This paper presents two new methods for evaluating the ergodic channel capacities of cooperative non-regenerative multirelay networks in a myriad of fading environments and under three distinct source-adaptive transmission policies: i optimal rate adaptation with a fixed transmit power; ii optimal joint power-and-rate adaptation; and iii truncated channel inversion with fixed rate. In contrast to the previous related works, our proposed unified analytical frameworks that are based on the moment generating function and/or the cumulative distribution function of end-to-end signal-to-noise ratio allow us to gain insights into how power assignment during different transmission phases, relay node placement, fade distributions, and dissimilar fading statistics across the distinct communication links impact the ergodic capacity, without imposing any restrictions on the channel fading parameters. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, the authors present a novel moment generating function‐based technique to unify the performance evaluation of an average energy detector for detecting unknown deterministic signals over generalised fading environments (including the η ‐ μ , κ ‐ μ , α ‐ μ , K , G and K G generalised fading distributions) with diversity reception. Specifically, the authors exploit a known exponential‐type integral representation for the generalised Marcum Q ‐function Q v ( a , b ) that is valid for any ratio of a / b but for positive integer order v to greatly simplify the task of finding the statistical expectations over the fading signal‐to‐noise ratio random variables in the computation of the average detection probability metric. This new approach leads to a very compact and an elegant solution for many practical cases of interest including the independent but non‐identically distributed fading statistics and/or arbitrarily correlated diversity branches in maximal‐ratio combining, square‐law combining and square‐law selection diversity receivers. The authors’ numerical results also show that the performance of average energy detector is superior to the classical total energy detector with the increasing number of samples owing to the noise averaging effect. We have also demonstrated the versatility and utility of the proposed analytical framework to investigate the impact of dissimilar mean signal strengths, fading parameters, time‐bandwidth product, diversity order and signal combining techniques on the receiver operating characteristics of diversity energy detectors in a myriad of fading environments that had heretofore resisted simple solutions.

A known exponential‐type integral representation for the generalised Marcum‐ Q function Q v ( a , b ) is exploited (which is valid for integer order v but for any ratio of a / b ) to unify the performance evaluation of the partial area under the receiver operating characteristics curve (partial AUC) metric of average energy detectors with diversity reception in a myriad of fading environments (including the η − μ , κ − μ , α − μ , K , G and K G generalised fading distributions). This new metric facilitates the comparison of two different energy detectors within a specified detection threshold range and can also be used to compute the total AUC as a special case. The numerical results also show that the partial AUC performance of an average energy detector is superior to that of the classical total energy detector with the increasing sample size owing to the noise averaging effect. The new analytical framework also facilitates the investigation of the effects of dissimilar fading parameters and/or signal strengths, diversity order and diversity combining techniques on the partial AUC performance of energy detectors.

This study derives several new and simple closed‐form approximations for the average symbol error rate (ASER) and outage probability performance metrics of digital communication systems (with/without diversity receivers) impaired by additive white Gaussian noise and fading. These approximations utilise the coefficients of the Poincare series expansion for the probability density function (PDF) of signal‐to‐noise ratio (SNR) random variable in conjunction with Mellin transform of the conditional error probability and/or its auxiliary functions to generalise some of the known asymptotic ASER/outage probability expressions to a wider range of modulation schemes and different types of propagation environments (including κ–μ , η–μ and α–μ fading channels). A new class of asymptotic approximations for the ASER/outage probability is also derived (based on a normalised asymptotic PDF of SNR) that is considerably better than the conventional high‐SNR approximation although both techniques need only the first non‐zero term of the Maclaurin (if exists) or the Poincare series expansion of the channel PDF. The authors’ also investigate the utility/efficacy of Welch–Satterthwaite and Moschopoulos approximations for yielding accurate predictions of the ASER in the low‐SNR regime for different fading environments. Closed‐form approximations for the ergodic (average) channel capacities of different types of fading channels with/without diversity reception are also derived.

In this paper, energy detector's performance over the wireless channels with composite multipath fading and shadowing effects is analyzed using the area under the receiver operating characteristic (ROC) curve (AUC) in contrast to the conventional ROC measurement. AUC is a single statistical parameter which can be used to describe energy detector's performance more meaningfully. An energy detector may not see the transmitter due to the shadowing and fading. Generalized-K (KG) distribution is considered to describe the composite effects because of its simplicity than the other available models such as the Nakagami-lognormal distribution. The analysis is then extended to the cases with diversity receptions including maximal ratio combining (MRC), square law combining (SLC), and selection combining (SC) as the representative of diverse receiver combining techniques. The developed framework is very simple and the analytical results could be used readily to design energy detection based cognitive radio network. Energy detector's performance analysis with the AUC parameter over the composite effects is new and thus this work contributes significantly in the wireless communications areas.

In this article, we investigate the performance of classical and modified periodogram based on the Neyman-Pearson (NP) criterion in terms of the false alarm and detection probabilities. We derive analytical expressions that allow us to compare the performance of the classical periodogram with the Bartlett's and the Welch's modified periodogram over generalized fading channels. Our analytical framework also captures the effect zero padding (more FFT points than the length of input sequence) on the detection performance. We show that an unpadded classical periodogram gives the same detection performance as the time domain (TD) equivalent. However, the use of zero padding leads to better energy detection performance. The Welch's overlapping periodogram averages is also shown to outperform Bartlett's method (non-overlapping periodogram). Thus we conclude that, it is advantageous to implement the energy detection in the frequency domain (FD) than in the TD. Numerical results have been generated for several representative cases and a careful review of previous works reveals that this is a new contribution to the performance analysis of modified periodogram over fading channels.

Reliable spectrum sensing is the very task upon which the entire operation of the cognitive radio rests. Energy detection is one of the solutions that have been proposed for enabling opportunistic spectrum access but its capability has limited sensitivity, no resolution and requires high sampling rate when employed in the detection of wideband heterogeneous spectrum. This article proposes a solution that can extend the capability of traditional energy detector to wideband sensing with improved performance. The solution involves the use of parallel detection circuitry with each tuned to different frequencies. The decision of each detection circuit can then be used to create a spectral map of the entire spectrum. This introduces some resolution component and improved sensitivity based on the number of parallel circuits and bandwidth of each detection circuit. Since the bandwidth of the incumbent signal is generally not known a priori, there is possibility that it spans across multiple detectors. The detection of such wideband signal can be achieved by either data or decision fusion of the results of each narrowband detector. We show that the use of parallel multi-channel detection can greatly enhance the detection of wideband signal compared to averaging while improving the resolution and sensitivity of energy detection of wideband spectrum. Numerical results have been shown for representative cases and careful review of previous works reveals that these have never been considered in literature.

In this article, we derive six distinct series representations of the generalized Nuttall Q-function. Interestingly, some of these expressions generalise some of the recent results on series representation of the Marcum Q-function since the Marcum Q-function is a special case of the Nuttall Q-function. To the best of our knowledge, five of these representations are novel and the other one is included for the completeness of the article. The performances of these representations are compared using the magnitude of the truncation error which gives a measure of the accuracy and rate of convergence and allow us to show the strength of each representation. We then discussed the area of applications of our result. We showed that our Nuttall Q-function representations and their corresponding special case (Marcum Q-function) (though not limited to only these), can be used in (i) the computation of outage probability of wireless communication system with co-channel interferers, (ii) the evaluation of detection probability of energy detector over generalized fading channels in cognitive radio system, and (iii) the computation of cumulative distribution of selection diversity combining in correlated Nakagami-m fading channel. In all these areas of application, our solution has no restriction on any parameter of interest.

The joint optimization of power allocation and relay position is known to be a frightening problem in the analysis of cooperative relay communication. In this article, we present an efficient framework that tackles this problem for 2-hop cooperative amplify-and-forward (CAF) multi-relay system over generalized fading channel. First, we consider single CAF relay where we investigate (i) the optimum power allocation when the relay is position is fixed, (ii) the optimum relay position when the power allocation is fixed and (iii) the joint optimization of power allocation and the relay position. We then tackle the multi-relay optimization by reducing the multi-parameter search problem to only a 2-parameter search. Our mathematical framework does not only allow us to solve this problem but to solve it in a unified manner over various fading channels. Our analysis also took into consideration the effect of dissimilarity of the channel condition of the relay path on the optimization. This provides additional dimension and new insight on the optimization problem. Numerical results have been presented for representative cases and after careful review of previous works on this subject, we can conclude that our contribution is new, and can be very useful in the deployment of highly efficient CAF relay networks.

