Partial ordering of communication channels has applications in performance analysis, and goes beyond comparisons of channels just on the basis of their Shannon capacity or error probability. Shannon defined a partial order of channel inclusion based on convex mixture of input/output degradations of a discrete memoryless channel (DMC). In this paper, extensions to channels other than DMCs are considered. In particular, additive noise channels and phase degraded channels, and multiple input multiple output (MIMO) linear Gaussian channels (LGC) are considered. For each of these models, the conditions under which the partial order becomes a lattice are also discussed.

A relationship between the growth-rate of log-optimal portfolios and capacity of fading single-input multiple output (SIMO) channels are established. Using this relation, stock vector stochastic processes that model the investment environments are stochastically ordered using different criteria. The presence of side information (SI) is considered, and a bound on the gains in the growth-rate due to SI is derived along with data processing inequality and convexity properties. A statistical test on the usefulness of SI that does not require the computation of the optimal portfolio vector in the presence of SI is introduced and its several variants are discussed.

A consensus based distributed algorithm to compute the spectral radius of a network is proposed. The spectral radius of the graph is the largest eigenvalue of the adjacency matrix, and is a useful characterization of the network graph. Conventionally, centralized methods are used to compute the spectral radius, which involves eigenvalue decomposition of the adjacency matrix of the underlying graph. Our distributed algorithm uses a simple update rule to reach consensus on the spectral radius, using only local communications. We consider time-varying graphs to model packet loss and imperfect transmissions, and provide the convergence characteristics of our algorithm, for both static and time-varying graphs. We prove that the convergence error is a function of principal eigenvector of adjacency matrix of the graph and reduces as O(1/t), where t is the number of iterations. The algorithm works for any connected graph structure. Simulation results supporting the theory are also presented.

In this innovative practice work-in-progress paper, we discuss novel methods to teach machine learning concepts to undergraduate students. Teaching machine learning involves introducing students to complex concepts in statistics, linear algebra, and optimization. In order for students to better grasp concepts in machine learning, we provide them with hands-on exercises. These types of immersive experiences will expose students to the different stages of the practical uses of machine learning. The data collection apparatus is based on applications (apps) developed for the Android platform. Due to the accessible nature of the app and the exercises based on the app, this approach is useful for students across all majors.We provide the students with three different sets of activities, the first of which will introduce the basics of machine learning with specially designed artificial datasets. The second and third activities involve data collection, modeling, training, and testing, as applied to machine learning algorithms. The second activity will involve collecting touch/swipe data on mobile devices from students as they use a touch logger app. The third activity uses the Reflections app to collect cross-correlation data from rooms with different purposes. These hands-on activities guide the students through every step of the machine learning process. Student learning is assessed for each activity by holding workshops for undergraduate students. A workshop with the first activity outlining the basics of machine learning was given in the fall of 2018 and significant student learning was demonstrated. Workshops for the second and third activities are planned for the fall semester of 2019. Results from these workshops will be presented at the conference.

We propose a novel graph filtering method for semi-supervised classification that adopts multiple graph shift matrices to obtain more flexibility in dealing with misleading features. The resulting optimization problem is solved with a computationally efficient alternating minimization approach. In simulation experiments, we implement both conventional and our proposed graph filters as semi-supervised classifiers on real and synthetic datasets to demonstrate advantages of our algorithms in terms of classification performance.

In this paper, we present a distributed array processing algorithm to analyze the power output of solar photo-voltaic (PV) installations, leveraging the low-rank structure inherent in the data to estimate possible faults. Our multi-agent algorithm requires near-neighbor communications only and is also capable of jointly estimating the common low rank cloud profile and local shading of panels. To illustrate the workings of our algorithm, we perform experiments to detect shading faults in solar PV installations within a single ZIP code. Additionally, we also derive a Bayesian lower bound on the shading parameter's mean squared estimation error. The results are promising and show that we can successfully estimate the fraction of partial shading in solar installations that can usually go unnoticed.

This paper aims to develop a fast dynamic-texture prediction method, using tools from non-linear dynamical modeling, and fast approaches for approximate regression. We consider dynamic textures to be described by patch-level non-linear processes, thus requiring tools such as delay-embedding to uncover a phase-space where dynamical evolution can be more easily modeled. After mapping the observed time-series from a dynamic texture video to its recovered phase-space, a time-efficient approximate prediction method is presented which utilizes locality-sensitive hashing approaches to predict possible phase-space vectors, given the current phase-space vector. Our experiments show the favorable performance of the proposed approach, both in terms of prediction fidelity, and computational time. The proposed algorithm is applied to shading prediction in utility scale solar arrays.

The authors consider a multi‐hop amplify‐and‐forward full‐duplex relay system. They take a signal flow graph approach for finding the input–output relationship using Mason's gain formula, and use this expression to compute the system outage probability for different equalisers. For sufficiently large target rates, full‐duplex relaying with equalisers has lower outage probability than half‐duplex relaying, despite the higher residual self‐interference (RSI) of the full‐duplex approach. The full‐duplex system with (unequalised) matched filter at the destination is seen to be sensitive to RSI which shows that equalisation at the destination is a feasible approach to combating the RSI for full‐duplex multi‐hop systems.

