ratio in a noisy Ricean fading channel is studied. Unlike most previous estimators where independent channel samples are assumed, in this paper, novel estimators that assume correlated channel samples are proposed. Both data-aided and non-data-aided designs are considered. The performances of the new estimators are examined. Several design issues are discussed. Numerical results are presented to show their good performances in a realistic Ricean fading channel

The problem of estimating the signal-to-noise ratio for time-hopping binary pulse position modulated signals, time- hopping binary phase shift keying signals, and direct-sequence binary phase shift keying signals in an ultra-wide bandwidth (UWB) system is studied. Both an additive white Gaussian noise channel and a multipath fading channel are considered. Several new estimators are derived by making use of different properties of the UWB signals. The performances of the estimators are examined and compared in terms of their root-mean-squared errors. Numerical results show that they have excellent performances when operating in an ultra-wide bandwidth system.

The performance of dual-branch predetection switch-and-stay combining (SSC) in correlated Rician fading is considered in conjunction with several modulation formats. Analytical expressions are derived for the average symbol error rate (SER) of predetection SSC in correlated Rician fading. Switching thresholds that minimize the average SER are obtained. The impact of fading factor and the fading correlation on the performance of predetection SSC is studied. Analytical expressions for the output average signal-to-noise ratio (SNR) and the outage probability are derived. The validity of the analytical expressions are verified using Monte Carlo simulation.

An exact expression for the bit error rate of a synchronous maximum-likelihood receiver used to detect a bandlimited binary phase-shift keying (BPSK) signal in the presence of a similar BPSK signal, additive white Gaussian noise and imperfect carrier phase recovery is derived. The users are assumed to employ pulse-shaping filters whose impulse responses satisfy Nyquist's first criterion. The receiver's error probability is compared with that of the perfect phase recovery case to show its sensitivity to carrier phase errors. It is shown that the receiver is more robust to carrier phase mismatch at high signal-to-interference ratios (SIR's) than low SIR's

An exact closed-form bit error rate (BER) expression is derived for an orthogonal frequency-division multiplexing system with π/4-shifted differentially encoded quadrature phase shift keying (π/4-DQPSK) in the presence of carrier frequency offset over frequency-selective fast Rayleigh fading channels. Different system configurations, including time domain differential modulation, frequency domain differential modulation, single channel reception, and multi-channel reception with maximal ratio combining diversity, are considered in the exact BER analysis. For a small number of subcarriers, the BER expression can be calculated directly. A Monte Carlo method is designed to evaluate the BER for a large number of subcarriers. The analytical expression can be used to investigate the effect of several channel parameters, including mean delay spread and maximum Doppler spread, on the system BER performance. Particularly, the effect of carrier frequency offset on the system performance, and the differences and opportunities to use frequency domain differential modulation or time domain differential modulation, can be studied in a quantitative way for a more realistic wireless channel environment model. By using the exact closed-form BER expression, an optimum number of subcarriers can be found, and the allowable carrier frequency offset, Doppler spread, and mean delay spread for given operating conditions can be determined.

No closed-form expression is known for the lognormal characteristic function. Computation of the characteristic function using numerical integration is time consuming and often converges poorly. Alternative published numerical methods for its evaluation are complex and often valid only for particular values of the dB-spread. A novel definite integral form of the lognormal characteristic function is derived. This form lends itself to rapid and convenient computation of the lognormal characteristic function using simple, common methods of numerical integration.

The question of how many receiver antennas to employ in a diversity system operating in cochannel interference is examined. The long term signal-power-to-interference-power ratio, the long term signal amplitude to the square root of the interference power ratio, the average instantaneous signal-to- interference ratio, and the average bit error rate of a maximal ratio combining diversity system in the presence of an arbitrary number of cochannel interferers are evaluated when the desired user signal and the interfering user signals experience correlated Ricean fading. The best number of antennas required for a fixed-size antenna array to achieve a good compromise between the system performance and system cost is investigated. The results show that, in general, the performance of a fixed-size antenna array containing the maximum number of independent antennas can not be significantly improved by adding more than one additional antenna. Some special cases where particular gains can be achieved by adding additional correlated antennas are also discusssed.

Signal-to-noise ratio estimators for binary phase shift keying signals in ultra-wide bandwidth (UWB) systems are proposed. Both time-hopping UWB systems and direct-sequence UWB systems are considered. Several new estimators are derived by making use of different properties of the UWB signals. The performances of the estimators are examined and compared in terms of their root-mean-squared error. Numerical results show that they have excellent performances when operating in an ultra- wide bandwidth system.

An analytical approach to study the effects of node mobility in mobile ad hoc wireless networks is presented. The bit error rate is evaluated over fast Rician fading channels. It is shown that there is a threshold node velocity, and that a network with a certain number of mobile nodes (following the random waypoint mobility scheme) with slower velocities than the threshold velocity performs better than the corresponding network with static nodes. In particular, for a given signal- to-noise ratio and transmission range, the minimum threshold velocity is obtained. Restricting the velocities of the nodes to be at most this minimum threshold velocity results in an improvement in the bit error rate performance of ad hoc networks with an arbitrary number of nodes.

A family of linear binary block codes is constructed from ordinary block repetition codes using cyclic shifts of the input information vector which greatly simplifies encoding. These codes have variable block length and variable minimum Hamming distance. Several sets of cyclic shifts are defined to constrain the search for good codes. Codeword enumeration strategies are discussed. The proposed codes are shown to be good candidates for adaptive coding, turbo product coding, retransmission schemes and multihop routing, and block differential encoding. A generic parallel encoder structure well suited to OFDM systems, and a non-recursive block differential encoder capable of arbitrarily increasing the code rate with the block length, for given minimum Hamming distance, are proposed. Numerical examples compare the bit-error rate assuming iterative soft- decision decoding and the union bound.

It is shown that regenerative relaying in a dual- hop diversity static or quasi-static relay channel can outperform non-regenerative relaying only if the source-relay link is reliable and power allocation to the source and the relay is optimized. In regenerative relaying, a maximal ratio combining receiver at the destination has an error floor at high signal-to-noise ratios. However, maximal ratio combining is not a maximum-likelihood structure in this application. Maximum-likelihood detection at the destination can remove this error floor, but cannot always make the performance of regenerative relaying surpass that of non- regenerative relaying. A hybrid protocol which avoids some of the limitations of previous relaying schemes is proposed. Conditions under which relaying increases the equivalent source-destination signal-to-noise ratio, and hence, the source-destination channel capacity are derived and the gain of the cooperation is calculated. The analysis provides quantitative measures for choosing the best relay among a set of candidates.

An integrated cross-noise component frequently arises in communications and in signal processing. One typical example in communication is the autocorrelation receiver. Integrated cross-noise generally appears when a noisy signal is recovered (detected) using correlation techniques with a noisy signal as the reference. The statistics of the integrated cross- noise component are analyzed in general for both the cases of uncorrelated and correlated noise terms in the integrand. The statistics are characterized theoretically by an approximate probability density function. This theoretical probability density function is verified by simulation and its convergence towards a Gaussian distribution is discussed.

The outage probability and the average bit error rate of a coherent binary phase-shift keying modulated cellular system using maximal ratio combining diversity with an arbitrary number of antennas in the presence of an arbitrary number of cochannel interferers and thermal noise are derived when the branch gains of the desired user signal and the interfering signals experience Rayleigh fading and have the same correlation matrix. Two special cases, when the correlation matrix is equi-correlated and when the correlation matrix has different eigenvalues, are considered for both the equal-power cochannel interference case and the unequal-power cochannel interference case. The effects of the average signal-to-noise ratio, the average signal-to- interference ratio, and the correlation between antennas on the system performances are examined.

To enable closed-loop operation of high-mobility systems, reliable channel prediction is needed to prevent the obsolescence of channel information due to feedback and processing delays. In this paper, novel linear pilot symbol-aided techniques are proposed for block-adaptive prediction of flat time-selective Rayleigh fading channels. Unlike many previous investigations, which assume that the fading statistics are known, we focus on practical conditions where prediction must take place over short noisy windows of unknown channels. Significant performance gains are observed when the method is applied, for example, to a selection transmitter diversity system operating in a fast fading environment.