This article develops a unified analytical framework for maximizing the user throughput of a cooperative multi-relay network over generalized wireless channels using the symbol rate, packet length and constellation size of M-ary PSK/QAM digital modulation schemes as optimization variables. Optimization equations for each of the above degrees of freedom are derived in closed-form. A low-complexity discrete optimization algorithm for finding the “optimal” parameter-triplet is also developed to solve the resulting non-linear joint optimization problem. Numerical results reveal that it is sufficient to adapt the number of cooperating relay nodes as well as the symbol rate in the low SNR regime while a joint-optimization of both the packet length and the constellation size parameters is desirable in the high SNR regime to achieve the maximum throughput.

Recent development in wireless communication has necessitated a high demand for radio resources. This has led to the development of cognitive radio technology in which radio equipments are now capable of identifying spectrum opportunity in their environment and take advantage of spectrum unused by licensed primary radio users for communication. One of the derivatives of the emerging technology is the ad hoc cognitive radio networks where control of the network resources is distributed among the users. In order to improve co-ordination in ad hoc cognitive radio networks, there is a need for selection of an appropriate leader that will guarantee quality of service (QoS), spectrum allocation and aggregation and synchronization of cognitive radios. In this paper we proposed a novel leader election algorithm that is robust for distributed ad hoc cognitive radio networks.

In this article, we present three moment generating function (MGF) based methods for performance evaluation of multi-hop, multi-relay cooperative amplify-and-forward (CAF) networks over a myriad of stochastic fading channel models. Method I is based on a recursive expansion of the MGF of effective SNR for a 2-hop CAF relay network developed in [10]. The second method is also similar to Method I except that it now requires the exact MGF of the end-to-end SNR for a 2-hop relay network. Method III involves the split of a multi-hop route path into two sections, evaluating the MGF of the “weakest link” in each section, and then finding the MGF of end-to-end SNR using the result in [10] for a 2-hop CAF network. We show that all the above mentioned methods closely approximate the `exact' MGF of end-to-end SNR and the average symbol error rate (ASER) of CAF relay networks. Unlike the existing bounds (which are restrictive to specific fading channels), our proposed solutions is quite general and can be applied to a wide range of fading environments while dramatically reducing the computational complexity of ASER for multi-hop multi-branch CAF relay networks. Moreover, our final solutions for the ASER are expressed in closed-form for first two methods, and in terms of a single integral for Method III. The accuracies of our approximations have been validated with “exact” formulas that are available for specific wireless fading environments and via Monte Carlo computer simulations.

In this article, we first develop very tight second and third-order exponential-type approximations for the Gaussian probability integral Q(.) and/or the complementary error function erfc(.) which are subsequently used to devise the conditional symbol error probability (CEP) formulas for several classes of digital modulation schemes that are both invertible and in a “desirable” exponential form. These invertible CEP formulas are of interest in the optimization of discrete-rate adaptive modulation designs and for computation of the symbol/bit error outage performance metric. We also present new non-invertible higher-order exponential-type approximations for the erfc(.) and erfcp(.) functions based on Gauss-Chebyshev quadrature method. Our analytical framework also facilitates the derivation of simple and tight closed-form approximation formulas for the average symbol error rate performance metric of both cooperative and non-cooperative diversity systems in conjunction with a wide range of digital modulation schemes over generalized fading channels via the moment generating function (MGF) approach. The accuracies of our closed-form approximations have been validated with that of the “exact” formulas in an integral form and via computer simulations.

Tight bounds for the mean achievable rates of amplify-and-forward cooperative relay networks are derived for three distinct source adaptive transmission policies in a myriad of fading environments: (i) constant power with optimal rate adaptation (ORA); (ii) optimal joint power and rate adaptation (OPRA); and (iii) fixed rate with truncated channel inversion (TCIFR). Our unified framework based on the moment-generating function (MGF) technique allows us to gain insights as to how power assignment during different transmission phases, fade distributions and dissimilar fading statistics across the distinct communication links affect the ergodic capacity, without imposing any restrictions on the fading parameters.

This article investigates the efficacy of a constant-power, rate-adaptive M-QAM transmission technique in amplify-and-forward cooperative wireless networks. Tight upper and lower bounds are derived for the mean achievable spectral efficiency, outage probability, and error probability performance of non-regenerative cooperative relay networks in Nakagami-m fading environments. We observe that the spectral efficiency of a practical discrete-rate MQAM comes within a constant gap of the theoretical ergodic capacity of that channel, although this gap is smaller for an adaptive continuous-rate M-QAM.

Future wireless communication systems and networks will be required to support a multitude of services with different reliability requirements. However, achieving such flexible systems are challenging in Mobile Ad-hoc Networks (MANET) due to limited battery resources at mobile nodes. However, by employing adaptive signaling techniques with Unequal Error Protection (UEP), we strive to improve the energy efficiency and increase the data rate (spectral efficiency) over a fading channel. In this article, we demonstrate the efficacy of the exponential approximation for the Adaptive Multiresolution Modulation (AMM) scheme in terms of PER using the asymmetric Phase-Shift Keying (PSK) and Quadrature Amplitude Modulation (QAM).

This paper investigates the effectiveness of a cross-layer design that combines adaptive modulation (AM) at the physical layer with an adaptive truncated automatic repeat request (ARQ) protocol at the data link layer to maximize the throughput of cooperative amplify-and-forward (CAF) relay networks under prescribed delay and/or error performance constraints. A by-product of our proposed analytical framework, that involves evaluation of the marginal moment generating function (MGF) of the end-to-end signal-to-noise ratio (SNR), for computing the average throughput and average packet error rate performance metrics is the unification and generalization of existing studies on cross-layer combining of AM and truncated ARQ for non-cooperative diversity systems to generalized fading channels. Our analytical methodology is motivated by the fact that the MGF of end-to-end SNR for multi-relay CAF networks is either available in the research literature (for certain fading environments) or it can be computed much more conveniently than its PDF, while the desired marginal MGF can be evaluated efficiently using a multi-precision Laplace inversion formula of an auxiliary MGF function. The efficacy of an adaptive Rmax(maximum retransmission limit) strategy over the classical fixed Rmaxscheme is also examined.

This paper investigates the performance of cooperative amplify-and-forward (CAF) relay networks with adaptive M-ary quadrature amplitude modulation (M-QAM) technique in Nakagami-m and Rice wireless fading environments. We derived closed form upper bound expression for the marginal MGF of end-to-end SNR of CAF relay system in Nakagami-m fading to compute average bit error rate (ABER), mean achievable spectral efficiency, and outage probability performance metrics. Additionally, along with the above bounding techniques, we have adopted an accurate approximate MGF of end-to-end SNR of CAF relay system to compute above mentioned performance metrics. Employing the above novel approach based on "approximate MGF" allows us to simplify the computation complexity of achievable spectral efficiency as well as ABER of CAF relay system in generalized fading environments by simply replacing appropriate single channel MGF as readily available. The accuracies of our analytical results have been validated via Monte Carlo simulations.

In this article, we present a novel moment generating function (MGF) approach for performance evaluation of twohops cooperative non-regenerative multi-relay networks over a myriad of stochastic channel models. First, we develop very tight exponential approximations for the erfc(.) and erfc2(.) functions which will facilitate the development of a unified closed-form expression for the average symbol error rate (ASER) of a wide range of digital modulation schemes over generalized fading channels (with and without cooperative diversity). Next, we derive a new "asymptotic" approximation for the MGF of signalto noise ratio (SNR) of a two-hops relayed path in cooperative amplify-and-forward (CAF) diversity systems, which closely approximates its "exact" MGF. Combining these two techniques allows us to dramatically reduce the computational complexity for ASER of CAF multi-relay networks that have been treated in the literature for specific fading environments, besides providing accurate ASER estimates for CAF relay networks in many fading environments that heretofore had resisted a simple solution. Moreover, our final expression for the MGF of end-to-end SNR is expressed in closed-form, which is a desirable attribute for system-level performance analysis and optimization such as optimal power assignment among cooperative relay nodes, ergodic capacity analysis with adaptive transmission policies, outage probability, joint PHY/MAC layer design, and so on. The accuracies of our approximations have been validated with "exact" closed-form formulas that are available for specific wireless fading environments (e.g., Rayleigh and Nakagami-m channels) and via Monte Carlo computer simulations.

This article analyzes the performance of CSI-assisted cooperative amplify-and-forward (CAF) relay networks that employ both the optimal power allocation strategy among collaborating nodes and adaptive M-ary quadrature amplitude modulation (M-QAM) technique in Nakagami-m wireless fading environments. In particular, we advocate a simple yet unified numerical approach based on the marginal moment generating function (MGF) of the total received SNR to derive tight approximations or upper and lower bounds for the average bit error rate (ABER), mean achievable spectral efficiency, and outage probability performance metrics. The proposed analytical framework is sufficiently general to characterize the performance of adaptive-link CAF relay networks over a wide range of fading distributions (i.e., not restricted to Rayleigh fading) with independent but non-identically distributed (i.n.d) fading statistics across the spatially distributed diversity paths. Numerical results reveal that the optimal transmit power allocation among cooperative nodes in a practical CAF relay topologies could lead to a further substantial increase in the mean spectral efficiency compared to the equal power assignment case but at the expense of higher network overhead. The accuracies of our analytical results have been validated via Monte Carlo simulations.