Channel estimation and optimal training sequence design for full-duplex one-way relays are investigated. We propose a training scheme to estimate the residual self-interference (RSI) channel and the channels between nodes simultaneously. A maximum likelihood estimator is implemented with the Broyden-Fletcher-Goldfarb-Shanno algorithm. In the presence of RSI, the overall source-to-destination channel becomes an inter-symbol-interference (ISI) channel. With the help of estimates of the RSI channel, the destination is able to cancel the ISI through equalization. We derive and analyze the Cramer-Rao bound (CRB) in closed-form by using the asymptotic properties of Toeplitz matrices. The optimal training sequence is obtained by minimizing the CRB. Extensions for the fundamental one-way relay model to the frequency-selective fading channels and the multiple relays case are also considered. For the former, we propose a training scheme to estimate the overall channel, and for the latter the CRB and the optimal number of relays are derived when the distance between the source and the destination is fixed. Simulations using LTE parameters corroborate our theoretical results.

Stochastic orders on point processes are partial orders which capture notions like being larger or more variable. Laplace functional ordering of point processes is a useful stochastic order for comparing spatial deployments of wireless networks. It is shown that the ordering of point processes is preserved under independent operations such as marking, thinning, clustering, superposition, and random translation. Laplace functional ordering can be used to establish comparisons of several performance metrics such as coverage probability, achievable rate, and resource allocation even when closed form expressions of such metrics are unavailable. Applications in several network scenarios are also provided where tradeoffs between coverage and interference as well as fairness and peakyness are studied. Monte‐Carlo simulations are used to supplement our analytical results.

A relay-aided cooperative underlay cognitive radio system with random number of secondary users (SU), and an interference constraint at the primary receiver (PR) is considered. When the primary (PU) is active, those SUs whose interference at the PR is above a threshold will amplify-and-forward PU's signal to enhance the PU's performance, and those SUs below this threshold will proceed with their own transmission in an underlay fashion. As the mean number of relay SUs increases, the PU's performance is improved but causes degradation of SU system performance. We study the optimal trade-off between the achievable rate of the SU and PU systems in the large mean number of SUs regime. This is then followed by a derivation of the optimal ratio between the mean number of relays and underlay SUs. Monte-Carlo simulations are used to verify our analytical results.

We consider the joint scheduling-and-power- allocation problem of a downlink cellular system. The system consists of two groups of users: real- time (RT) and non-real-time (NRT) users. Given some average power constraint on the base station, the problem is to find an algorithm that satisfies the RT and NRT quality-of-service (QoS) constraints. The RT QoS constraints guarantee the portion of RT packets that miss their deadline are no more than a pre-specified threshold. On the other hand, the NRT QoS is only to guarantee the stability of their queues. We propose a sum-rate- maximizing algorithm that satisfy all QoS and average power constraints. The proposed power allocation policy has a closed form expression for the two groups of users. However, the power policy of the RT users differ in structure from the NRT users. The proposed algorithm is optimal for the on-off channel model with a polynomial-time scheduling complexity. Using extensive simulations, the throughput of the proposed algorithm is shown to exceed existing approaches.

This paper proposes to unify fading distributions by modeling the magnitude-squared of the instantaneous channel gain using generalized gamma convolutions (GGC). A random variable is said to be GGC, if it can be written as the limit of a sum of independent gamma variables potentially with different parameters. We show that GGC random variables have many useful mathematical properties, that are applied in the performance analysis of wireless systems. The proposed unification subsumes several classes of multipath and shadowing fading distributions previously proposed in the wireless communications literature.

Device-to-Device (D2D) communications has been proposed to provide high data rate service in cellular networks via direct transmissions between clients. A cooperative D2D communications system allowing multiple D2D pairs overlaying a downlink cellular network simultaneously is considered. Each individual D2D transmitter will allocate its transmission power to decode-and-forward cellular users' traffic while superimposing its own signal. We provide accurate second order approximations and closed form expressions for the average achievable rates of both cellular user and individual D2D user for various spectrum accessing policies. We show that having multiple D2D users, the per-user rates of both cellular and D2D systems can be improved simultaneously.

Training schemes for full duplex two-way relays are investigated. We propose a novel one-block training scheme with a maximum likelihood estimator to estimate the channels between the nodes as well as the residual self-interference (RSI) channel simultaneously. A quasi-Newton algorithm is used to solve the estimator. As a baseline, a multi-block training scheme is also considered. The Cramer-Rao bounds of the one-block and multi-block training schemes are derived. By using the Szegö's theorem about Toeplitz matrices, we analyze how the channel parameters and transmit powers affect the Fisher information. We show analytically that exploiting the structure arising from the RSI channel increases its Fisher information. Numerical results show the benefits of estimating the RSI channel.

An uplink cognitive radio system with a single primary user (PU) and multiple secondary users (SUs) is considered. The SUs have an individual average delay constraint and an aggregate average interference constraint to the PU. If the interference channels between the SUs and the PU are statistically different due to the different physical locations of the SUs, the SUs will experience different delay performances. This is because SUs located closer to the PU transmit with lower power levels. A dynamic scheduling-and- power-allocation policy that uses the dynamic programming, is proposed. The proposed policy can provide the required average delay guarantees to all SUs irrespective of their location as well as protect the PU from harmful interference. The policy is shown to be asymptotically delay optimal in the light traffic regime. Motivated, by the high complexity of the dynamic programming algorithm in the optimal policy we exploit the structure of the problem's solution to present an alternative suboptimal policy. Through simulations we show that in both light and heavy traffic regimes, the delay performance of the suboptimal policy is within 0.3% from the optimal policy and both outperforming existing methods.