The performance of the selection diversity combiner is studied. Unlike most previous works where perfect knowledge of the signal amplitude and the noise power is assumed, in this analysis, knowledge of the signal amplitude and the noise power is obtained by using practical estimators that introduce estimation errors. The average symbol error rate of the combiner is derived for non-coherent M-ary frequency shift keying signals, independent and non-identically distributed diversity branches and unequal noise powers. The effect of estimation errors on the performance of the combiner is evaluated and illustrated by numerical examples. An interesting and useful conclusion is that it is disadvantageous to employ signal-to-noise ratio as a branch selection criterion when the branch noise powers are known a priori to be equal.

A maximum a posteriori (MAP) estimator for the Nakagami m parameter in an ultra-wide bandwidth (UWB) indoor channel is proposed. Previous work exclusively studies maximum likelihood (ML) estimation and moment method (MM) estimation of the Nakagami m parameter. This paper derives the MAP estimator for the Nakagami m parameter by using the a priori probabilities of the Nakgami fading parameters in an indoor UWB channel. The performance of the MAP estimator is examined and compared with those of the ML estimator and the MM estimator. Numerical results demonstrate that the new MAP estimator is superior to the ML estimator and the MM estimator in an indoor UWB channel, especially when the sample size in the estimation is small.

The problem of estimating the K parameter and the local average signal-to-noise ratio in a noisy Ricean fading channel is studied. Unlike previous estimators where independent or noiseless channel samples are assumed, in this paper, novel estimators are designed to operate with noisy correlated channel samples. Both data-aided and non-data-aided designs are considered. The performances of the new estimators are examined in detail. Numerical results are presented to show their good performances in a realistic Ricean fading channel.

An asymptotic error rate performance analysis has been reported recently for maximum ratio combining on correlated Rician channels; however, a similar approach cannot be applied to equal gain combining or selection combining. A novel approach is introduced to analyze the asymptotic error rate performances of equal gain combining and selection combining on dual-branch correlated Rician channels. The asymptotic error rate performances of popular diversity combining techniques are compared and some insights are obtained that explain some behaviors previously considered unexpected. The impacts of various channel parameters on the asymptotic performances of these diversity combining techniques are studied comprehensively. Some previous observations on diversity performances on correlated Rician channels are unified and further extended.

We present new closed-form analytical expressions for the probability of connectivity and average delay of a mobile ad hoc network with N nodes which move according to the random waypoint (RWP) mobility model. The minimum transmission range for which the network is connected is also derived. Our results show that by increasing the number of nodes, the probability of connectivity increases and the minimum transmission range decreases. It is also shown that the average delay is maximum for the minimum transmission range and this maximum increases by increasing the number of users. In transmission ranges for which the networks are disconnected, increasing the number of users increases the average delay; however, this is reversed when the networks are connected. Particularly, our results show that mobility contributes to the network connectivity, but at the expense of tolerating more average delay when the networks are disconnected. However, mobility decreases the average delay in the connected regions.

We study the exact bit error rate (BER) performance of convolutional codes with hard decision Viterbi decoding when used over fading additive white Gaussian noise (AWGN) channels with maximum ratio combining (MRC) diversity. Analytical expressions for the bit error rates in Rayleigh, Rician and Nakagami-m fading channels are derived. The accuracy of the analytical results is verified by computer simulation.

The performance of binary frequency-shift keying (BFSK) with dual-branch postdetection switch and stay combining (SSC) in correlated Rayleigh fading is considered. A closedform expression for the average bit error rate (BER) of BFSK with dual-branch postdetection SSC is derived. Optimum switching thresholds that minimize the average BER are obtained. It is shown that, for a fixed value of average signal-to-noise ratio (SNR), the optimum switching threshold is a decreasing function of branch correlation. Our analytical results are validated using Monte Carlo simulation results. The performance of dual-branch postdetection SSC is compared to the performance of dual-branch predetection SSC in correlated Rayleigh fading and it is shown that postdetection SSC has superior performance over predetection SSC for all values of SNR.

In this paper, accurate closed-form approximations for the distribution and density of a sum of Nakagami random variables are presented. The proposed approximations are then used to analyze the probability of error of a L-branch predetection equal gain combiner with different fading parameters. Coherent and noncoherent binary signaling as well as coherent M-ary signaling are considered. In addition, a closed-form expression for the outage probability of these systems is derived. These closed-form expressions permit rapid evaluation of the performance of equal gain combining diversity systems without resorting to numerical integration as required by previous solutions.

A precise bit-error probability analysis method for multicode DS-CDMA systems in Rayleigh fading is derived. The proposed method applies to a multicode DS-CDMA system with an arbitrary number of multiple code sequences and any selection of multiple code sequences. The method gives accurate results for Rayleigh fading while requiring only a single numerical integration of an integrand involving the well-known Q-function. The solution discriminates the effect of the selection of different multiple code sequences on the bit-error probability, whereas Gaussian approximations do not. The numerical examples show that the differences between methods for a multicode DS-CDMA system operating over Rayleigh fading channels may be more significant than for a single code system in Rayleigh fading channels or a multicode system in AWGN channels when the spreading factor is not large compared to the number of multiple code sequences.

Analytical results for the symbol error rate (SER) of M-ary phase shift keying (MPSK) in a slow, flat Rayleigh fading channel for a multiple-input multiple-output (MIMO) system using an Alamouti transmission scheme and generalized selection combining (GSC) scheme are given. Two new receiver selection schemes, generalized space-time sum-of-squares (GSTSoS) selection diversity and generalized space-time magnitude (GSTSoM) selection diversity are proposed. They are proved to provide almost the same performance as conventional GSC, but with much simpler implementations. The SER of MPSK in Rayleigh fading using these two selection schemes is studied and compared to that of conventional GSC. The effects of channel estimation errors on each selection scheme are examined.

A unified multiple access channel model based on the time-bandwidth dimensionality is considered for the user capacity analysis of a wide variety of multiuser spread spectrum systems contaminated by smart jamming. Different users are distinguished by signatures of either direct sequence or hopping type. It is found that the jammer should spread its energy evenly over all degrees of freedom in order to minimize the average capacity or maximize the outage probability. Also, for the communicator to best make use of the channel resources, it is necessary to avoid hopping type signatures. As a practical realization, we consider the performance analysis of a synchronous frequently cited multicarrier frequency hopping CDMA system in AWGN and Rayleigh fading jammed uplink channels. We show that the best counter-jamming performance is attained when the number of subcarriers is maximal. It is demonstrated that when the receiver does not know the jammer state, concentrating instead of spreading the jamming power over the channel degrees of freedom will give rise to the worst performance for the communicators. Optimal weights for the receiver soft outputs in different channels are also obtained, for practical purposes.

An exact expression for the bit error probability of a maximum-likelihood receiver used to detect two bandlimited binary phase-shift keying signals in a synchronous additive white Gaussian noise channel in the presence of carrier phase recovery errors is derived. The users employ pulse-shaping filters whose impulse responses satisfy Nyquist's first criterion for zero intersymbol interference. The receiver's error probability is compared with that of the perfect phase recovery case for various values of signal-to-interference ratio (SIR) to show its sensitivity to carrier phase errors. It is shown that the receiver is more robust to carrier phase mismatch at large values of SIR than at small values of SIR.

A characteristic function-based method is used to derive closed-form bit error probability (BEP) expressions for orthogonal frequency-division multiplexing (OFDM) systems in the presence of channel estimation error over frequency-selective Rayleigh fading channels and frequency-selective Ricean fading channels. Both single channel reception and diversity reception with maximal ratio combining (MRC) are examined. The BEP expressions are shown to sums of several conditional probability functions which can be calculated by using proper complex Gaussian random variable theory and a characteristic function method. The closed-form BEP expressions can be used to accurately investigate the bit error rate performance degradation caused by channel estimation error under different wireless channel environment models. The performances of two interpolation methods, a sinc interpolator with Hamming windowing and a Wiener interpolator, are compared.

The exact performance of selection combining (SC), hybrid selection/maximal-ratio combining (H-S/MRC), and threshold-based hybrid selection/maximal-ratio combining (T-HS/MRC) in correlated Nakagami-m fading for positive integer values of fading parameter m, is analyzed for a particular correlation structure. This correlation model though not general, is much more general than the equal correlation case and includes equal correlation as a special case. The symbol error rate and outage probability of the three schemes are obtained by transforming the correlated branch gains into a set of conditionally independent branch gains. Numerical and simulation results show excellent agreement with theoretical results.