In this article, we present a unified approach for the asymptotic analysis of symbol error rates for two-hops cooperative non-regenerative multi-relay networks over a myriad of stochastic channel models. The analysis can be also extended to other types of cooperative strategies and multi-hop networks without much difficulty. The proposed moment generating function (MGF) framework is also sufficiently general to encapsulate all types of coherent and non-coherent digital modulation schemes. In addition to simplifying the computation complexity of average symbol error rate (ASER) for cooperative amplify-and-forward (CAF) diversity schemes treated in the literature, we also provide accurate ASER approximations for many fading environments that heretofore had resisted a simple solution. The accuracy of our approximations has been validated with closed-form formulas that are available for specific fading environments (e.g., Rayleigh and Nakagami-m channels) and via computer (Monte Carlo) simulations.

Reliable spectrum sensing is the very task upon which the entire operation of cognitive radio rests. Blind sensing of spectral-holes using a radiometer (energy detectors) is one of the solutions that have been proposed for enabling opportunistic spectrum access. This article revisits the problem of energy detection of an unknown deterministic signal over a myriad of fading environments. Specifically, a new approach (based on the canonical series representations of the generalized Marcum Q-function of real order in conjunction with the derivatives of the moment generating function of signal-to-noise ratio) is proposed to analyze the performance of maximal-ratio combining (MRC) and square-law combining (SLC) energy detectors with independent but non-identically distributed (i.n.d) fading statistics, including Rice and mixed-fading channels. Our analytical framework is also capable of treating the Nakagami-m channels with non-integer fading severity indices as well as halfodd integer values for the time-bandwidth product u. Many of these cases were either intractable with the classical probability density function/contour integral approaches, or that heretofore had resisted simple/computationally efficient solutions. Selected numerical results are also provided for the receiver operating characteristic (ROC) of MRC and SLC diversity energy detectors over Rice and Nakagami-m channels.

Efficient spectrum sensing is one of the most crucial components in the entire operation of cognitive radio rests. Blind sensing of spectral-holes using energy detectors is one of the solutions that have been proposed for enabling opportunistic spectrum access. This article revisits the problem of energy detection of an unknown deterministic signal over a myriad of fading environments. We proposed yet another novel approach (based on the approximate finite series representations of the generalized Marcum Q-function of real order in conjunction with the derivatives of the moment generating function of signal-to-noise ratio) to analyze the performance of maximal-ratio combining (MRC) and square-law combining (SLC) energy detectors with independent but non-identically distributed (i.n.d) fading statistics, including Rice and mixed-fading channels. Our analytical framework is also capable of treating the Nakagami-m channels with non-integer fading severity indices as well as half-odd integer values for the time-bandwidth product u. Many of these cases were either intractable with the classical probability density function/contour integral approaches, or that heretofore had resisted simple/computationally efficient solutions. Comparison is also made with other series solutions that have been presented in literature and selected numerical results are provided for the receiver operating characteristic (ROC) of MRC and SLC diversity energy detectors over Rice fading channel.

In this article, we derive closed-form expressions for the area under the receiver operating characteristics (ROC) curve (hereafter, referred to as AUC metric) of energy detectors with/without diversity receiver over a myriad of fading environments. Our "unified" expression for the AUC performance metric only requires the knowledge of the derivatives of the moment generating function (MGF) of fading signal-to-noise ratio (SNR) at the receiver output. Aside from developing a new analytical framework for evaluating the AUC of energy detectors, we show that our approach also facilitates the treatment of a more generalized/realistic propagation environment (i.e., not restricted to Rayleigh/Nakagami-m channels). Moreover, the AUC analysis enables comparisons between various overlapping ROC curves to be performed easily. Different factors affecting the spectrum sensing performance were also analyzed and our key results and findings are useful in the design of cognitive radio networks.

In this paper, energy detector's performance is investigated for the blind (fixed gain) amplify & forward (AF) dual-hop relay networks using the area under the receiver operating characteristic curve (AUC) metric. Different from the well-known receiver operating characteristics (ROC) metric, AUC is a single statistical parameter which can be used to describe and compare performance of different types of energy detectors. In this article, we derive closed-form AUC expressions for the fixed-gain AF relay networks over the Rayleigh fading channels. The analysis is then extended to the maximum ratio combing (MRC) and square-law combing (SLC) diversity detectors for a dual-hop but multi-relay systems. Our analytical framework and the closed-form AUC expression is based on the kthorder derivatives of the moment generating function (MGF) of the combiner output signal-to-noise ratio (SNR).

This article develops a unified mathematical framework for maximization of the user throughput over generalized wireless channels using the symbol rate, packet length and constellation size of two distinct classes of digital modulation schemes (M-PSK and M-QAM) as optimization variables. First, we show that the throughput optimization problem for truncated selective-repeat automatic repeat request (SR-ARQ) is identical to that of no retransmission case ( NRMAX= 0 ) or the conventional SR-ARQ ( NRMAX= ∞ ) protocol that guarantees the end-to-end delivery of packet. Subsequently, we derive optimization equations for each of the above degrees of freedom in closed-form. A simple algorithm for triplet-parameter optimization is also presented. Numerical results reveal that it is sufficient to adapt symbol rate alone in the low average signal-to-noise (SNR) regime while joint optimization of both the packet length and the constellation size parameters is required in the high average SNR regime, to achieve maximum throughput in a myriad of wireless fading environments.

Cognitive radio network requires an efficient and effective means of detecting holes in the spectrum. Energy detection is one of the solutions that have been proposed for enabling opportunistic spectrum access. In this article, we present yet other simplified unified approaches to the analysis of performance of the energy detector under different fading channels. One is based on the kthorder derivative of the moment generating function (MGF) of the fading channel and the other is based on the kth moment of the output SNR of the receiver of energy detector. Both methods are derivatives of two complementary alternative series representations of Marcum-Q function using the Laguerre polynomial recently developed by [12]. Due to its faster rate of convergence, we employ the form with kth derivative of MGF of SNR of fade distribution in our computational analysis. However, the same proposed framework is easily applicable to the form requiring kthmoment of SNR of fading channel. The method presented is applicable to common multipath fade distribution (e.g., Rayleigh, Rice and Nakagami-m channels) and composite multipath/shadowing fade distribution. It also has the capability of providing results for fractional fading index, m and half-integer time-bandwidth product, u. Selected numerical results are also provided for the receiver operating characteristics (ROC) of single channel, MRC and SLC diversity energy detectors over Rice channels.

In this article, we present three novel moment generating function (MGF) based approaches for performance evaluation of multi-hop, multi-relay cooperative amplify-and-forward (CAF) networks over a myriad of stochastic channel models. Method I is based on a recursive expansion of the MGF of effective SNR for a 2-hop CAF relay network developed in [15]. The second method is also similar to Method I except that it requires the exact MGF of the end-to-end SNR for a 2-hop relay network. Method III involves the split of a multi-hop route path into two sections, evaluating the MGF of the “weakest link” in each section, and then finding the MGF of end-to-end SNR using the result in [15] for a 2-hop CAF network. We show that all the above mentioned methods closely approximate the `exact' MGF and yield performance comparable to existing bounds. Unlike the existing methods (which are restrictive to specific fading channels), our proposed solutions is quite general and can be applied to a wide range of fading environments while dramatically reducing the computational complexity of average symbol error rate (ASER) for multi-hop multi-branch CAF relay networks. Moreover, our final solutions for the MGF of end-to-end SNR are expressed in closed-form for first two methods, and in terms of a single integral for Method III. The accuracies of our approximations have been validated with “exact” formulas that are available for specific wireless fading environments and via Monte Carlo computer simulations.

The current and future wireless systems need to support a multitude of services with a wide range of data rates and reliability requirements. The limited battery resource at the mobile terminals coupled with the hostile multipath fading channel makes the problem of providing reliable multimedia services challenging. In this article, we develop a novel method to mechanize a prioritized unicast transmission at the physical layer in response to the disparate quality of service requirements for multimedia traffic (imposed by upper layers) and investigate how the unequal bit error protection offered by multiresolution modulation is capitalized at the data link layer to yield a substantial throughput gain and minimize the packet loss probability of the "more important" packets in an integrated voice/data and delay-sensitive applications (especially in poor and moderate channel conditions). However, there exists a slight throughput penalty in the high signal-to-noise ratio regime due to competitive nature of the "optimal reliable signaling rate" in an unknown time-varying channel.