A distributed consensus algorithm for estimating the degree distribution of a graph is proposed. The proposed algorithm is based on average consensus and in-network empirical mass function estimation. It is fully distributed in the sense that each node in the network only needs to know its own degree, and nodes do not need to be labeled. The algorithm works for any connected graph structure in the presence of communication noise. The performance of the algorithm is analyzed. A discussion on how the properties of the graph degree distribution can be exploited for post-processing after consensus is reached is given. Simulation results corroborating the theory are also provided.

An uplink multisecondary user (SU) cognitive radio system having average delay constraints as well as an interference constraint to the primary user (PU) is considered. If the interference channels between the SUs and the PU are statistically heterogeneous due to the different physical locations of the different SUs, the SUs will experience different delay performances. This is because SUs located closer to the PU transmit with lower power levels. Two dynamic scheduling-and-power-allocation policies that can provide the required average delay guarantees to all SUs irrespective of their locations are proposed. The first policy solves the problem when the interference constraint is an instantaneous one, while the second is for problems with long-term average interference constraints. We show that although the average interference problem is an extension to the instantaneous interference one, the solution is totally different. The two policies, derived using the Lyapunov optimization technique, are shown to be asymptotically delay optimal while satisfying the delay and interference constraints. Our findings are supported by extensive system simulations and shown to outperform the existing policies as well as shown to be robust to channel estimation errors.

This paper introduces diffusion adaptation strategies over distributed networks with nonlinear transmissions, motivated by the necessity for bounded transmit power. Local information is exchanged in real-time with neighboring nodes in order to estimate a common parameter vector via constrained nonlinear transmissions, using an adaptive learning algorithm. We propose nonlinear diffusion strategies for such an adaptive estimation. We will study convergence properties of the proposed algorithm in the mean and the mean-square sense. Simulations support the performance analysis and show that the proposed algorithm performs close to the linear case with the added advantage of power savings.

A new stochastic order between two fading distributions is introduced. A fading channel dominates another in the ergodic capacity ordering sense, if the Shannon transform of the first is greater than that of the second at all values of average signal-to-noise ratio. It is shown that some parametric fading models, such as the Nakagami-m, Rician, and Hoyt are distributions that are monotonic in their line of sight parameters with respect to the ergodic capacity order. Some operations under which the ergodic capacity order is preserved are also discussed. Through these properties of the ergodic capacity order, it is possible to compare under two different fading scenarios, the ergodic capacity of a composite system involving multiple fading links with coding/decoding capabilities only at the transmitter/receiver. Such comparisons can be made even in cases when a closed form expression for the ergodic capacity of the composite system is not analytically tractable. Applications to multiple access channels, and extensions to multiple-input multiple-output systems are also discussed.

This paper studies several problems concerning channel inclusion, which is a partial ordering between discrete memoryless channels (DMCs) proposed by Shannon. Specifically, majorization-based conditions are derived for channel inclusion between certain DMCs. Furthermore, under general conditions, channel equivalence defined through Shannon ordering is shown to be the same as permutation of input and output symbols. The determination of channel inclusion is considered as a convex optimization problem, and the sparsity of the weights related to the representation of the worse DMC in terms of the better one is revealed when channel inclusion holds between two DMCs. For the exploitation of this sparsity, an effective iterative algorithm is established based on modifying the orthogonal matching pursuit algorithm.

A single primary user cognitive radio system with multiuser diversity at the secondary users (SUs) is considered, where there is an interference constraint between SUs and the primary receiver. The SU with the highest instantaneous signal-to-noise ratio is selected for communication from a set of active users, which also satisfies the interference constraint. The active number of SUs is shown to be binomial, negative binomial, or Poisson-binomial distributed depending on various modes of operation. The outage probability in the slow-fading scenario is also studied. This is then followed by a derivation of the scaling law of the ergodic capacity and bit error rate (BER) averaged across the fading and the user distribution for a large mean number of users. The ergodic capacity and average BER under the binomial user distribution are shown to outperform the negative binomial case with the same mean number of users. Moreover, the Poisson distribution is used to approximate the user distribution under the non-independent and identically distributed interference scenario and compared with binomial and negative binomial distributions in a stochastic ordering sense. Monte Carlo simulations are used to supplement our analytical results and compare the performances under different user distributions.

In this paper, we describe a new set of software functions and associated exercises that can be used for teaching orthogonal frequency division multiplexing (OFDM) concepts in undergraduate DSP and communications courses. These tools can be used to simulate, visualize, and analyze the performance and behavior of OFDM systems by considering different input signals and communication channels. OFDM is a compelling paradigm because of its utility in WiFi and LTE. It is also a good demonstration of the use of the FFT in a communication system. We have developed the proposed set of functions as a part of the Java-DSP (J-DSP) visual programming environment. The functions can be used in undergraduate DSP and communications courses, in order to demonstrate to students, the application of DSP concepts in a communication system, as well as concepts such as FIR filter design, properties of the DFT matrix, random signals, and circular effects.