One- and two-dimensional ad hoc wireless networks with uniformly distributed (static) nodes and networks with nodes which move according to the random waypoint mobility model are considered. The inter-distance distributions between any two nodes within these networks are obtained. The network connectivity is considered and the minimum transmission range is derived. The bit error rate performance is then analytically evaluated in the connected regions of the networks taking into account the effect of path loss and Nakagami-mor Rician fading. It is shown that increasing the number of users increases the network connectivity, decreases the minimum transmission range, and improves the performance. It is also shown that node mobility enhances the network connectivity and performance.

The performance of dual-diversity predetection switch-and-stay combining (SSC) in correlated Rician fading is considered in conjunction with several modulation formats. Analytical expressions are derived for the average symbol error rate (SER) of predetection SSC in correlated Rician fading. Switching thresholds that minimize the average SER are obtained. The impacts of fading parameter and the fading correlation on the performance of predetection SSC are studied. Analytical expressions for the output average signal-to-noise ratio (SNR) and the outage probability are derived. The validity of our analytical expressions are verified using Monte Carlo simulations.

A new ultra-wide bandwidth communication system using both a time-hopping sequence and a direct spreading sequence, called direct-sequence impulse radio, has recently been proposed. The performance of this new scheme in multi-user interference is investigated. A precise expression for calculating the bit error probability of direct-sequence impulse radio is derived. Our precise analysis indicates that the Gaussian approximation substantially overestimates the performance at large values of signal-to-noise power ratio. Ultra-wideband communication systems employing time-hopping, direct-sequence and the newly proposed direct-sequence impulse radio schemes operating in multi-user interference are accurately compared in terms of the bit error rate. Our results indicate that direct-sequence impulse radio outperforms the time-hopping binary phase-shift keying system. However, its performance is poorer than the performance of conventional direct sequence binary phase-shift keying systems

Two new receiver selection schemes, space-time sum-of-squares (STSoS) selection diversity and space-time magnitude (STSoM) selection diversity, are proposed for a MIMO system using the Alamouti space-time block code (STBC) at the transmitter in a slow, flat Rayleigh fading channel. They are proved to provide almost the same performance as signal-to-noise ratio (SNR) selection, but with much simpler implementations. The bit error rate (BER) of binary phase-shift-keying (BPSK) in Rayleigh fading using these two selection schemes is studied and compared to that of previous selection schemes. The effects of channel estimation errors on each selection scheme are examined

The average symbol error rate of threshold-based hybrid selection/maximal-ratio combining (T-HS/MRC) with correlated Nakagami-m fading channels is obtained for positive integer values of fading parameter m for a special correlation structure. An accurate approximate analysis of T-HS/MRC in arbitrarily correlated Nakagami-m fading channels is presented by using a Green's matrix approximation. The derivation allows different M-ary linear modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example

An accurate approximation to the average symbol error rate of hybrid selection/maximal-ratio combining (H-S/MRC) in correlated Nakagami-m fading with positive integer values of m, is obtained by using a Green's matrix approximation. This approach is valid for different M-ary linear modulation schemes. We illustrate our methodology using M-ary phase-shift keying (MPSK) as an example

A useful integral, representing the average over Rayleigh fading of the product of two Gaussian Q-functions, is solved in closed-form. A closed-form solution for the symbol-error probability of general rectangular quadrature amplitude modulation in Rayleigh fading is derived.

Accurate average bit-error rate analysis of asynchronous bandlimited binary direct-sequence code-division multiple-access (DS-CDMA) systems in Nakagami-m fading is studied. The fading is assumed to be flat and slow. The spectrum raised-cosine (SRC) and Beaulieu-Tan-Damen (BTD) pulse-shapes are employed. A new method which combines the characteristic function (CF) method with the improved Gaussian approximation (GA) is proposed for evaluating the BER of bandlimited DS-CDMA. A substantial computational complexity reduction is achieved. The well-known standard GA, Holtzman's simplified improved GA, and improved Holtzman's GA methods are also considered. The accuracies of the approximation methods are assessed using Monte Carlo simulation. For a system employing a deterministic sequence for the desired user and random sequences for the active interfering users, a CF method is employed to derive precise BER results. The new BTD pulse outperforms the SRC pulse in all situations

Time variation on fading channels hinders accurate channel estimation in differential space-time modulation and deteriorates the performance. Decision-feedback differential detection is studied for block differential space-time modulation, and compared with conventional differential space-time modulation. It is observed that the proposed scheme does not suffer effective fading bandwidth expansion, as does the conventional scheme. An improved effective signal-to-noise ratio approach is proposed for analyzing the performance of the proposed scheme in time-varying flat Rayleigh fading. Theoretical analysis and simulations show the improved performance of the proposed scheme over the conventional scheme.

Error rates of orthogonal frequency-division multiplexing (OFDM) signals in multipath slow fading Nakagami-m fading channels are considered. The exact probability density function of a sum of Nakagami-m random phase vectors is used to derive a closed-form expression for the error rates of OFDM signals. The precise error-rate analysis is extended to a system using multichannel reception with maximal ratio combining. An asymptotic error-rate analysis is also provided. For a two-tap channel with finite values of Nakagami-m fading parameters, our analysis and numerical results show that the asymptotic error-rate performance of an OFDM signal is similar to that of a single carrier signal transmitted over a Rayleigh fading channel. On the other hand, our analysis further shows that a frequency-selective channel that can be represented by two constant taps has similar asymptotic error-rate performance to that of a one-sided Gaussian fading channel. It is observed that, depending on the number of channel taps, the error-rate performance does not necessarily improve with increasing Nakagami-m fading parameters.

The performances of general M-ary and binary orthogonal noncoherent frequency-shift keying signal-plus-noise (S+N) receiver structures in slow, flat Rician fading channels are examined. The fading on the diversity branches is assumed to be independent, but not necessarily identically distributed. For each receiver, a symbol-error probability expression is derived as a single integral with finite integration limits. Extensive Monte Carlo simulation results are presented to validate the analytical expressions. The results indicate that, unlike previously published results, the performance of S+N selection combining (SC) is not always superior to that of classical SC in fading and is dependent on the value of the signal-to-noise ratio (SNR), the modulation order, the diversity order, the multipath intensity profile, and the fading parameter. It is further shown that increasing the number of diversity branches in a S+N SC receiver does not necessarily decrease the probability of error if the system is operating in the low-SNR region. The performances of S+N SC schemes are also compared with the performances of equal-gain combining and square-law combining receivers.

The performances of dual-branch postdetection switch-and-stay combining (SSC) for noncoherent orthogonal binary frequency-shift keying and noncoherent orthogonal M-ary frequency-shift keying operating over slow, flat Rician fading channels are a topic of current interest. It is shown that recently published analyses obtain incorrect final results because some incorrect probability distribution parameters are used in the analyses. The previous results are corrected, and it is seen that the final results change significantly. The revised results are used to obtain optimum switching thresholds that minimize the average bit-error rate (BER) performance of these systems. Monte Carlo simulations are presented to verify the results, and it is shown that for a given BER, the signal-to-noise ratio difference of postdetection SSC and predetection SSC is much less than previously reported

An analysis is derived for calculating the bit-error probability of an ultra-wideband (UWB) communication system operating with binary phase-shift keying and quaternary phase-shift keying narrowband interference in additive white Gaussian noise. The analytical expressions are valid when phase transitions of the interfering symbols can be ignored. The accuracy of the Gaussian approximation is assessed, and several modulation schemes proposed for UWB communication are evaluated in terms of capability of interference suppression.

A precise bit-error probability (BEP) analysis method is derived for a multicode direct-sequence code-division multiple-access (DS-CDMA) system in an additive white Gaussian noise channel. The method is applicable to a multicode DS-CDMA system with an arbitrary number of multiple code sequences, and any selection of multiple code sequences. The precise method gives results that discriminate the effect of the selection of different multiple code sequences on the BEP, whereas Gaussian approximations (GAs) do not. Thus, the new method can be used to select the best multicode set for a given system, a task that cannot be achieved using GAs. A two-step analytical procedure enables deriving an explicit, compact form for the CF of the receiver decision statistic in a DS-CDMA system with an arbitrary number of multiple code sequences, and for any selection of multiple code sequences.