This article develops a mathematical framework for analyzing the average bit error rate (ABER) performance of four different selection diversity combining (SDC) schemes over slow, frequency non-selective Nakagami-m fading channels. Aside from the traditional SDC, generalized selection combining (¿-GSC) and 'maximum matched filter output' selection methods, two new selection rules based on choosing the branch providing the largest magnitude of log-likelihood ratio (LLR) for binary phase shift keying signals (with and without phase compensation in the selection process) are also investigated. The new framework is sufficiently general to examine the effects of dissimilar fading parameters and unequal mean received signal strengths across the diversity paths. The accuracies of our analytical expressions have been validated via Monte Carlo simulation.

Compressive sampling (CS) is based on the principle of sampling signals according to their sparsity or compressibility as opposed to the rate specified by the Nyquist/Shannon sampling theorem. Shannon's separation principle of source and channel coding cannot always be used to improve CS reconstruction performance in the presence of noise, including conditions when the channel is time-varying and there is a delay constraint, or when multiple channels are present as in broadcast/multicast applications. In this paper, we propose performing joint design of the source and channel coding to improve noisy CS performance in multicast and time varying channels.

Tight bounds for the Shannon capacity of amplify-and-forward cooperative diversity networks are derived for three different adaptive source transmission policies in a myriad of fading environments: (i) constant power with optimal rate adaptation (ORA); (ii) optimal joint power and rate adaptation (OPRA); and (iii) fixed rate with truncated channel inversion (TCIFR). Our unified framework based on the moment-generating function (MGF) approach allows us to gain insights as to how fade distributions and dissimilar fading statistics across the distinct communication links will affect the Shannon capacity, without imposing any restrictions on the fading parameters.

A new exponential-type integral for the generalized M-th order Marcum Q-function QM(alpha, beta) is obtained when M is not necessarily an integer. This new representation includes a classical formula due to Helstrom for the special case of positive integer order M and an additional integral correction term that vanishes when M assumes an integer value. The new form has both computational utility (numerous existing computational algorithms for QM(alpha, beta) are limited to integer M) and analytical utility (e.g., performance evaluation of selection diversity receiver in correlated Nakagami-m fading with arbitrary fading severity index, unified analysis of binary and quaternary modulations over generalized fading channels, and development of a Markovian threshold model for block errors in correlated Nakagami-m fading channels). Tight upper and lower bounds for QM(alpha, beta) that holds for any arbitrary real order M ges 0.5 are also derived.

The current and future wireless systems need to support a multitude of services with a wide range of data rates and reliability requirements. The limited battery resource at the mobile terminals coupled with the hostile multipath fading channel makes the problem of providing reliable multimedia services challenging. In this article, we develop a novel method to mechanize a prioritized unicast transmission at the physical layer in response to the disparate quality of service requirements for multimedia traffic (imposed by upper layers) and investigate how the unequal bit error protection offered by multiresolution modulation is capitalized at the data link layer to yield a substantial throughput gain and minimize the packet loss probability of the "more important" packets in an integrated voice/data and delay-sensitive applications (especially in poor and moderate channel conditions). However, there exists a slight throughput penalty in the high signal-to-noise ratio regime due to competitive nature of the "optimal reliable signaling rate " in an unknown time-varying channel.

One of the challenges in Cognitive Radio (CR) is efficiently monitoring a wideband radio frequency (RF) spectrum in order to identify unoccupied bands. Compressive Sensing (CS) has recently been proposed to address this problem. Typical CS techniques, however, involve random projections followed by a computationally intensive signal reconstruction process. Since spectral monitoring does require full signal reconstruction - only identification of occupied regions to avoid - we propose a novel spectrum monitoring approach based on the Nyquist Folding Receiver (NYFR) in conjunction with the Analytic Wavelet Transform. The NYFR performs analog compression via a non-uniform sampling process that induces a chirp-like modulation on each received signal. This induced modulation can be measured using time-frequency analysis techniques to determine the original RF band of origin without full signal reconstruction. This paper investigates the feasibility of using the Analytic Wavelet Transform to perform NYFR information recovery in support of CR wideband spectrum sensing.

This paper presents a novel idea of Koay-Vaman (KV) transform coding technique which is based on block coding technique. It provides the ability to detect errors, correct errors and identifies the remaining block error in each of the transmission ensembles. Exploiting this property will allow design of bandwidth efficient MANET and sensor networks to support provisioning of multi-service applications. Moreover, KV Transform technique permits recovery of end user information at low Eb/N0 which is typically observed in a heavy multi-path fading environment, which is suitable for both in-door and out-door real time applications. It addresses the challenges of MANETs that require bandwidth and power efficiency, quality of service (QoS) provisioning of multi-services and scalability. KV transform technology is based on discrete sample orthogonal and invertible transform using time-frequency variation analysis. This paper presents BER performance (-7) on Rayleigh fading channel using the proposed KV transform technique with sample error correction, single selective retransmission of blocks that are in error and sample interleaving at very low Eb/No.

This paper presents exact ABER performance analysis for selective decode and forward (SDF) cooperative diversity system with BPSK modulation under Rayleigh fading where the relay has a MAP based receiver and the retransmission is based on log- likelihood-ratio (LLR) threshold. We also derive the optimum LLR threshold that minimizes ABER performance. It is shown that the LLR relay based SDF cooperative diversity system performs better than a SNR threshold based SDF system with lower implementation complexity than lambda-MRC and C-MRC schemes.

This paper develops an efficient analytical framework for evaluating the average bit-error probability (ABER) of bandlimited coherent binary phase shift keying (BPSK) in generalized fast fading channels, where the fading rate is approximately equal to the symbol rate, subject to timing errors and asynchronous cochannel interferers. Selected simulation and computational results are presented that are of interest for outdoor microcellular and macrocellular system studies. Aside from this, our ABER results also serve as lower performance bounds for practical realizable receivers (where ideal coherent detection is difficult to implement) and as an upper performance bound for bandlimited BPSK in slow fading channels where the fading rates are much slower than the symbol rate.

Outage probability and ergodic capacity are important performance measures of communication systems over fading channels. Point-to-point communication systems are known to achieve tremendous improvements in channel capacity when MIMO schemes are applied. In this paper we investigate an efficient Fixed-Talbot algorithm for numerical Laplace inversion and apply it to evaluate the outage probability and ergodic capacity of OSTBC system. The framework developed can be applied to a wide range of fading distributions (including Rice, Nakagami-m, Nakagami-Hoyt and Weibull stochastic channel models) with unequal channel gains and also to independent and non-identically distributed (i.n.d) MIMO channels.

This paper discusses the potential interference that ultra-wideband (UWB) devices can cause on third-generation (3G) mobile wireless networks. We analyze the UWB-3G coexistence problem at the link level, showing the degradation on maximum cell range due to UWB interference. We discuss the importance of proper modeling of the mobility and randomness associated with UWB and 3G, and propose a system level simulation algorithm to simulate the behavior of a 3G network in the presence of UWB interference, accounting for the multiple elements that determine and influence its performance. We present simulation results for a theoretical UMTS network, to illustrate its performance variation as the density of UWB interference sources changes.

This paper investigates the impact of multiple-input multiple-output (MIMO) implementations on both capacity and coverage of reverse link direct spread / code division multiple access (DS/CDMA) cellular systems. For the analytical analysis of the impact on the system, signal-to-interference ratio (SIR) of the reverse link DS/CDMA cellular systems with MIMO implementations is derived, and the outage probability is evaluated based on the derived formula.

This paper investigates the efficacy of MIMO implementations with adaptive spatial diversity in the uplink of direct spread/code division multiple access (DS/CDMA) cellular systems. Analytical framework to analyze both system capacity and coverage is developed based on the evaluation of outage probability of signal-to-interference ratio (SIR). It is shown that MIMO implementations can significantly improves the system performances; however, transmit diversity and receive diversity shows different system performances contrary to their link level bit error rate (BER) performances.

This paper discusses a method for analyzing the potential interference that ultra-wideband (UWB) devices can cause on UMTS networks. We discuss the UWB-UMTS coexistence problem at the link level, showing the degradation on maximum cell range due to UWB interference. Further, we discuss the importance of proper modeling of the mobility and randomness associated with UWB and UMTS, and propose a system level simulation algorithm to simulate the behavior of a UMTS network in the presence of UWB interference, accounting for the multiple elements that determine and influence its performance. We present simulation results for a theoretical UMTS network, to illustrate its performance variation as the density of UWB interference sources changes.