Although considerable effort has been devoted to the problem of reconstructing compressively sensed video, no existing algorithm achieves results comparable to commonly available video compression methods such as H.264. One possible avenue for improving compressively sensed video reconstruction is the use of optical flow information. Current efforts reported in the literature have not fully utilized optical flow information, instead focusing on limited cases such as stationary backgrounds with sparse foreground motion. In this paper, a reconstruction method is presented which fully utilizes optical flow information to increase the quality of reconstruction. The special cases of known image motion and constant global image motion are presented, and the performance of the algorithm on existing datasets is evaluated.

Localization accuracy is crucial in sensor networks. A wireless sensor network (WSN) with M anchors and one node is considered in this paper. The estimation is based on time of arrival (TOA) in the presence of fading channels. The Cramer-Rao lower bound (CRLB) for localization error in the presence of fading is derived under different scenarios. Firstly, fading coefficients are considered as unknown random parameters with a prior distribution. The ML estimator for this case is also derived. If the distribution of fading is unknown to the estimator then the modified CRLB (MCRLB) is applied and shown to be equal to the CRLB in the absence of fading. This is used to conclude that fading always deteriorates the CRLB in localization. It is shown that there is a loss of about 5dB in CRLB due to Rayleigh fading.

The symbol error rate of an arbitrary multidimensional constellation in the absence of coding impaired by additive white Gaussian noise is characterized as the product of a completely monotone function with a nonnegative power of the signal-to-noise ratio, when the minimum distance detector is used. This representation is also shown to apply to cases when the impairing noise is compound Gaussian. Using this general result, it is proved that the symbol error rate is completely monotone if the rank of its constellation matrix is either one or two. Further, a necessary and sufficient condition for the complete monotonicity of the symbol error rate of a constellation of any dimension is also obtained. Applications to stochastic ordering of wireless system performance are also discussed.

Photovoltaics (PV) is an important and rapidly growing area of research. With the advent of power system monitoring and communication technology collectively known as the “smart grid,” an opportunity exists to apply signal processing techniques to monitoring and control of PV arrays. In this paper a monitoring system which provides real-time measurements of each PV module's voltage and current is considered. A fault detection algorithm formulated as a clustering problem and addressed using the robust minimum covariance determinant (MCD) estimator is described; its performance on simulated instances of arc and ground faults is evaluated. The algorithm is found to perform well on many types of faults commonly occurring in PV arrays.

In this paper, a new stochastic order between two fading distributions is introduced. A fading channel dominates another in the capacity ordering sense, if the ergodic capacity of the first is greater than that of the second at all values of average signal to noise ratio. We show that many parametric fading models such as the Nakagami-m, Rician and Hoyt fading satisfy the capacity order, in the sense that the distribution with a larger line of sight parameter is larger in the ergodic capacity sense. Further, we obtain closure properties of the capacity order for the first time, because such a stochastic order has not been considered in either stochastic ordering literature, or information theory literature. Through these properties, we develop sufficient conditions for comparing the ergodic capacity of a composite system involving multiple capacity ordered fading links with coding/decoding capabilities only at the transmitter/receiver, when operated in two different fading scenarios. Such comparisons can be made even in cases when a closed form expression for the ergodic capacity of the composite system is not analytically tractable. We also show that capacity ordering of point-to-point links has applications to multiple access channels.

In this paper, it is shown that the symbol error rate of an arbitrary multi-dimensional constellation impaired by independent and identically distributed additive white Gaussian noise under maximum likelihood detection is completely monotonic in the average SNR, if the rank of the constellation matrix is either one or two. Further, under minimum distance detection, this result generalizes to the case when the noise follows a dependent and identically distributed compound Gaussian distribution. Classes of constellations with dimensionality greater than two, which have completely monotone and convex error rates are also identified herein. The applications of the complete monotonicity of the symbol error rate in obtaining generic comparisons of average error rates over pairs of fading channels are also discussed.

This paper studies several problems concerning channel inclusion, which is a partial ordering between discrete memoryless channels (DMCs) proposed by Shannon. Specifically, checkable conditions are derived for channel inclusion between DMCs with certain special structure, and these conditions are related to the mathematical theory of majorization. The conditions for channel inclusion between binary erasure channel (BEC) and binary symmetric channel (BSC) are also derived, which are shown to be equivalent to those for channel output degradation. Furthermore, the determination of channel inclusion is considered as a convex optimization problem, and the sparsity of the weights related to the representation of the worse DMC in terms of the better one is revealed when channel inclusion holds between two DMCs.

Asymptotic comparisons of ergodic channel capacity at high and low SNRs are provided for several adaptive transmission schemes over fading channels with general distributions, including optimal power and rate adaptation, rate adaptation only, channel inversion and its variants. Analysis of the high-SNR pre-log constants of the ergodic capacity reveals the existence of constant capacity difference gaps among the schemes with a pre-log constant of 1. Closed-form expressions for these high-SNR capacity difference gaps are derived, which are proportional to the SNR loss between these schemes in dB scale. The largest one of these gaps is found to be between the optimal power and rate adaptation scheme and the channel inversion scheme. Based on these expressions it is shown that the presence of space diversity or multi-user diversity makes channel inversion arbitrarily close to achieving optimal capacity at high SNR with sufficiently large number of antennas or users. A low-SNR analysis also reveals that the presence of fading provably always improves capacity at sufficiently low SNR, compared to the additive white Gaussian noise (AWGN) case. Numerical results are shown to corroborate our analytical results.