The bit-error rate (BER) of binary phase-shift keying in Rayleigh fading, using the Alamouti transmission scheme and receiver selection diversity in the presence of channel-estimation error, is studied. Closed-form expressions for the BER of log-likelihood ratio selection, signal-to-noise ratio (SNR) selection, switch-and-stay combining selection, and maximum ratio combining are derived in terms of the SNR and the cross-correlation coefficient of the channel gain and its corrupted estimate. Two new selection schemes, space-time sum-of-squares combining selection diversity and space-time sum-of-magnitudes selection diversity, are proposed and proven to provide almost the same performance as SNR selection, but with much simpler implementations. The effects of channel-estimation errors on each selection scheme are examined.

A precise method for calculating the bit-error probability (BEP) of a discrete cosine transform (DCT)-based orthogonal frequency-division multiplexing (OFDM) system on additive white Gaussian noise (AWGN) channels in the presence of frequency offset is derived. These accurate results are used to examine and compare the BEP performance of a DCT-OFDM system and the conventional discrete Fourier transform (DFT)-based OFDM system in an AWGN environment. Several signaling formats, such as binary phase-shift keying, quaternary phase-shift keying, and 16-ary quadrature amplitude modulation are considered. The performance of a DCT-OFDM with a zero-padding guard-interval scheme is then compared with a zero-padded DFT-OFDM with the employment of minimum mean-square error (MMSE) detection and MMSE decision-feedback detection with ordering scheme over frequency-selective fast Rayleigh fading channels. Analysis and simulation results show that the DCT-OFDM system outperforms the DFT-OFDM system in the presence of frequency offset, and in frequency-selective fast-fading environments

An accurate approximation to the average symbol-error rate of hybrid selection/maximal-ratio combining (H-S/MRC) in correlated Nakagami-m fading with positive integer values of m is obtained by using a Green's matrix approximation. This approach is valid for different M-ary linear modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example.

The exact performance of selection combining, hybrid selection/maximal-ratio combining (H-S/MRC), and threshold-based H-S/MRC in correlated Nakagami-m fading for positive integer values of fading parameter m, is analyzed for a particular correlation structure. This correlation model, though not general, is much more general than the equal-correlation case, and includes equal correlation as a special case. The symbol-error rate and outage probability of the three combining schemes are obtained by transforming the correlated branch gains into a set of conditionally independent branch gains. Numerical and simulation results show excellent agreement with theoretical results

A simple and general form of threaded algebraic space–time (TAST) codes and constellations for arbitrary numbers of transmit and receive antennas and arbitrary input alphabets is given and analyzed. This new form gives revealing insights on the TAST framework, elucidates the connection between space–time constellation expansion and the peak-to-average power ratio (PAR), and establishes the equivalence between a certain class of TAST constellations and constellations derived from division algebras.

A novel paradigm is proposed to design time-limited pulse shapes for ultra-wideband communication systems. Pulses can be designed using the new paradigm that not only conform to spectral emission constraints, but also achieve good bit error rate performance in multiple access interference environments. Compared with previously proposed pulses, the novel pulses provide the same multiple access performance as the Gaussian monocycles yet have advantages over them in terms of power spectrum and spectral emission constraints. Our pulse design paradigm provides a flexible and effective method for designing suitable pulses for ultra-wideband communication applications that comply with frequency emission constraints

The performance of the selection diversity combiner in slowly and flatly fading channels is studied. Unlike most previous works where perfect knowledge of the signal amplitude and the noise power is assumed, in this analysis, knowledge of the signal amplitude and the noise power is obtained by using practical estimators that introduce estimation errors. The average symbol error rate of the combiner is derived for noncoherent M-ary frequency shift keying signals, independent and non-identically distributed diversity branches and unequal noise powers. The effect of estimation errors on the performance of the combiner is evaluated and illustrated by numerical examples. An interesting and useful conclusion is that it is disadvantageous to employ signal-to-noise ratio as a branch selection criterion when the branch noise powers are known a priori to be equal

Novel diversity receivers that operate in the presence of Gaussian channel estimation errors are proposed for L independent and identically distributed fading channels. Previous work concerned with channel estimation errors has mainly examined the performance of maximal ratio combining (MRC) with estimation errors. It is shown here that MRC is not optimal when estimation errors occur. Moreover, it is shown that better diversity receivers that operate in the presence of Gaussian channel estimation errors can be obtained by using knowledge of the channel estimate statistics. Numerical results show that the derived new diversity receivers can perform as much as 2.0 dB in signal-to-noise ratio better than the conventional MRC receiver in some cases.

The performance of M-ary orthogonal noncoherent frequency-shift keying (NCFSK) with N branch signal-plus-noise (S + N) selection combining (SC) in Nakagami-m fading (m, integer) is studied. Both independent, identically distributed (i.i.d) and independent, nonidentically distributed (i.n.d) diversity branches are considered and two S + N SC receiver structures are examined. The performances of the S + N SC receivers are compared to those of classical SC and square-law combining (SLC) receivers. The effects of modulation order, fading parameter and the number of diversity branches on the performance of S + N SC are compared to the effects on the performances of classical SC and SLC. For example, it is shown that in an i.n.d fading channel, the value of signal-to-noise ratio (SNR) at which the error rate curves of classical SC and S + N SC cross, decreases as the modulation order, M, increases. Our results indicate that in i.n.d fading channels classical SC outperforms S + N SC for small ranges of SNR, while for moderate to large SNR values S + N SC has superior performance over classical SC. It is also shown that increasing the diversity order will increase the performance gap of S 4N SC over classical SC and over SLC in both i.i.d and i.n.d Nakagami-m fading channels

In hybrid selection/maximal ratio combining (H-S/MRC) the receiver selects the L branches with the largest signal-to-noise ratios (SNRs) from N available diversity branches and performs maximal ratio combining (MRC). A penalty is incurred with respect to MRC which can be defined as the increase in SNR required for H-S/MRC to achieve the same symbol error probability as MRC. Recently, this penalty was investigated specifically for two-dimensional modulations. In this paper, we derive the asymptotic SNR penalties in slow Rayleigh fading for small and large values of SNR for general uncoded signaling constellations.

The statistical properties of Clarke's fading model with a finite number of sinusoids are analyzed, and an improved reference model is proposed for the simulation of Rayleigh fading channels. A novel statistical simulation model for Rician fading channels is examined. The new Rician fading simulation model employs a zero-mean stochastic sinusoid as the specular (line-of-sight) component, in contrast to existing Rician fading simulators that utilize a non-zero deterministic specular component. The statistical properties of the proposed Rician fading simulation model are analyzed in detail. It is shown that the probability density function of the Rician fading phase is not only independent of time but also uniformly distributed over [-pi, pi). This property is different from that of existing Rician fading simulators. The statistical properties of the new simulators are confirmed by extensive simulation results, showing good agreement with theoretical analysis in all cases. An explicit formula for the level-crossing rate is derived for general Rician fading when the specular component has non-zero Doppler frequency

The effects of several Nyquist windows, including the raised-cosine window, the "better than" raised-cosine window, the second order continuity window, and the Franks window on the performance of an OFDM windowing reception system are considered. The intercarrier interference analysis and bit error rate calculation of this system are provided

Optimum detectors for pilot symbol assisted modulation signals in a Rician fading channel are derived. Conventional pilot symbol assisted modulation (CPSAM) as used on Rayleigh fading channels has been employed on Rician fading channels. It is shown that the intuitive CPSAM structure is suboptimal for Rician fading. The optimum pilot symbol assisted modulation (OPSAM) signal detector uses knowledge of the specular component power and also jointly processes the pilot symbols and the data symbol. The performance of the optimum detector is analyzed and compared with that of the conventional detector. It is concluded that substantial gains can be achieved by exploiting knowledge of the specular component while joint processing of the data symbol with the pilot symbols may offer only small benefits.

Time variation on fading channels hinders accurate channel estimation in differential space-time modulation and deteriorates the performance. Decision-feedback differential detection is considered for block differential space-time modulation and compared with conventional differential space-time modulation. It is observed that the proposed scheme does not suffer effective fading bandwidth expansion as does the conventional scheme. An improved effective signal-to-noise ratio approach is proposed for analyzing the performance of the system. Theoretical analysis and simulation show the improved performance of the proposed scheme over the conventional scheme.

A new scheme, selective time domain filtering, that has significantly reduced complexity compared to the SLM scheme, which only relies on conventional channel estimation and demodulation techniques for multipath fading channels to recover the data, is proposed. Computer simulations indicate that the new scheme suffers only a small loss in performance in exchange for significant reduction in complexity.