This paper studies the in-band interference of timehopping spread spectrum (TH-SS) UWB signals to narrow band receivers. Based on the analysis of general power spectral density (PSD) of TH-SS UWB signal, the interference of UWB signal can be partitioned into two parts: (1) additive white Gaussian noise interference (2) jamming tone interference. Following this framework, a novel analytical symbol error rate (SER) evaluation method of BPSK signal due to UWB interferences is proposed. It has been found out that as the number of inband jamming tones increases, the UWB interference effect tends to be closer to the effect of equivalent Gaussian noise.

Distributed multiple-input-multiple-output system (e.g., inter-cluster communication via cooperating nodes in a wireless network) is a topic of emerging interest. Much of previous studies assume perfect synchronization among cooperating nodes and identically distributed communication links. Such assumptions are rarely valid in practical operating scenarios. This paper develops an efficient analytical framework for computing average bit error rate of a distributed multiple-input-single- output (MISO) space-time coded system with intersymbol interference (due to imperfect location predictions and clock jitters between cooperating nodes, as well as the choice of data pulse shaping filters) over generalized fast fading channels. We show that under certain conditions distributed MISO system can outperform perfectly synchronized single-input-single-output (SISO) system.

Distributed multiple-input-multiple-output system (e.g., inter-cluster communication with cooperating nodes in a wireless sensor network) is a topic of emerging interest. Much of the previous studies in this area, however, assumed perfect synchronization among cooperating nodes and identically distributed communication links. Such assumptions are rarely valid in practical operating scenarios. This paper develops an analytical framework for computing an upper bound on the average bit error rate of a distributed space-time coded system with inter-symbol interference (due to imperfect location predictions and clock jitters between cooperating nodes and choice of data pulse shaping filters) over generalized fast fading channels. As an illustrative example, the performance of 2x1 multiple-input-single-output system that uses distributed orthogonal space-time block coding is presented, although this approach can be readily extended to analyze distributed transmit maximal ratio diversity and other variants of space-time schemes

This paper presents an analytical framework for evaluating the performance of a threshold-based generalized selection combining (GSC) scheme in equally correlated Nakagami-m fading channels. The framework extends previously published results by allowing arbitrary fading index values (mges0.5) in the analytical solution. Also, we exploit a second method which is computationally more efficient than the first approach, when fading index m is a positive integer

Using analytical approach, we investigate the impact of spatial diversity on the Erlang capacity of reverse link direct sequence code division multiple access (DS/CDMA) system. Several parameters which can affect the capacity are considered: transmit diversity order, spatial receive diversity order, the number of multipaths, fade distribution and arbitrary multipath intensity profile, maximum transmit power, soft-handoff, and traffic distribution with call admission control scheme.

The study on generalized selection combining (GSC(N,L)) diversity systems that adaptively combines a subset of N paths with the highest instantaneous signal-to-noise ratios (SNRs) out of L available diversity paths has both theoretical and practical importance in the design of low-complexity receiver structures for cellular wideband CDMA, indoor millimeter-wave and ultra-wideband communications. This paper presents a novel mathematical framework to tackle the problem at hand by deriving a single integral expression for the moment generating function (mgf) of the GSC(N,L) output SNR when the L resolvable multipaths are independent with nonidentical fading statistics. The mgf is then used to unify the performance evaluation of a broad range of digital modulation/detection schemes in practical wireless channels.

Signal fading is a ubiquitous problem in mobile and wireless communications. In digital systems, fading results in bit errors, and evaluating the average error rate under fairly general fading models and multichannel reception is often required. Predominantly to date, most researchers perform the averaging using the probability density function method or the moment generating function (MGF) method. This paper presents a third method, called the characteristic function (CHF) method, for calculating the average error rates and outage performance of a broad class of coherent, differentially coherent, and noncoherent communication systems, with or without diversity reception, in a myriad of fading environments. Unlike the MGF technique, the proposed CHF method (based on Parseval's theorem) enables us to unify the average error-rate analysis of different modulation formats and all commonly used predetection diversity techniques (i.e., maximal-ratio combining, equal-gain combining, selection diversity, and switched diversity) within a single common framework. The CHF method also lends itself to the averaging of the conditional error probability involving the complementary incomplete Gamma function and the confluent hypergeometric function over fading amplitudes, which heretofore resisted to a simple form. As an aside, we show some previous results as special cases of our unified framework.

We analyze the performance of two selective repeat automatic repeat request (SR-ARQ) protocols, which exploit the differences in bit protection levels of M-ary PSK symbols (with Gray code mapping), to support multimedia multicasting in wireless networks. Our simulation results reveal that the throughput performance of the proposed SR-ARQ schemes are significantly better than the traditional SR-ARQ protocol in a myriad of fading environments. The relative throughput improvement is generally greater for channels that experience severe deep fades and fast fading. However, the power efficiency improvement appears to be relatively insensitive to both the fade distribution and node mobility.

The article presents an analytical framework for evaluating the performance of an equally correlated multi-branch predetection equal gain combining (EGC) diversity receiver in Nakagami-m fading channels. Specifically, the characteristic function (CHF) of the EGC output signal-to-noise ratio (SNR) with L correlated inputs is derived. Selected numerical examples are provided to illustrate the effects of branch correlation and fade distribution on the average error rate and outage probability of EGC receivers.

This paper develops an analytical framework for characterizing the average symbol error rate and outage performance of a smart antenna system in cellular mobile radio environments. Specifically, the carrier-to-interference ratio statistics with N remaining (uncancelled) "weakest" cochannel interference (CCI) signals from a total of N/sub I/ signals are derived, given that both the desired user signal and the CCI signal amplitudes are subjected to Rayleigh, Rice, Nakagami-m, or Nakagami-q fading. General expressions for the outage probability and the average symbol-error rate performance of different digital modulation schemes in the presence of CCI signals are derived. Selected numerical results are presented to demonstrate the utility of the analysis in assessing the selective interference nulling performance in different fading environments.

The ability to capture significant amount of transmitted signal energy present in the resolvable multipaths using only a modest number of RAKE fingers (correlators) is an important receiver design consideration for ultra-wideband (UWB) and wideband CDMA communication systems. This, however, is achieved at the expense of RAKE receiver performance. Motivated by this need, several suboptimal hybrid receiver structures have been proposed in the literature. The study on generalized selection diversity combining with normalized threshold test per branch (T - GSC(/spl mu/,L)) is also important from a theoretical standpoint because this model encapsulates both the traditional selection diversity and maximal-ratio combining (coherent detection) or post-detection equal-gain combining (noncoherent detection) schemes as limiting cases. However, mathematical analysis for T - GSC(/spl mu/,L) has been limited to i.i.d. Rayleigh fading channels. This paper derives simple to evaluate formulas for the moment generating function (mgf) of T - GSC(/spl mu/,L) output SNR with L resolvable multipaths. In addition to providing new results for many cases that heretofore has resisted solution in a simple form, our approach also allows some of the previously obtained results to be simplified both analytically and computationally.

A generalized selection combiner (GSC) ranks the L available diversity paths and then combines a subset of M paths with the highest signal-to-noise ratios (SNRs). The cumulative distribution function (cdf) and moment generating function (mgf) of a linear sum of ordered random variables are therefore needed for computing the outage probability and error rates needed for computing the outage probability and error rates of a GSC receiver. Unfortunately, except for simple cases, these functions are either not known in closed form or exist only as multidimensional integrals. Consequently, an exact performance analysis is extremely difficult and time-consuming for many fading environments specifically when L is large. This paper therefore derives new upper and lower bounds for the cdf of GSC output SNR over generalized fading channels. These bounds are then used to derive new bounds for the average symbol error rates for a multitude of binary and M-ary digital modulation schemes in a variety of fading channel models that heretofore had resisted simple solutions.

Using a circular contour integral representation for the generalized Marcum-Q function, Q/sub m/(a,b), we derive a new closed-form formula for the moment generating function (MGF) of the output signal power of a dual-diversity selection combiner (SC) in bivariate (correlated) Nakagami-m fading with positive integer fading severity index. This result involves only elementary functions and holds for any value of the ratio a/b in Q/sub m/(a,b). As an aside, we show that previous integral representations for Q/sub m/(a,b) can be obtained from a contour integral and also derive a new, single finite-range integral representation for Q/sub m/(a,b). A new infinite series expression for the MGF with arbitrary m is also derived. These MGFs can be readily used to unify the evaluation of average error performance of the dual-branch SC for coherent, differentially coherent, and noncoherent communications systems.