A distributed detection problem over fading Gaussian multiple-access channels is considered. Sensors observe a phenomenon and transmit their observations to a fusion center using the amplify and forward scheme. The fusion center has multiple antennas with different channel models considered between the sensors and the fusion center, and different cases of channel state information are assumed at the sensors. The performance is evaluated in terms of the error exponent for each of these cases, where the effect of multiple antennas at the fusion center is studied. When there is channel information at the sensors, the gain in error exponent due to having multiple antennas at the fusion center is shown to be limited to a factor of 8/π for Rayleigh fading channels between the sensors and the fusion center, and independent of the number of antennas at the fusion center. Simple practical schemes and numerical methods using semidefinite relaxation techniques are presented that utilize the limited possible gains available. Simulations are used to establish the accuracy of the results.

Novel average bit or symbol error rate (BER/SER) bounds are obtained for systems with instantaneous signal-to-noise ratios (SNRs) given by a sum of \(N\) statistically independent non-negative random variables (RVs). Their tightness is quantified analytically at high SNR by calculating the SNR gap, and shown to be within O(1/N) of the true value. The bounds are most useful when the distribution of the sum is intractable. The bounds are illustrated with the maximum ratio combining (MRC), the combined average performance for amplify-and-forward (AF) relay networks using multiple relays, and AF multiple-input multiple-output (MIMO) single relay systems with beamforming (BF) using multiple antennas at the source, relay, and destination. As a result, the bounds lead us to obtain tight closed-form combined expressions for AF relay networks with multiple relays and with multiple antennas in fast fading, for the first time in the literature. In addition, applicability of the bounds to non-Gaussian noise is addressed. Finally, Monte-Carlo simulations confirm the tightness of the bounds.

Multi-user diversity (MUD) is considered when the number of users in the system is random. Average throughput of a MUD system is shown to have a completely monotone derivative with respect to (deterministic) number of users. Following this, randomization of number of users is shown to give degraded throughput averaged across the number of users distribution. Using stochastic ordering theory, a framework for comparison of performance for different user distributions is provided. For Poisson distributed number of users communicating over Rayleigh faded channels, long-term average throughput is shown to scale as a double logarithmic function of average number of users.

This paper derives high-SNR asymptotic average error rates over fading channels by relating them to the outage probability, under mild assumptions. The analysis is based on the Tauberian theorem for Laplace-Stieltjes transforms which is grounded on the notion of regular variation, and applies to a wider range of channel distributions than existing approaches. The theory of regular variation is argued to be the proper mathematical framework for finding sufficient and necessary conditions for outage events to dominate high-SNR error rate performance. It is proved that the diversity order being d and the cumulative distribution function (CDF) of the channel power gain having variation exponent d at 0 imply each other, provided that the instantaneous error rate is upper-bounded by an exponential function of the instantaneous SNR. High-SNR asymptotic average error rates are derived for specific instantaneous error rates. Compared to existing approaches in the literature, the asymptotic expressions are related to the channel distribution in a much simpler manner herein, and related with outage more intuitively. The high-SNR asymptotic error rate is also characterized under diversity combining schemes with the channel power gain of each branch having a regularly varying CDF. Numerical results are shown to corroborate our theoretical analysis.

An optimal training strategy is devised for the linearly decoded orthogonal space–time block coded (OSTBC) wireless systems in quasi-static fading channel, based on the performance analysis using pairwise error probability (PEP) and symbol error probability (SEP). The PEP/SEP analyses allow us to find a generic expression for the performance improvement due to optimal training compared to the conventional case for OSTBC system equipped with any number of transmit and receive antennas and any linear modulation scheme. It is observed that the linear processing in the receiver, the most attractive feature of OSTBC, although destroys the orthogonality in the presence of channel estimation error, does not reduce diversity, but causes performance penalty as a loss of signal-to-noise ratio (LoSNR) due to training. This loss is quantified analytically and minimised by optimal allocation of power between training and data symbols. The performance of optimal power allocation improves with the higher number of space–time blocks in a frame. Furthermore, the LoSNR depends only on the OSTBC and is independent of any modulation scheme and the full rate Alamouti and other high rate OSTBCs suffer more in terms of performance due to training compared to the lower rate OSTBC.

A distributed estimation problem is considered with multiple-access channels between sensors and a fusion center. The sensors phase-modulate their noisy observations before transmitting them to the fusion center, where a signal parameter is estimated. The asymptotic efficiency of this estimator is then determined by using two inequalities that relate the Fisher information and the characteristic function. A necessary and sufficient condition for equality is found for the first time in the literature. The loss in efficiency of the distributed estimation scheme relative to the centralized approach is quantified for different sensing noise distributions. It is shown that this distributed estimation system does not incur an efficiency loss if and only if the sensing noise distribution is Gaussian.

Stochastic orders are binary relations defined on probability distributions which capture intuitive notions like being larger or being more variable. This paper introduces stochastic ordering of instantaneous SNRs of fading channels as a tool to compare the performance of communication systems over different channels. Stochastic orders unify existing performance metrics such as ergodic capacity, and metrics based on error rate functions for commonly used modulation schemes through their relation with convex and completely monotonic (c.m.) functions. Toward this goal, performance metrics such as instantaneous error rates of M-QAM and M-PSK modulations are shown to be c.m. functions of the instantaneous SNR, while metrics such as the instantaneous capacity are seen to have a completely monotonic derivative (c.m.d.). It is shown that the frequently used parametric fading distributions for modeling line of sight (LoS) exhibit a monotonicity in the LoS parameter with respect to the stochastic Laplace transform order. Using stochastic orders, average performance of systems involving multiple random variables are compared over different channels, even when closed form expressions for such averages are not tractable. These include diversity combining schemes, relay networks, and signal detection over fading channels with non-Gaussian additive noise, which are investigated herein. Simulations are also provided to corroborate our results.