The bit error rate of a binary phase shift keying signal in Ricean-faded cochannel interference is studied. A precise bit error rate expression based on a characteristic function method is derived for a bandlimited binary phase shift keying signal corrupted by an arbitrary number of asynchronous Ricean-faded interfering signals. For the special case when there is one synchronous Ricean-faded interfering signal, a Chernoff bound analysis is performed and it predicts that the error floor of the desired user signal decreases with an increase of the Rice factor in the interfering user's fading channel. However, our precise bit error rate analysis results reveal that the opposite phenomenon can also happen, in particular when the signal-to-interference power ratio is low. A saddle-point approximation based error rate analysis is also provided. It is shown that this approximation is highly accurate. An asymptotic analysis based on the saddle-point approximation further reveals that a minimum signal-to-interference power ratio is required to have the desired user's error rate performance improved by a less-faded interfering signal.

The performance of M-ary orthogonal noncoherent frequency-shift keying (NCFSK) with N branch signal-plus-noise (S + N) selection combining (SC) in Nakagami-m fading is studied. Both independent, identically distributed and independent, nonidentically distributed diversity branches are considered. Two S + N SC receiver structures are studied and their performances are analyzed. Tractable expressions are derived for the symbol error rate performance of these receiver structures in Nakagami-m fading with integer values of m. The performances of the S + N SC combiners are compared to those of classical SC and square-law combining (SLC). The effects of the modulation order, the fading parameter, the average decay factor and the number of diversity branches on the performance of S + N SC are examined and compared to the cases of classical SC and SLC. Monte Carlo simulation results are presented to test the validity of our analytical expressions.

The all-Rake and selective-Rake receiver structures are examined for different transmission scenarios, including multiple access interference and intersymbol interference environments. The results show that the all-Rake receiver does not necessarily offer the best performance when operating in intersymbol interference environments. Some candidate modulation schemes proposed for ultra-wideband communications are assessed and compared using a measurements-based fading model. Although some analytical and semi-analytical methods using the Gaussian approximation predict the same bit error rate estimates for several modulation schemes, our results show that the actual performances of these modulation schemes are different

A precise bit-error probability analysis method is derived for a multicode DS-CDMA system in an additive white Gaussian noise channel. The method is applicable to a multicode DS-CDMA system with an arbitrary number of multiple code sequences and any selection of multiple code sequences. The precise method gives results that discriminate the effect of the selection of multiple code sequences on the bit-error probability, whereas Gaussian approximations do not. Thus, the new method can be used to select the best multicode set for a given system, a task that cannot be achieved using Gaussian approximations. A two-step analytical procedure enables deriving an explicit, compact form for the characteristic function of the receiver decision statistic in a DS-CDMA system with an arbitrary number of multiple code sequences, and for any selection of multiple code sequences.

A new and intuitive expression for the bit error probability (BEP) of a two-user synchronous jointly optimum receiver in an additive white Gaussian noise (AWGN) channel is derived. The desired and interfering users are assumed to use binary phase-shift keying (BPSK) modulation. The new expression decomposes into the BEP of BPSK in AWGN plus a term due to the interference. It is shown that the term due to interference vanishes when the interference power or its correlation with the desired signal tends to zero.

The exact bit error rate (BER) of a synchronous individually optimal receiver (IOR) used to detect a binary phase-shift keying (BPSK) signal distorted by a like-modulated signal and additive white Gaussian noise (AWGN) is derived. It is shown that the BER expression decomposes into the probability of error of BPSK in AWGN plus an interference term. It is observed that as the noise decreases the IOR performance approaches the performance of a single cochannel interferer jointly optimal receiver.

A precise method for calculating the bit error probability of a discrete cosine transform (DCT)-based orthogonal frequency-division multiplexing (OFDM) system on AWGN channels in the presence of frequency offset is derived. These accurate results are used to examine and compare the bit error probability performances of a DCT-OFDM system and the conventional discrete Fourier transform (DFT)-based OFDM system. Several signaling formats, such as binary phase shift keying (BPSK), quaternary phase shift keying (QPSK), and 16-ary quadrature amplitude modulation (16-QAM) are considered. Analysis and simulation results show that the DCT-OFDM system outperforms the DFT-OFDM system in the presence of carrier frequency offset.

The Nakagami-m distribution is an important fading model in wireless communications. The simulation for bi-variate Nakagami-m samples is useful when study dual branch diversity systems in Nakagami-m fading channels. However, no simple and efficient method for simulating Nakagami-m fading channels is available in the literature. This letter proposes a simple efficient method for generating bivariate Nakagami-m fading envelope samples for arbitrary values of m > 0.8.

Absolute threshold generalized selection combining (AT-GSC) is a combining scheme which intends to reduce the power consumption and hence, extend the battery life at the terminal end. An AT-GSC scheme requires channel estimation for its operation. Previous works studying AT-GSC have exclusively examined AT-GSC systems under the assumption of perfect channel estimation. Maximal-ratio-combining is a special case when the threshold is set very low and all the branches are chosen, which consumes maximum power. We derive the average bit error rate (BER) and the cumulative distribution function (cdf) of the output signal-to-noise ratio (SNR) for AT-GSC when there is channel estimation error. The effects of channel estimation errors on the BER and combiner output SNR are studied.

In this paper, we consider the performance of M-ary orthogonal noncoherent frequency shift keying (NCFSK) with two signal-plus-noise (S + N) selection combining (SC) models in slow, flat Rician fading channels. We assume the fading branches are independent but not necessarily identically distributed. The probability of error for each model is derived as a single integral with finite integration limits. Extensive Monte Carlo simulation results are presented to assess the validity of our analytical expressions. Our results indicate that, unlike previously published results, the performance of S + N SC is not always superior to that of classical SC in fading and is dependent on the value of the signal-to-noise ratio, the modulation order, the multipath intensity profile and the fading parameter. The performances of S + N SC schemes are also compared to the performances of equal gain combining and square-law combining receivers.

An exact analysis is derived for precisely calculating the bit error probability of an ultra-wideband communication system operating in IEEE 802.11a narrowband interference. The analytical expressions are used to assess the accuracy of the Gaussian approximation, a widely adopted method for estimating the interference. The Gaussian approximation is shown to be inaccurate for predicting the bit error rate for some system parameters. The performance degradation of the ultra-wideband communication system in the presence of interference from orthogonal frequency division multiplexing signals is accurately evaluated. Several modulation schemes proposed for ultra-wideband communications are compared in terms of capability for OFDM interference suppression. The effects of system parameters on the bit error rate performance are also addressed through numerical examples.

The conventional multiple-symbol differential detection (MSDD) of differential phase-shift keying (DPSK) signals is studied in the presence of frequency offset. It is shown that in the case of nonzero frequency offset, the performance of the conventional MSDD receiver degrades by increasing the number of observed samples. A double DPSK (DDPSK) modulation scheme is then introduced and it is shown that in the presence of nonzero frequency offset, an MSDD receiver with DDPSK modulation outperforms a conventional MSDD receiver with DPSK modulation, when both receivers use a large number of received samples. Examples lead to a conjecture that the performance of an optimum MSDD receiver with DDPSK modulation and an infinite number of received samples, approaches that of a conventional DPSK demodulator with two received samples.

Ultra-wideband (UWB) communications is a new technology being developed for high-speed, short distance wireless communications. One possible modulation scheme is pulse amplitude and position modulation (PAPM), which has a flat power spectral density that is highly suited to UWB. Closed-form expressions for the error rate performance of a PAPM UWB receiver based on maximal ratio combining (MRC) in a lognormal fading channel have been derived using Wilkinson's approximation for lognormal sums. The receiver is analyzed using a more accurate approximation to the lognormal sum distribution. Our approach is extended to obtain accurate closed-form expressions for the performance of equal gain combining (EGC). The performances of MRC and EGC diversity are calculated and compared to the results obtained using Wilkinson's approximation.