Abstract The generalized selection combining (GSC) scheme that adaptively combines a subset of M strongest paths out of L available diversity paths finds applications in several wideband receivers and broadband wireless communications. In this paper, exact closed‐form expressions for the moment generating function (MGF), the probability density function (PDF) and the cumulative density function (CDF) of the GSC(M, L) output signal‐to‐noise ratio (SNR) in independent and identically distributed (i.i.d) Nakagami‐m fading channels are derived while the fading index is a positive integer. These expressions hold for any M and L and provide a comprehensive framework for performance analysis including the derivation of closed‐form formulas for the average symbol error probability (ASEP) of a broad class of binary and M‐ary modulations, mean combined SNR and the outage probability of GSC(M, L) receiver structures. When the Nakagami‐m fading index is not an integer, the MGF of GSC(M, L) output SNR is derived as an (M − 1)‐fold infinite series. With this MGF, analytical expressions for both the outage probability and error rates can be readily obtained. An easily programmable recursive solution of the MGF of GSC(M, L) output SNR is also outlined for both the positive integer and noninteger fading severity index cases. Copyright © 2002 John Wiley & Sons, Ltd.

Motivated by practical considerations in the design of low-complexity receiver structures for wideband cellular CDMA, millimeter-wave and ultra-wideband communications, the study on the generalized selection combining receiver that adaptively combines a subset of M "strongest" paths out of L available paths has intensified over the past few years. The study on GSC(M, L) receiver is also important from a theoretical standpoint because this model encapsulates both the classical selection diversity and maximal-ratio combining (coherent detection) or post-detection equal-gain combining (noncoherent detection) receiver structures as limiting cases. We first derive a concise analytical expression for the moment generating function (MGF) of the GSC(M, L) output signal-to-noise ratio with independent and identically distributed diversity paths over Rician fading channels (in terms of only a single finite range integral whose integrand is composed of tabulated functions). Previous studies have only treated either Rayleigh or Nakagami-m (1960) channel models using numerous ad-hoc approaches to simplify an M-dimensional nested integral that arise in the computation of the MGF. The novelty of our mathematical framework for computing the MGF relies on the fact that it allows us to treat all common multipath fading channel models (Rayleigh, Rician, Nakagami-m and Nakagami-q) in a unified sense, it leads to a much More elegant and computationally efficient expression than those available in the literature, and it holds for any combinations of M and L values. Using this newly derived MGFs, we provide a unified error probability analysis for many coherent and noncoherent digital modulation/detection schemes in a myriad of fading environments.

Performance evaluation of equal-gain combining (EGC) diversity receivers are known to be a much more difficult task in comparison with other diversity combining techniques such as the selection diversity or the maximal-ratio combining method. The difficulty of the above mathematical problem is compounded when the diversity branches are correlated. This paper presents a novel mathematical framework for analyzing a dual-branch EGC receiver performance over nonidentical Rayleigh and Nakagami-m fading channels when the diversity branches are correlated. It is also shown that the average bit error rate (ABER) formula for coherent BPSK and BFSK schemes reduces to the familiar expressions in the literature for the limiting case of independent diversity paths by setting the correlation coefficient to zero. Selected numerical plots that illustrate the effect of branch correction on the ABER performance are also provided.

The paper examines the impact of Gaussian distributed weighting errors (in the channel gain estimates used for coherent combination) on both the output statistics of a hybrid selection/maximal-ratio (SC/MRC) receiver and the degradation of the average symbol-error rate (ASER) performance as compared with the ideal case. New expressions are derived for the probability density function, cumulative distribution function and moment generating function (MGF) of the coherent hybrid SC/MRC combiner output signal-to-noise ratio (SNR). The MGF is then used to derive exact, closed-form, ASER expressions for binary and M-ary modulations in conjunction a nonideal hybrid SC/MRC receiver in a Rayleigh fading environment. Results for both selection combining (SC) and maximal-ratio combining (MRC) are obtained as limiting cases. Additionally, the effect of the weighting errors on both the outage rate of error probability and the average combined SNR is investigated. These analytical results provide insights into the tradeoff between diversity gain and combination losses, in concert with increasing orders of diversity branches in an energy-sharing communication system.

Abstract This article outlines a general numerical procedure for computing the probability of outage of a cellular mobile radio system that is equipped with a smart antenna to suppress a few strongest co‐channel interferers (CCI) out of a total ofNIactive interferers by adaptive null‐steering. Aside from the interference‐limited case, refined outage criterion that either treat receiver noise as CCI or consider a minimum detectable receiver signal threshold are studied. Exact closed‐form expressions for both the basic and refined outage criterion are also derived by assuming that all the CCI signals are subject to Nakagami‐mfading with a positive integer fading severity index. Selected numerical examples are provided to illustrate the application of the theory which includes the investigation into the effects of fade distribution of the CCI signals and traffic loading on the outage probability, and also the study of spectrum utilization efficiency improvement using a selective co‐channel interference nulling (cancellation) technique. Copyright © 2002 John Wiley & Sons, Ltd.

This article first presents a general numerical procedure for computing the probability of outage of a cellular mobile radio system that is equipped with a smart antenna to suppress a few strongest co-channel interferers out of a total of N/sub 1/ active interferers by adaptive null-steering. Aside from the interference-limited case, refined outage criterions that either treat receiver noise as co-channel interference (CCI) or consider a minimum detectable receiver signal threshold are studied. Exact closed-form formulas for both the basic and refined outage criterions are also derived by assuming that all the CCI signals are subject to Nakagami-m fading (positive integer fading index). Selected numerical examples are provided to illustrate the application of the theory which include the investigation into the effects of fade distribution of the CCI signals and traffic loading on the outage probability, and also the study of spectrum utilization efficiency improvement using a selective co-channel interference nulling technique.

Motivated by potential applications to wideband cellular DS-CDMA and millimeter-wave communications, the study of the generalized selection combining (GSC) receiver that adaptively combines a subset of M "strongest" paths out of L available paths has intensified over the past few years. The study of the GSC(M, L) receiver is also important from a theoretical standpoint because this model encapsulates both the classical selection combining receiver and the maximal-ratio combining receiver as limiting cases. Despite its importance, published results on GSC(M, L) receiver performance in a generalized fading channel are still very limited, mainly due to the mathematical difficulty encountered while computing the first-order statistics of a linear sum of ordered random variables. This paper provides a partial solution to the problem on hand by deriving relatively simple-to-evaluate expressions for the moment generating function (MGF) of GSC output SNR in a variety of fading environments given that the individual branch SNRs are independent and identically distributed. Moreover, our generic single integral expression for the MGF of GSC output SNR reduces to a closed-form formula if the branch amplitudes follow either Rayleigh or Nakagami-m (positive integer fading index) distribution. An easily programmable recursive solution of the MGF in Nakagami-m channels is also provided. Our expressions hold for any M and L values, and thus facilitate a comprehensive analysis of GSC systems including the average symbol error probability (ASEP) analysis of a broad class of binary and M-ary modulations, average combined SNR and the outage rate of error probability analysis.

Exact error probability expressions for noncoherent M-ary frequency-shift-keying (MFSK) systems that employ postdetection equal-gain diversity over Rayleigh, Rician and Nakagami-m channels are derived using a Laplace derivative formula. Both independent and generically correlated fading cases are considered. For independent fading, closed-form solutions are also derived for both Nakagami-q fading (either with identical or dissimilar fading statistics) and mixed fading cases. Previous results are shown to be specific instances of our general expressions. Additionally, a new concise, derivative formula is obtained for calculating the bit error rate of square-law detected multichannel binary differential phase-shift-keying (BDPSK) signals. All these expressions are applicable in many cases of practical interest and provide accurate predictions of the performance of both binary and M-ary orthogonal signalling over generalized fading channels (with arbitrary fading parameters). Several numerical examples are presented to illustrate the application of the theory, including the investigation into optimal diversity order in energy-sharing communications, characterization of block orthogonal codes with soft-decision decoding (i.e., MFSK may also be viewed as a form of repetition coding) and analysis of MFSK with space (antenna) diversity.

This paper derives new closed-form formulas for the error probabilities of single and multichannel communications in Rayleigh and Nakagami-m (1960) fading. Closed-form solutions to three generic trigonometric integrals are presented as part of the main result, providing a unified method for the derivation of exact closed-form average symbol-error probability expressions for binary and M-ary signals with L independent channel diversity reception. Both selection-diversity and maximal-ratio combining (MRC) techniques are considered. The results are generally applicable for arbitrary two-dimensional signal constellations that have polygonal decision regions operating in a slow Nakagami-m fading environments with positive integer fading severity index. MRC with generically correlated fading is also considered. The new expressions are applicable in many cases of practical interest. The closed-form expressions derived for a single channel reception case can be extended to provide an approximation for the error rates of binary and M-ary signals that employ an equal-gain combining diversity receiver.