We consider a distributed detection problem over fading multiple-access channels. Sensors observe a phenomenon and transmit their observations to a fusion center using the amplify-and-forward scheme. The fusion center has multiple antennas and uses the transmissions from the sensors to run a detection algorithm. The channels are Ricean fading, and the sensors have no channel information. The performance is evaluated in terms of error exponent and compared with the AWGN channels case. The benefit of having multiple antennas at the fusion center is also quantified.

A scheme, which beamforms from the source to the stronger of direct and relay links, is analyzed in amplify/decode and forward (AF/DF) fixed relay networks. Novel upper-bounds and selection relaying for strong-path beamforming (BF) are presented for AF/DF relaying with known and unknown channel information of the relay link at the source and destination. Performance comparisons are shown among strong-path BF and optimized BF with a corresponding lower-bound.

A distributed estimation scheme where the sensors transmit with constant modulus signals over a multiple access channel is considered. The proposed estimator is shown to be strongly consistent for any sensing noise distribution in the i.i.d. case. When the distributions of the sensing noise are not identical, the existence of a bound on the variances is shown to establish strong consistency. The estimator is shown to be asymptotically normal with an asymptotic variance (AsV) that depends on the characteristic function of the sensing noise. Optimization of the AsV is considered with respect to a transmission phase parameter, and simulations are shown to corroborate our analytical results.

This paper addresses the bit error rate performance of diversity combining schemes for a single-user communication system operating over Rayleigh flat fading channels subject to impulsive alpha-stable noise, which is known to arise due to network interference from a Poisson field of interference sources. Under this setting, a theoretical benchmark receiver is analyzed, the maximum possible diversity order attainable is derived to be Lα/2, where L is the number of antennas and α is the characteristic exponent of the noise. Moreover, trade-offs between the diversity gain and the array gain have been identified. The conventional linear matched filter receiver (also known as maximum ratio combining in the Gaussian case) has been shown to have a diversity order of α/2, thereby not benefiting from spatial diversity. Closed form expressions for the diversity gain and array gain of post-detection combining have been derived. As an improvement to conventional combining schemes, the optimum maximum likelihood detector is derived. A simpler high SNR approximation of the detector is shown to not depend on the noise parameters, and is compared to the generalized Cauchy detector under stable noise. Monte-Carlo simulations are used to supplement our analytical results and compare the performance of the detectors.

This paper addresses power adaptation in the context of beamforming in the downlink of a cellular system. Specifically, we consider a system consisting of a base station (BS) with multiple antennas and multiple users each with a single antenna, in which the BS selects the user with the best channel for transmission. Compared to the scheme minimizing the bit error rate (BER) using a fixed instantaneous power, the BER performance can be further improved by adapting the instantaneous power according to the channel of the selected user. The optimal power adaptation (OPA) policy is derived, and its BER is compared with the case of a sub-optimal policy called channel inversion (CI). With a novel analytical approach, the BER performances of OPA and CI are quantified and CI is shown to be near-optimal for a multi-user multi-antenna system at moderate to large SNR, unlike the single-user single-antenna case. Finite peak power constraint is also considered for both OPA and CI.

Switch and stay diversity combining offers a substantial complexity reduction at the cost of modest performance degradation compared to systems implementing selection diversity. In this work, the design and performance of space time coded multiple input multiple output (MIMO) systems employing switch and stay combining at the receiver, with two antennas, is considered. Assuming known channel at the receiver, a novel switching algorithm is proposed and an upper bound on the pairwise error probability (PEP) is derived. Based on this upper bound, the optimal switching threshold is derived and it is shown that full diversity is achieved when the optimal switching threshold is used. For the case when the channel has to be estimated at the receiver, a minimal complexity training scheme suitable for both switching and channel estimation is described, where it is shown that full diversity is still achievable. By comparing the PEP expressions for the system with perfect channel knowledge at the receiver against the system with imperfect channel knowledge, the power distribution between the training and the data space-time (ST) codewords is optimized to minimize the loss suffered due to channel estimation. Simulation results have also been included to corroborate our results.

In this paper we consider distributed detection in ultra-wideband(UWB) wireless sensor networks with asynchronous transmissions over frequency-selective channels. Three amplify-and-forward schemes with different requirements on channel state information (CSI) are investigated. Performances are studied and compared by using the large deviation principle and simulations.

We consider a wireless sensor network for distributed estimation over Rayleigh fading channels. The sensors transmit their observations over fading channels to a fusion center, where a source parameter is estimated. Since the sensor transmissions add incoherently over a multiple access channel, we consider partial channel knowledge at the sensors to improve performance. We calculate the variance of the estimate when the channel phase is quantized uniformly and fed back to the sensors. We show that as few as 3 bits of feedback is sufficient for a loss in performance of about 5%. We also show that the performance is robust in the presence of feedback errors.