An exact closed-form bit error rate expression is derived for an orthogonal frequency-division multiplexing system, each subcarrier modulated by /spl pi//4-shifted differentially encoded quadrature phase shift keying, in the presence of carrier frequency offset over frequency-selective fast Rayleigh fading channels. Both single channel reception and diversity reception with maximal ratio combining are considered. The closed-form expression allows us to investigate the effect of several channel parameters, including mean delay spread and maximum Doppler shift, on the system bit error rate performance. Particularly, the effect of carrier frequency offset on the system performance can be studied for a more realistic wireless channel environment model. Small carrier frequency offsets have slight influences on the system performance. Compared with the same amount of Doppler shift, carrier frequency offset usually leads to a greater degree of performance degradation. Systems with fewer subcarriers are more sensitive to the channel mean delay spread. By using the exact closed-form bit error rate expression, an optimum number of subcarriers can be found, and the allowable carrier frequency offset, Doppler shift, and mean delay spread for given operating conditions can be determined.

A discrete cosine transform (DCT)-based orthogonal frequency-division multiplexing (OFDM) system is described. The performance of the DCT-OFDM system with a zero-padding guard interval scheme and a minimum mean-square error (MMSE) receiver over time-varying multipath Rayleigh fading channels is investigated. The results show that employing the proposed DCT-OFDM system rather than the conventional DFT-OFDM system can provide better bit error rate performance in practical systems, by as much as 5.5 dB in signal-to-noise ratio (SNR).

Differential unitary space-time modulation is an attractive space-time technique because it does not require channel estimation. In this paper, we propose a new differential space-time code with rate 2.5 bit/s/Hz for two transmit antennas. In contrast to the original unitary space-time codes with one level of amplitude, the powers of the matrices in this new differential space-time code are different. We design a decoding algorithm based on the Viterbi algorithm to differentially detect the transmitted data. Simulation results show that the new two amplitude level differential space-time code outperforms the original unitary space-time code with rate 2.5 bit/s/Hz.

A new class of differential unitary space-time codes, namely, differential monomial space-time codes, is proposed. In contrast to many other differential unitary space-time codes, this new class of differential monomial space-time codes does not require the transmitted matrices to form a group. Instead, the signals at each transmit antenna are constrained in MPSK constellations. Due to this feature, the transmitted signals on each transmit antenna can be generated by a simple table lookup and modulus-add operation with low complexity. We give design examples for 4 transmit antennas and show the performance improvement over conventional differential unitary space-time codes.

A closed-form expression for the pairwise error probability of cyclic unitary space-time codes with t=2 and r=1 is obtained. Additionally, this result is used to obtain an upper bound to the symbol error rate of cyclic unitary differential space-time group codes. It is also shown that these techniques can be used to approximate the symbol error rate of dicyclic unitary differential space-time group codes.

Recent work has examined the performance of dual branch postdetection switch-and-stay combining (SSC) for noncoherent binary orthogonal frequency-shift keying (BFSK) and noncoherent M-ary orthogonal frequency-shift keying (MFSK) operating in the presence of slow, flat fading modeled by Rayleigh, Nakagami-m, and Rician distributions. These studies are important, in particular, because they quantify the improvement of postdetection SSC over predetection SSC. However, previous work on the performance of postdetection SSC over Rician fading is incorrect. In this paper, we present correct analyses of the bit error rate (BER) performance of BFSK and MFSK with dual-branch postdetection SSC in Rician fading. Extensive Monte Carlo simulations are carried out to verify the validity of the analytical results. Our results show that the performance gain of postdetection SSC over predetection SSC is much less than previously reported.

A sample rejection scheme introduced previously is generalized for the simulation of multidimensional communication systems. We consider the use of sample rejection (a special case of importance sampling) for efficient simulation of uncoded continuous transmission with periodic trellis-termination over static intersymbol interference (ISI) channels and maximum likelihood sequence detection. Previously proposed rejection regions are applicable only for finite lattices with rectangular or circular symmetries and moderate dimensionality. However, these regions are not applicable or are inefficient if the dimensionality is increased for large block-lengths, or if the lattice symmetries are absent because of the ISI. Hence, we investigate sliding-window (near) maximum-likelihood sequence decoding (MLSD) to resolve the dimensionality problem. In particular, we study the truncated Viterbi algorithm and feedback decoding. We propose several modifications to these two algorithms using sample rejection principles to improve the simulation efficacy for the conventional Viterbi algorithm while achieving near MLSD performance. Finally, numerical examples confirm that feedback decoding and its modifications can be more efficient for simulations of ISI channels and near MLSD than the Viterbi algorithm.

A whitening matched filter receiver for multiple access interference suppression is considered for a bandlimited DS-CDMA system in Nakagami fading. The whitening matched filter, while maximizing the signal-to-noise-plus-interference ratio, introduces intersymbol interference in the decision statistic. A fractionally spaced linear MMSE equalizer is introduced to combat the intersymbol interference. The Beaulieu-Tan-Damen pulse and the conventional spectrum raised-cosine pulse are employed as chip pulse shapes. Asynchronous timing and slow flat fading are assumed. The precise BER expressions are derived using characteristic function and Fourier series methods.

Accurate average bit error rate analysis of diversity receivers for asynchronous bandlimited binary DS-CDMA systems operating over Nakagami-m fading channels is studied. Predetection equal gain combining (EGC) and selection combining (SC) are considered. The fading is assumed to be flat and slow, and random spreading sequences are considered. The spectrum raised cosine (SRC) and Beaulieu-Tan-Damen (BTD) pulse shapes are employed. The improved Gaussian approximation for multiple access interference is employed with characteristic function and Fourier series methods for the performance analysis. Our results are valid for arbitrary diversity order and arbitrary Nakagami fading parameter and the computational complexity does not grow with the diversity order. The new Beaulieu-Tan-Damen pulse outperforms the spectrum raised-cosine pulse in all situations examined.

The problem of estimating parameters of two main fading distributions, Ricean and Nakagami-m, is considered. Unlike most previous estimators which are designed to use samples from a noiseless channel, new estimators which use noise-corrupted samples are proposed. Both maximum-likelihood designs and moment-based designs are considered. The performances of the new estimators are examined and compared with those of previous estimators derived in the literature. Numerical results show the superiority of the new estimators for operation in noisy channels.

In two recent papers, the performances of dual-branch postdetection switch-and-stay combining (SSC) for noncoherent orthogonal binary frequency-shift keying (BFSK) and noncoherent orthogonal M-ary frequency-shift keying (MFSK) operating in the presence of slow flat fading modeled by Rayleigh, Nakagami-m, and Rician distributions have been analyzed. In this paper, we show that these previous analyses for the Nakagami-m fading model, which are restricted to integer values of m, are incorrect, and we derive the correct bit-error rate (BER) performances of BFSK and MFSK with dual-branch SSC in Nakagami-m fading for all values of m. Optimum switching thresholds that minimize the BER of BFSK and MFSK with postdetection SSC in Nakagami-m fading are obtained. The performance of postdetection SSC is compared with the performance of predetection SSC, and it is shown that postdetection SSC outperforms predetection SSC for all values of signal-to-noise ratio (SNR). We also show that for a given BER, the performance gain of postdetection SSC over predetection SSC has been overestimated by several decibels in SNR in previous publications.

An exact analysis is derived for precisely calculating the bit error probability of time-hopping and direct-sequence ultra-wideband systems with multi-user interference in an additive white Gaussian noise environment. The analytical expressions are validated by simulation and used to assess the accuracy of the Gaussian approximation proposed for estimating the performance of ultra-wideband communication systems. The Gaussian approximation is shown to be inaccurate for predicting the bit error rate for medium and large signal-to-noise ratio values. The performances of time-hopping and direct-sequence modulation schemes are accurately compared for different numbers of users and frame widths. It is shown that direct-sequence binary phase-shift keying outperforms time-hopping binary phase-shift keying for medium and large values of signal-to-noise ratio, which contradicts some previous results obtained using a Gaussian approximation.

We re-examine sample rejection (SR), introduced previously as an easy-to-implement efficient simulation technique. Since the decoding operation often represents a major part of the required simulation time, SR can be used to avoid decoding of the received sequences that are known beforehand to be decoded error-free. Previous work seems to indicate that SR may be effective only for simulations having small dimensionality, less than 10. We assume estimation of decoded bit-error probabilities for a general coding scheme of finite block length transmitted over an additive white Gaussian noise channel with quantized output using binary antipodal signaling and maximum-likelihood sequence decoding. We show that knowledge of the minimum Hamming distance of the code and conditioning on the transmitted sequence can be exploited to form the rejection regions. In particular, we investigate hypersphere, hypercube, and hyperquadrant rejection regions. Our analysis shows that SR can be effective for some systems with dimensionality on the order of hundreds with soft-decision decoding, and some systems with dimensionality more than a thousand with hard-decision decoding if the rejection regions are properly chosen.