Two unified expressions for computing the refined outage criterion (which considers the receiver noise) in cellular mobile radio systems are derived using the Laplace and Fourier inversion formulas. Since these expressions do not impose any restrictions on the signal statistics while being easy to program, they provide a powerful tool for outage analysis over generalized fading channels. We also assess compatibility and applicability of previously published approaches that treat noise as cochannel interference (noise-limited model) or consider a minimum detectable receiver signal threshold and receiver noise. The outage probability in an interference-limited case can be evaluated directly by setting the minimum power threshold to zero. The analysis of correlated interferers is presented. Results are also developed for a random number of interferers. Several new closed-form expressions for the outage probability are also derived. Some previous studies have suggested approximating Rician desired signal statistics by a Nakagami-m (1960) model (with positive integer fading severity index) to circumvent the difficulty in evaluating the outage in Rician fading. The suitability of this approximation is examined by comparing the outage performance under these two fading conditions. Surprisingly, some basic results for Nakagami-m channel have been overlooked, which has led to misleadingly optimistic results with the Nakagami-m approximation model. However, similar approximation for the interferer signals is valid.

The moment generating function (MGF) of the signal power at the output of dual-branch switch-and-stay selection diversity (SSD) combiners is derived. The first-order derivative of the MGF with respect to the switching threshold is also derived. These expressions are obtained for the general case of correlated fading and nonidentical diversity branches, and hold for any common fading distributions (e.g., Rayleigh, Nakagami-m, Rician, Nakagami-q). The MGF yields the performance (bit or symbol error probability) of a broad class of coherent, differentially coherent and noncoherent digital modulation formats with SSD reception. The optimum switching threshold (in a minimum error rate sense) is obtained by solving a nonlinear equation which is formed by using the first-order derivative of the MGF. This nonlinear equation can be simplified for several special cases. For independent and identically distributed diversity branches, the optimal switching threshold in closed form is derived for three generic forms of the conditional error probability. For correlated Rayleigh or Nakagami-m fading with identical branches, the optimal switching threshold in closed form is derived for the noncoherent binary modulation formats. We show previously published results as special cases of our unified expression. Selected numerical examples are presented and discussed.

Abstract The Cauchy–Schwarz bounding technique is used to derive useful bounds on the generalized Marcum Q‐function and its complement. Three new exponential‐type bounds on QM (α, β) are derived, and these are found to be tight and useful for a number of applications of interest. One such example is the derivation of an upper bound on the average symbol error rate probability for noncoherent and differentially coherent communication systems over generalized fading channels. It is shown that these exponential‐type bounds are considerably tighter than the Chernoff bound (Rappaport SS. IEEE Trans. on Information Theory 1971; 17: 497–498) counterpart. Numerical results also reveal that the tightness of one of the exponential‐type bounds is comparable to the bound obtained in Simon and Alouini (IEEE Trans. on Communications 2000: 359–366), while another is found to be superior than that obtained in Simon and Alouini over a wide range of arguments. Copyright © 2001 John Wiley & Sons, Ltd.

This paper presents a general method for calculating the average error rates and outage performance of a broad class of coherent, differentially coherent and noncoherent communication systems with/without diversity reception in a myriad of fading environments. Unlike the moment generating function (MGF) technique, the proposed characteristic function (CHF) method based on Parseval's theorem enables us to unify the average error rate analysis of different modulation formats and all commonly used predetection diversity techniques (i.e., maximal-ratio combining (MR), equal-gain combining (EG), selection diversity (SD), switched diversity (SW) and hybrid diversity systems) in a single common framework. The CHF method also lends itself to the averaging of the conditional error probability (CEP) involving the complementary incomplete Gamma function and the confluent hypergeometric function over fading amplitudes, which heretofore resisted to a simple form. As an aside, we show previous results as special instances of our unified framework.

The paper examines the impact of Gaussian distributed weighting errors (in the channel gain estimates used for coherent combination) on the statistics of the output of hybrid selection/maximal-ratio (SC/MRC) receiver as well as the degradation of the average symbol error rate (ASER) performance from the ideal case. New expressions for the probability density function (PDF), cumulative distribution function (CDF) and moment generating function (MGF) of the coherent hybrid SC/MRC combiner output signal-to-noise ratio (SNR) are derived. The MGF is then used to derive exact closed form ASER formulas for binary and M-ary modulations employing a nonideal hybrid SC/MRC receiver in Rayleigh fading. Results for both SC and MRC are obtained as limiting cases. The effect of the weighting errors on the outage rate of error probability and the average combined SNR are also investigated. These analytical results provide some insights into the trade-off between diversity gain and combination losses with the increasing order of diversity branches in an energy-sharing communication system.

The efficacy of an hybrid M/L-SC/MRC receiver structure (also known as generalized selection combining) in a variety of fading environments is analyzed by deriving considerably simpler expressions for the statistics (i.e., moment generating function (MGF) and cumulative distribution function (CDF)) of the combiner output signal-to-noise ratio (SNR) on Nakagami-m channels with arbitrary parameters. Different from previous studies, these results hold for arbitrary orders of M and L. As well as for any real values of fading severity index m/spl ges/0.5. A simple procedure for deriving an exact closed-form expression for the MGF of SNR when the fading index assumes a positive integer m value is also outlined. These MGFs are then used to derive the average symbol error probability (ASEP) for a broad class of binary and M-ary modulations employing coherent SC/MRC receiver. Analytical expressions for computing the outage rate of error probability and the average combined output SNR are also derived. Finally, computationally efficient but approximate solutions for the MGF of SNR are presented.

Performance analysis of equal-gain combining (EGC) diversity systems is notoriously difficult only more so given that the closed-form probability density function (PDF) of the EGC output is only available for dual-diversity combining in Rayleigh fading. A powerful frequency-domain approach is therefore developed in which the average error-rate integral is transformed into the frequency domain, using Parseval's theorem. Such a transformation eliminates the need for computing (or approximating) the EGC output PDF (which is unknown), but instead requires the knowledge of the corresponding characteristic function (which is readily available). The frequency-domain method also circumvents the need to perform multiple-fold convolution integral operations, usually encountered in the calculation of the PDF of the sum of the received signal amplitudes. We then derive integral expressions for the average symbol-error rate of an arbitrary two-dimensional signaling scheme, with EGC reception in Rayleigh, Rician, Nakagami-m (1960), and Nakagami-q fading channels. For practically important cases of second- and third-order diversity systems in Nakagami fading, both coherent and noncoherent detection methods for binary signaling are analyzed using the Appell hypergeometric function. A number of closed-form solutions are derived in which the results put forward by Zhang (see ibid., vol.45, p.270-73, 1997) are shown to be special cases.

A new, infinite series representation for the error function is developed. It is especially suitable for computing erfc(x) for large x. For instance, for any x/spl ges/4, the error function can be evaluated with a relative error less than 10/sup -10/ by using only eight terms. Similarly, the error function can be evaluated with a relative error less than 8/spl times/10/sup -7/ for any x/spl ges/2 using just six terms. An analytical bound is derived to show that the total error due to series truncation and undersampling rapidly decreases as x increases. Comparisons with two other series are provided.

A frequent problem in digital communications is the computation of the probability density function (PDF) and cumulative distribution function (CDF), given the characteristic function (CHF) of a random variable (RV). This problem arises in signal detection, equalizer performance, equal-gain diversity combining, intersymbol interference, and elsewhere. Often, it is impossible to analytically invert the CHF to get the PDF and CDF in closed form. Beaulieu (1990, 1991) has derived an infinite series for the CDF of a sum of RVs that has been widely used. We rederive his series using the Gil-Pelaez (1951) inversion formula and the Poisson sum formula. This derivation has several advantages including both the bridging of the well-known sampling theorem with Beaulieu's series and yielding a simple expression for calculating the truncation error term. It is also shown that the PDF and CDF can be computed directly using a discrete Fourier transform.

New, simple yet very accurate closed-form expressions for calculating the symbol error probability (SER) of multilevel quadrature amplitude modulation (MQAM) in conjunction with L-fold antenna diversity on a Nakagami (1960) fading channel are presented. Both maximal-ratio (MRC) and equal-gain (EGC) predetection diversity combining techniques have been considered. The exact closed-form formula for a MRC diversity system removes the limitations of previous studies in the literature which have been limited to Rayleigh fading. Moreover, an exact analysis of EGC for MQAM has not been reported previously despite its practical interest. The exact SER is expressed as a finite-range integral. Our unified expressions are sufficiently general to handle arbitrary fading parameters as well as dissimilar mean signal strengths across the diversity branches. The generality and computational efficiency of these new formulas render themselves as a powerful tool for SER analysis in different fading conditions.