We consider distributed estimation of a source observed by sensors in additive Gaussian noise, where the sensors are connected to a fusion center with unknown orthogonal (parallel) flat Rayleigh fading channels. We adopt a two-phase approach of (i) channel estimation with training, and (ii) source estimation given the channel estimates, where the total power is fixed. We prove that allocating half the total power into training is optimal, and show that compared to the perfect channel case, a performance loss of at least 6 dB is incurred. In addition, we show that unlike the perfect channel case, increasing the number of sensors will lead to an eventual degradation in performance. We characterize the optimum number of sensors as a function of the total power and noise statistics. Simulations corroborate our analytical findings.

Estimation of the mobile speed, or equivalently, the maximum Doppler frequency, is of importance in a variety of applications in wireless mobile communications. In this paper, a unified framework for the performance analysis of several major speed estimation techniques is presented, which allows a fair comparison between all the methods, analytically. Interestingly, it is proved that all these methods are equivalent, asymptotically, i.e., for large observation intervals. In addition, we have derived closed-from expressions for the bias and variance of a recently proposed covariance-based method. We have also introduced a new estimator which relies on the average number of maxima of the inphase component, and have calculated its variance, analytically. Our extensive performance analysis, supported by Monte Carlo simulations, have revealed that depending on the channel condition and the observation interval, one needs to use a crossing- or a covariance-based technique, to achieve the desired estimation accuracy over a large range of mobile speeds.

In this paper, we study the effectiveness of the multipath energy combining for the coarse acquisition of UWB signals. The performances of different detectors, including single pulse correlator (SPC), energy detector (ED), and transmittedreference (TR), are derived and compared in terms of the mean acquisition time (MAT) and the false acquisition rate (FAR) using flow graph analysis in a two-step random search framework. The results show that both the ED and the TR can achieve a lower acquisition time than the SPC under the same FAR constraint due to their multipath energy combining capabilities. Simulation results also reveal that the ED scheme is more vulnerable to multiuser interference than the TR and the SPC schemes.

Synchronization is a key issue for ultra-wideband (UWB) radios. Most UWB receivers require a sub-nanosecond level synchronization accuracy for pulse detection, usually leading to a very long acquisition time. In this paper, we propose a novel acquisition algorithm for UWB receivers, which jointly achieves pulse acquisition (PA) and symbol timing in a short time. Novel and practical error-resistant approaches are developed to keep the false alarm (FA) rate under a desired low level. Detailed analysis based on finite state machine and flow graph theory is carried out to evaluate its acquisition performance. Comparison with the PA-only case is made, illustrating the effectiveness of our joint approach. Simulations corroborate our theoretical results.

Focusing on the uplink, where mobile users (each with a single transmit antenna) communicate with a base station with multiple antennas, we treat multiple users as antennas to enable spatial multiplexing across users. Introducing distributed closed-loop spatial multiplexing with threshold-based user selection, we propose two uplink channel-assigning strategies with limited feedback. We prove that the proposed system also outperforms the standard greedy scheme with respect to the degree of fairness, measured by the variance of the time averaged throughput. For uplink multi-antenna systems, we show that the proposed scheduling is a better choice than the greedy scheme in terms of the average BER, feedback complexity, and fairness. The numerical results corroborate our findings.

We study space-time-frequency coded multiple- input-multiple-output (MIMO) orthogonal frequency-division multiplexed (OFDM) systems employing antenna selection at the receiver where optimal training has been utilized for performing linear minimum mean square error (LMMSE) based channel estimation. The maximum signal power antenna selection rule is introduced. By upper bounding the pairwise error probability (PEP) expression, we show that the system with channel estimation error (CEE) still achieves full diversity. The loss in coding gain (LCG) and the loss in performance (LP) expressions are derived. It is shown that while equal power training performs about 3 dB worse than the perfect CSI case, the optimal power training performs between the two depending on the number of subcarriers assigned per OFDM word. Simulation results are presented to validate our analysis.

The sparsely pulsed ultra-wideband (UWB) waveform has to be detected using efficient search strategies. Consecutive serial search (CSS) and permuted search strategies have been used for pulse detection. CSS results in a large average acquisition time when low duty cycle pulses are used. Permuted search strategies circumvent this problem by exploiting the dense multipath characteristic of the UWB signal. A host of parameters influence the acquisition performance in the case of CSS and permuted search strategies. This paper discusses the significance of step size in the acquisition performance of coherent impulse radio ultra-wideband (IR-UWB) receivers. Using theoretical analysis and simulations, it is established that for channel models with different multipath spreads, the step size minimally affects the acquisition performance of a single pulse correlator in the case of permuted search strategies. For CSS, the acquisition performance changes with step size.

The estimation of the mobile speed, or equivalently, the maximum Doppler frequency, is of importance in a variety of applications in wireless mobile communications. In this paper, a unified framework for the performance analysis of several major speed-estimation techniques is presented, which allows a fair comparison between all the methods, analytically. Interestingly, it is proved that all these methods are equivalent, asymptotically, i.e., for large observation intervals. In addition, we have derived closed-form expressions for the bias and variance of a recently proposed covariance-based method. We have also introduced a new estimator that relies on the average number of maxima of the inphase component, and have calculated its variance, analytically. Our extensive performance analysis, supported by Monte Carlo simulations, have revealed that depending on the channel condition and the observation interval, one needs to use a crossing- or a covariance-based technique, to achieve the desired estimation accuracy over a large range of mobile speeds.