The average symbol-error rate of threshold-based hybrid selection/maximal-ratio combining (T-HS/MRC) with correlated Nakagami-m fading channels is obtained for positive integer values of fading parameter m for a special correlation structure. An accurate approximate analysis of T-HS/MRC in arbitrarily correlated Nakagami-m fading channels is presented by using a Green matrix approximation. The derivation allows different M-ary linear modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example.

Autoregressive stochastic models for the computer simulation of correlated Rayleigh fading processes are investigated. The unavoidable numerical difficulties inherent in this method are elucidated and a simple heuristic approach is adopted to enable the synthesis of accurately correlated, bandlimited Rayleigh variates. Startup procedures are presented, which allow autoregressive simulators to produce stationary channel gain samples from the first output sample. Performance comparisons are then made with popular fading generation techniques to demonstrate the merits of the approach. The general applicability of the method is demonstrated by examples involving the accurate synthesis of nonisotropic fading channel models.

A new parametric approach is proposed for the estimation of the maximum Doppler frequency, or equivalently the mobile speed, in narrowband mobile radio channels. In this work, simple and efficient Doppler-frequency estimators are formulated based on using a small number of samples of the channel autocorrelation function. Unlike previous approaches, the chosen parameterization is shown to be robust in a microcellular propagation environment, which may be characterized by nonisotropic scattering and/or a specular component of unknown strength. Simulation results are described to illustrate the effects of additive noise and the finite data-record performance.

Closed-form expressions for computing the average bit error rate (BER) for a class of modulation schemes in Ricean flat fading channels with maximal-ratio combining diversity and channel estimation errors are derived. The results are valid for a general multichannel model that includes Ricean and Rayleigh fading channels. The results are applicable to channel estimators that are jointly Gaussian with the channel gain. The BER performance of pilot symbol-assisted modulation is studied. The effects of estimation error on the diversity system are examined as well as the influences of varying the Ricean factor K and changing the number of diversity branches L.

An accurate bit-error-rate (BER) calculation method is derived for a binary direct-sequence (DS) spread-spectrum multiple-access (SSMA) system using conventional matched filter receivers and random sequences on flat-fading Nakagami channels. A closed-form expression for the characteristic function of a sum of multiple Nakagami interfering signals is found. The accuracy of the standard Gaussian approximation (SGA) is assessed for DS code-division multiple-access (CDMA) systems operating on Nakagami fading channels.

A novel algorithm is proposed to design time-limited pulse shapes for ultra-wideband communication systems. The new algorithm can be used to design pulses that not only conform to spectral emission constraints, but also achieve good bit error rate performance in multiple access interference environments. Compared with previously proposed pulses, the novel pulses provide the same multiple access performance as Gaussian monocycles, yet have advantages over them in terms of power spectrum and spectral emission constraints. Our pulse design algorithm provides a flexible and effective method for designing suitable pulses for ultra-wideband communication applications that comply with frequency emission constraints.

Cochannel interference mitigation in bandwidth efficient BPSK systems operating in slow, flat fading microcellular environments is considered. The desired and interfering users undergo Nakagami-m and Rayleigh fading, respectively. A whitening matched filter and fractionally spaced linear minimum mean square error equalizer are employed in the receiver. While whitening maximizes the signal-to-noise-plus-interference ratio, the whitening matched filter introduces intersymbol interference in the decision statistic. A minimum mean square error equalizer is used to combat the intersymbol interference. Important observations regarding the performance of the proposed receiver structure are made. The performance with Beaulieu-Tan-Damen pulse shaping is always better than with spectrum raised-cosine pulse shaping. The performance is considerably better than the conventional matched filter receiver under a variety of fading conditions for the desired user. The performance gain decreases with the severity of the fading of the desired user. When the cochannel interference is synchronous, the performance can approach the optimum single user performance by appropriately choosing the tap spacing and length of the equalizer.

Hybrid selection/maximal-ratio combining (H-S/MRC) diversity is a very important diversity combining technique in wideband systems. It can be employed to reduce the complexity of RAKE receivers, which are needed to achieve acceptable performance on frequency selective fading channels. A method for calculating the bit error rate (BER) of H-S/MRC diversity systems with channel estimation error is introduced. It is applied to derive BER expressions for binary shift keying (BPSK), quadrature shift keying (QPSK) and M-ary quadrature amplitude modulation (M-QAM). Results for selection combining (SC) and MRC are also obtained as two special cases. The effects of the estimation errors on the system performances are studied in detail. The sensitivities of different modulation schemes to channel estimation errors are examined.

Optimum diversity receivers that operate in the presence of estimation errors are proposed. Previous work has mainly examined the performance of maximal ratio combining (MRC) with estimation errors. It is shown that MRC is not optimal when estimation errors occur. Moreover, it is shown that the optimum diversity receiver in the presence of estimation errors can be derived by using knowledge of the channel estimate statistics. Numerical results show that the optimum diversity receiver can perform as much as 2.0 dB in signal-to-noise ratio better than the conventional MRC receiver in some cases.

The error rates of orthogonal frequency division multiplexing (OFDM) signals on frequency selective Nakagami-m fading channels are considered. The exact probability density function of a sum of Nakagami-m random vectors is used to derive a closed-form expression for the error rate of OFDM signals. The exact error rate analysis is also extended to a system using multichannel reception with maximal ratio combining. Our analysis and numerical results show that the error rates obtained using a previous Nakagami-m approximation can be unreliable. It is observed that, depending on the number of channel taps, the error rate performance may degrade with increasing values of Nakagami fading parameters.

In traditional selection combining, the branch having the largest signal-to-noise ratio is employed for signal detection. However, many practical systems choose the branch with the largest signal-plus-noise (S+N) at the filter output. Recent work has studied the performance of noncoherent orthogonal frequency shift keying (NCFSK) with S+N selection combining in slow, flat Rayleigh fading channels. We consider the performance of NCFSK with dual-branch S+N selection combining in slow, flat Rician and Nakagami-m fading channels. Two S+N receiver structures for NCFSK are examined and analytical expressions for the bit error rate (BER) performances of these receivers are obtained both for Rician and Nakagami-m fading channels. The channel fadings are assumed to be independent, but not necessarily identically distributed. It is shown that both the S+N receiver structures considered outperform the traditional selection combiner and their performances are compared to the performances of equal gain and square law combiners.

An exact method for calculating the bit error rate of pulse-shaped orthogonal frequency-division multiplexing systems in the presence of frequency offset is derived. This method represents a unified way to calculate the bit error rate of different one-dimensional and two-dimensional subcarrier modulation formats, such as, binary phase shift keying (BPSK), quaternary phase shift keying (QPSK), and 16-ary quadrature amplitude modulation (16-QAM). The precise bit error rate expressions are obtained using a characteristic function method. These accurate analytical results are used to examine and compare the bit error rate performance of pulse-shaped orthogonal frequency-division multiplexing systems employing the rectangular pulse, the raised-cosine pulse, and the "better than" raised-cosine pulse when a frequency offset is present. The dependence of the bit error rate on the roll-off factor of the pulse employed for a specific system in the presence of frequency offset is also investigated. Analysis and numerical results show that employing the "better than" raised-cosine pulse rather than the raised-cosine pulse can provide better bit error rate performance in practical systems, by as much as 2-3 dB in SNR.

The paper analyzes the average symbol error rate and outage probability of threshold-based hybrid selection/maximal-ratio combining (T-HS/MRC) in generalized fading environments. Using the moment generating function (MGF) method, a unified analysis of T-HS/MRC over various slow and frequency-nonselective fading channels is presented. Both independent, identically distributed and independent, nonidentically distributed diversity branches are considered. The derivation allows different M-ary linear modulation schemes. The theory is illustrated using coherent M-ary phase-shift keying in Nakagami-m fading as an example. It is shown that previously published results are incorrect.

The problem of estimating the Ricean and Nakagami-m distribution parameters in noisy slowly fading channels is studied. Previous published works have mainly examined estimation based on a noiseless sample model. The predicted performances of these estimators can only be achieved by having knowledge of the values of the individual noise samples and subtracting them from the noisy signals, an impractical case. In this paper, a system model which uses samples corrupted by noise is examined. The probability density functions of noisy channel samples are derived. Novel maximum likelihood estimators as well as moment-based estimators for operation in noisy environments are developed based on these density functions. The sample means and sample root mean square errors of the estimators are determined. Numerical results show the new estimators have superior performances over estimators designed for noiseless samples in applications where noise is present.