A unified expression for computing the probability of outage in cellular mobile radio systems is derived. The method handles non-integer Nakagami fading indexes, unequal Rice factors, dissimilar shadowing spreads, unequal transmit powers as well as all the common fading distributions (Rayleigh, Rice, Nakagami-m, Nakagami-q, lognormal-Rice, Suzuki and lognormal-Nakagami-m). The exact outage probability is expressed in terms of a finite-range integral. The integral can also be approximated by a Gauss-Chebychev quadrature (GCQ) formula requiring the knowledge of the moment generating function (MGF) at only a small number of points. An estimate of the remainder term is also derived. This technique lends itself to a powerful tool for outage analysis since it does not impose any restrictions while being easy to program. Some previous studies have suggested approximating Rician desired signal statistics by a Nakagami-m model to circumvent the difficulty in evaluating the outage in Rician fading. We asses the suitability of this approximation by providing a comparison study of the outage performance in these two fading conditions. Surprisingly, some basic results for Nakagami-m channel have been overlooked, which has led to misleadingly optimistic results with the Nakagami-m approximation model.

This paper outlines an efficient optimization method to determine the optimal power allocation plan that guarantees the quality of service contracts for multimedia traffic while ensuring minimal power consumption in a systematic manner. Both perfect and imperfect power-controlled cases in a multicell operating environment have been considered. This method may also be used to determine the capacity region of the integrated network for a given set of system parameters.

An exact analytical expression in a simple form for computing the average symbol error rate (SER) of an arbitrary two-dimension signaling format with equal-gain diversity (EGC) receiver is not available in the literature despite its practical and theoretical importance. The principle difficulty is finding a closed-form expression for the probability density function (PDF) of a sum of L (i.e., diversity order) random fading amplitudes. We develop an alternative, direct technique to evaluate the exact performance of EGC diversity systems (expressed in terms of a single or double finite-range integrals) in Rayleigh, Rician and Nakagami fading channels. Our new approach relies on the use of Parseval's theorem to transform the error integral into the frequency domain. Since the Fourier transform of the PDF is the characteristic function (CHF), which is available in this case, our solution is general and exact. The CHF method also circumvents the need to perform an L-fold convolution integral which is usually encountered in the calculation of the PDF of the sum of the received signal amplitudes. Interestingly, we can also get some new closed-form solutions for binary CPSK and CFSK in the Nakagami fading channel for all L/spl les/3. Closed-form formulas for binary DPSK and NCFSK with EGC may also be obtained for L<3.

This paper outlines a unified approach to performance evaluation of a broad class of coherent, differentially coherent and noncoherent digital communication systems, with dual-branch switched diversity (SWC) reception over generalized fading channels. The moment generating function (MGF) of the signal power at the output of the SWC combiner and the first-order derivative of the MGF with respect to the switching threshold are derived. These expressions are obtained for the general case of correlated fading and nonidentical diversity branches, and hold for any common fading distributions (e.g., Rayleigh, Nakagami-m, Rician, Nakagami-q). The optimum switching threshold (in a minimum error rate sense) is obtained by solving a nonlinear equation which is formed by using the first-order derivative of the MGF. This nonlinear equation can be simplified for several special cases: (a) closed-form expressions for the optimal switching threshold are derived for three generic forms of the conditional error probability by assuming independent and identically distributed diversity branches; and (b) a closed-form formula for the optimal switching threshold is derived for the non-coherent binary modulation formats in correlated Rayleigh or Nakagami-m fading with identical fading statistics.

An analytical framework to evaluate the performance of different predetection diversity techniques in various mobile radio environments is developed. The average bit-error rate analysis applies to phase coded spread-spectrum systems, over Nakagami multipath fading channels. A simple and practical selection combining rule is considered. Our numerical results reveal that this new low-complexity receiver structure exhibits comparable performance to that of an optimum linear diversity combiner when the channel does not experience severe fading and for small diversity orders, conditioned on the situation that all the diversity branches have identical mean signal strengths. In this study, we also investigate the effect of variations in the mean signal and noise power levels on each of the independent diversity branches. This is an important consideration because in practice equal mean signal strengths rarely occur, which results in loss of diversity gain. We found that the signal-plus-noise-and-interference selection model outperforms the traditional signal-to-interference-plus-noise ratio selection scheme if the discrepancy between the mean signal strengths are small, owing to the statistical nature of the multiple-access interference.

This article investigates the asymptotic error-rate behavior for the noncoherent on-off keying (OOK) signaling scheme in different fading environments and at both extremes of the signal-to-noise ratio (SNR). A transcendental equation to compute the optimum threshold level of noncoherent OOK operating over a Rician fading channel is derived. The optimum threshold level and its corresponding ratio of the mark and space error probabilities in additive white Gaussian noise (AWGN). Rayleigh, and Rician channels are tabulated as a function of the SNR. Geist (see ibid., vol.42, p.225, 1994) has shown that mark and space errors contribute equally to the average error probability in an AWGN channel when the SNR is large with optimum threshold setting. We show that mark errors predominate when the SNR is small and/or in fading channels.

Exact integral expressions are derived for calculating the symbol-error rate (SER) of multilevel quadrature amplitude modulation (MQAM) in conjunction with L-fold antenna diversity on arbitrary Nakagami fading channel. Both maximal-ratio combining (MRC) (in independent and correlated fading) and equal-gain combining (EGC) predetection (in independent fading) diversity techniques have been considered. Exact closed-form SER expressions for two restricted Nakagami fading cases (MRC reception) are also derived. An exact analysis of EGC for MQAM has not been reported previously, despite its practical interest. Remarkably, the exact SER integrals can also be replaced by a finite-series approximation formula. A useful procedure for computing the confluent hypergeometric series is also presented.

This paper surveys some of the diversity techniques commonly used in cellular radio and satellite communication systems to mitigate the detrimental effects of signal fading. Subsequently, an analytical technique well suited to numerical analysis is presented for computing the average symbol error probability (SER) of a wide class of coherent, differentially coherent and noncoherent communication systems with microdiversity reception under a myriad of fading scenarios. We restrict our analysis to a predetection maximal-ratio combining (MRC) scheme, although this method applies to other diversity combining techniques as well. Our novel derivation relies upon the properties of the moment generating function (MGF) of the fading channels, the use of an alternative exponential form of the complementary error function, and the application of Gauss-Chebychev quadrature (GCQ) rules. The closed-form expressions obtained are sufficiently general to allow for arbitrary fading parameters as well as dissimilar mean signal strengths across the diversity branches. Moreover, this method is computationally stable and approximates the true value of average SER within any degree of accuracy.

This paper outlines an efficient method to concurrently optimize a multiplicity of design variables for continuous selective-repeat (SR) and go-back-N (GBN) automatic repeat request (ARQ) strategies, both in noiseless and noisy feedback channels. For these ARQ protocols, we adapt either the number of identical message blocks sent in each transmission (in the case of GBN scheme) or the number of copies of a block retransmitted to handle a NACKed codeword (for the SR protocol) dynamically to the estimated channel condition. The channel state information is obtained by counting the contiguous acknowledgment (ACK or NACK) messages. Exploiting the asymptotic properties of the steady state probability expressions, we show analytically that the optimum solution indeed lies in the infinite space. Subsequently, a simple expression to estimate the suboptimal design parameters is suggested. Our approach of minimizing the mean-square error function yields to a quantitative study of the appropriateness of the selected parameters. Exact analytical expressions that allows us to compute the throughput crossover probability between any two arbitrary multicopy transmission modes are derived. The results provide fundamental insights into how these key parameters interact and determine the system performance.

This letter presents a simple method to simultaneously optimize a multiplicity of design parameters for the adaptive automatic repeat request strategy previously reported, and subsequently provides a quantitative measurement that reflects the appropriateness of the selected parameters. An exact analytical expression that allows us to compute the throughput crossover probability between the two different protocols is derived. The results provide fundamental insights into how these key parameters interact and determine the system performance.

This paper outlines a systematic and efficient method to concurrently optimize a multiplicity of design variables for an adaptive go-back-N ARQ strategy both in noiseless and noisy feedback channels. For this continuous ARQ protocol, we adapt the number of identical message blocks sent in each transmission dynamically to the estimated channel condition. The channel state information is obtained by counting the contiguous ACK and NACK messages. Exploiting the asymptotic properties of the steady-state probability expressions, we show analytically that the optimum solution indeed lies in the infinite space. Subsequently, a simple method to estimate the suboptimal design parameters is suggested. Our approach of minimizing the mean square error (MSE) function also yields to a quantitative study of the appropriateness of the selected parameters. The results provide fundamental insights into how these key parameters interact and determine the system performance.

Future multi-media wireless communications systems will require high spectral efficiencies, with reduced receiver complexity. MC-CDMA systems using orthogonal spreading codes systems can increase the spectral efficiency while employing low complexity correlation receivers. A major limitation of multi-carrier systems is the potential for a high crest factor. We examine the requirements for reducing the crest factor in multi-carrier systems, and emphasise the benefits of orthogonal codes for correlation detectors. Our results demonstrate the effectiveness of orthogonal codes in reducing the crest factor while providing low complexity receiver solutions.