A characteristic function method is proposed for precisely calculating the bit error probability of time-hopping ultra-wideband systems with multiple access interference. The analytical expressions are validated by simulation and used to assess the accuracy of the Gaussian approximation. The sensitivity of the performance of the modulation schemes to the system parameters is also addressed through numerical examples. The performances of time-hopping pulse position modulation and binary phase-shift keying modulation schemes are accurately compared based on the new analytical results.

Sample rejection has been proposed as an easy-to-implement efficient simulation technique for estimating the probability of decoded bit-error of a communication system. Previous work, however, seems to indicate that sample rejection may be effective only for simulations having small dimensionality, less than 10. While past work has considered a hypersphere rejection region, in this paper, we investigate hypercube and hyperquadrant rejection regions. We assume binary signaling and maximum-likelihood sequence decoding. The results indicate that the knowledge of the minimum Hamming distance of the code and conditioning on the transmitted sequence can be used to improve the gains achievable using sample rejection. The analysis shows that sample rejection can be effective for systems with dimensionality of the order of hundreds with soft-decisions and more than a thousand with hard-decision decoding if the rejection regions are properly chosen.

A novel, remarkably simple semianalytical method for average error-rate evaluation over slowly fading channels is presented. Assume that an error-rate curve conditioned on the instantaneous signal-to-noise ratio at the detector input is known either analytically or can be estimated at a few points by a computer simulation. In the first step, a sum of the first-order exponentials is fitted to the conditional error-rate curve. The curve fitting by a sum of exponentials is well-known in many areas of data processing as Prony approximation. A universal numerical algorithm to find the parameters of Prony approximation is developed. In the second step, knowledge of the moment generating function of the signal-to-noise ratio is required to obtain an average error-rate. Hence, the proposed method can be shown to be an extension of the moment generating function method. The method is illustrated on an example of average bit-error rate evaluation for M-ary phase-shift keying over a generalized Ricean fading and over correlated multichannel Rayleigh fading with maximum ratio combining.

Accurate performance analysis of asynchronous bandlimited binary DS-CDMA systems in Nakagami-m fading is considered. The fading is assumed to be flat and slow. The spectrum raised-cosine and Beaulieu-Tan-Damen pulse shapes are employed. A new accurate approximation for computing the bit error rate of bandlimited DS-CDMA systems employing random spreading sequences is proposed. A substantial computational complexity reduction is achieved. The well-known standard Gaussian approximation, Holtzman's simplified improved Gaussian approximation, and the improved Holtzman's Gaussian approximation are also considered. The accuracies of the approximations are assessed using Monte-Carlo simulation. For a system employing a deterministic sequence for the desired user and random sequences for the active interfering users, a characteristic function method is employed to derive exact BER results. The new Beaulieu-Tan-Damen pulse outperforms the spectrum raised-cosine pulse in all situations examined.

The performances of coherent diversity receivers with noisy channel estimation are examined. Fading channel gain estimates are modeled as sums of the true fading channel gain values plus independent Gaussian distributed estimation errors. The optimal diversity receiver for coherent reception with noisy channel state information and independent and identically distributed fading channels is derived. Exact expressions for the average error probability of optimal diversity MPSK with noisy channel estimation are derived for Rayleigh and Ricean fading channels; closed-form expressions are obtained for some special cases. Some interesting observations regarding practical diversity receiver design for higher-order modulation formats are drawn.

Closed-form expressions for computing the average bit error rate (BER) for a class of modulation schemes in Ricean flat fading channels with maximal-ratio combing (MRC) diversity and channel estimation errors are derived. The results are applicable to channel estimators that are jointly Gaussian with the channel gain. The BER performance of pilot symbol assisted modulation (PSAM) is studied. The effects of estimation error on the diversity system are examined as well as the influences of varying the Ricean factor, K, and changing the numbers of diversity branches, L.

We consider pilot symbol assisted modulation (PSAM) implemented with a sinc interpolator. The sensitivity of the error rate performance to different window functions applied to the sinc interpolator is investigated. The BER's for diversity M-ary quadrature amplitude modulation (MQAM) with different window functions applied to the sinc interpolator are compared. The Kaiser window is found superior to the other windows considered. A thorough discussion of the dependency of the BER performance on the symbol location is also given.

We study maximum ratio combining with correlated generalized Ricean branch fadings. The L received signals are represented as vectors in a 2m-dimensional signal space where m is the fading severity, and 2m is assumed to he an integer. Then, the channel model is a non-zero mean L/spl times/2m Gaussian random matrix. We discuss the optimality of maximum ratio combining when the branch fadings are correlated. A novel derivation of the multivariate moment generating function of noncentral chi-square distributed and correlated random variables is presented. The average bit-error performance evaluation is illustrated for constant, exponential and Gaussian branch signal-to-noise ratio correlation models.

A quadrature sub-branch hybrid selection/maximal-ratio combining (QBHS/MRC) scheme for one-dimensional modulations in Rayleigh fading is proposed. At the receiver, N diversity branches are split into 2N in-phase and quadrature sub-branches. Traditional hybrid selection/maximal-ratio combining (H-S/MRC) is then applied over the 2N sub-branches. The symbol error rate (SER) of M-ary pulse amplitude modulation (PAM), including coherent binary phase shift keying (BPSK), with QBHS/MRC is derived. The mean output signal-to-noise ratio (SNR) of a QBHS/MRC combiner is given. The performances of QBHS/MRC and H-S/MRC are compared. Results show that QBHS/MRC systems outperform traditional H-S/MRC systems.

The computer generation of multiple cross-correlated Rician fading channels is investigated. We prove that the output sequences of existing multichannel fading simulators are restricted to have cross-correlation statistics that have the same functional form as the component autocorrelation functions. To overcome this limitation, vector autoregressive stochastic models are proposed for the generation of multiple Rician fading processes with specified realizable autocorrelation and cross-correlation statistics. This capability is desirable, for example, to permit realistic performance assessments of space-time modem designs by enabling the simulation of space-time-selective wireless channel models. The utility of the simulation approach is demonstrated by the accurate synthesis of some bandlimited multichannel Rayleigh and Rician processes.

The bit-error rate (BER) of bandlimited binary phase-shift keying in a fading and cochannel interference (CCI) environment is derived for the case of perfect coherent detection. The fading-and-interference model assumed is general and of interest for microcellular system studies. The model allows both desired signal and interfering signals to experience arbitrary amounts of fading severity. A precise BER expression is derived using a characteristic function method. Using this accurate analytical result, the impact of the interfering users' fading severity on the desired user-error rate is examined. The BERs obtained under perfect coherent detection are also valid as lower performance bounds for practical realizable receivers where ideal coherent detection is difficult to implement. The error-rate performance of a novel bandwidth-efficient pulse shape is determined for the general fading and CCI environment. Analysis and numerical results show that the new pulse can provide better BER performance than the widely used raised-cosine pulse.

A novel parametric approach for constructing families of intersymbol-interference (ISI)-free pulses is presented and examined. Some new pulses so constructed have smaller maximum distortion, a more open receiver eye, and a smaller probability of error in the presence of symbol-timing error than the Nyquist raised-cosine pulse for the same excess bandwidth. The parametric approach gives more degrees of freedom in the design of ISI-free pulses, and subsumes previous ISI-free pulses as special cases. A number of theorems that relate time-domain behaviors of a pulse to the pulse's frequency spectrum are proved. A previously known result relating pulse tail-time decay to discontinuity of the pulse-frequency spectrum is corrected and clarified.

The bit-error rate (BER) performance of multilevel quadrature amplitude modulation with pilot-symbol-assisted modulation channel estimation in static and Rayleigh fading channels is derived, both for single branch reception and maximal ratio combining diversity receiver systems. The effects of noise and estimator decorrelation on the received BER are examined. The high sensitivity of diversity systems to channel estimation error is investigated and quantified. The influence of the pilot-symbol interpolation filter windowing is also considered.

A closed-form expression is derived for the moment-generating function of the Weibull distribution, valid when its fading parameter assumes integer values. Expressions for average signal-to-noise ratio, signal outage, and average symbol-error rate are derived for single-channel reception and independent multichannel diversity reception operating on flat Weibull slow-fading channels.