Impulsive, non-Gaussian noise is prevalent in wireless environments. We adopt an impulsive noise model over multi-input-multi-output (MIMO) channels and discuss receiver and code design over fading channels with impulsive noise. We derive code design criteria for the so-called genie-aided, and minimum distance receivers, both of which yield criteria identical to the nonimpulsive, Gaussian noise case. We also study the performance of certain space-time block codes (STBCs) and space-time trellis codes (STTC) over impulsive noise channels with the genie-aided receiver (GAR) and minimum distance receiver (MDR). The performance loss incurred by the impulsive nature of the noise is shown to increase with the diversity order for the MDR. To approximate the good performance of the practically unrealistic GAR, we propose a maximum a posteriori (MAP) receiver, whose performance can be tightly lower bounded by the GAR. We simplify the optimal MAP receiver by an approximation and show that for alt cases of practical interest, only 2 terms in the approximation are sufficient to get a near-MAP performance. Simulations corroborate our analytical findings

A frame-level synchronization (FLS) algorithm for the UWB transmitted-reference (TR) receiver is designed and analyzed in this paper. The algorithm exploits the robustness of the TR receiver to synchronization errors (N. He and C. Tepedelenlioglu, 2004), and has a moderate accuracy but a very low complexity and fast synchronization speed compared to conventional approaches requiring subnanosecond-level accuracy. Detailed analysis of the algorithm is carried out. Synchronization performance of both blind and non-blind approaches are derived and compared in terms of the average acquisition time. Error detection and correction strategies are built in to further improve the performance of the algorithm. Parameter selections that minimize the average acquisition time are also discussed, based on our in-depth analysis

We compare the achievable performance of adaptive beamforming (A-BF) and adaptive orthogonal space time block coding (A-OSTBC) with outdated channel feedback. We extend our single user setup to multiuser diversity systems employing adaptive modulation, and illustrate the impact of feedback delay on the multiuser diversity gain with either A-OSTBC or A-BF. Using closed-form expressions for spectral efficiency and average BER of a multiuser diversity system derived in this paper, we prove that the A-BF scheme outperforms the A-OSTBC scheme with no feedback delay. However, when the feedback delay is large, the A-OSTBC scheme achieves better performance due to the reduced diversity advantage of A-BF. We observe that more transmit antennas bring higher spectral efficiency for BF. With small feedback delay, this becomes inverted using OSTBC, due to the effect of channel-hardening. Interestingly, however, we show that A-OSTBC with multiple users enjoys improved spectral efficiency when the number of transmit antennas is increased and the feedback delay is significant

This paper studies the performance of antenna selection (AS) for space-time (ST) coded systems with noisy channel estimates. For coherent AS systems over Rayleigh flat fading channels, we derive the pairwise error probability (PEP) in the presence of imperfect channel estimation, where the channel is estimated using training insertion and minimum mean square error (MMSE) estimation. Multiplexed training is employed, where the antennas are multiplexed to the small number of RF chains available in the AS system. AS is performed only at the receiver, using the maximum estimated channel power selection rule. Both the maximum likelihood (ML) decoder taking into account the channel estimation error, and the minimum distance decoder are considered, and full diversity gain is shown to be preserved for both cases. Based on the derived training-based PEP, the effective SNR and the coding gain loss due to training are quantified for square unitary and orthogonal codes. The optimal power allocation between the training and data symbols is obtained by minimizing the PEP. For AS systems employing orthogonal designs, we further derive the exact PEP expression in closed-form. We also show that when square unitary training is employed, AS using the norm of MMSE channel estimates is equivalent to AS using the norm (power) of the received signal. Exploiting this fact, we propose an alternate training scheme which avoids multiplexing, has higher spectral efficiency, and better performance compared to the multiplexed training scheme. Simulations are shown to validate our analysis

Some practical issues in parameter estimation over fading channels with type-based multiple access (TBMA) sensor networks is studied in this paper, where the parameter of interest is estimated through the empirical distribution of the observations. In the literature, the asymptotically optimal estimator requires the transmitted signal waveforms to be orthogonal to represent different observations. Meanwhile, the channels between the sensors and the fusion center need to be non zero-mean. If the channel is zero-mean, channel state information (CSI) at sensor side is required. However, in practice, imperfect CSI, or interference between the orthogonal waveform dimensions, such as synchronization error, cannot be avoided, and may be unknown at the fusion center. How these practical issues affect the asymptotic optimality of the existing estimator and its performance are discussed in this paper. A unified framework for estimation with these practical constraints is proposed, which includes the imperfect CSI and synchronization error as special cases. The conditions under which the asymptotically optimal estimator requires the knowledge of the channel or interference statistics at the fusion center are derived. Furthermore, how the interference affects the performance of the asymptotically optimal estimator is characterized. Simulation results corroborate our analysis.

Non-coherent transmitted reference (TR) scheme is a popular technique in ultra-wideband (UWB) communications. Comparisons of the TR receiver with the coherent UWB receiver have not yet been studied in terms of their acquisition performance. In this paper, the acquisition performance of coherent and TR receivers is analyzed over a common acquisition stage. Closed-form expressions of their average acquisition time (AAT) and false-alarm rate (FAR) are derived, which enables the AAT comparison under the same FAR threshold. Results show that the TR receiver has a better acquisition performance than the coherent receiver despite of its noisy template signal and energy loss on pilot signals.

Assuming a base station with multiple antennas, we propose two channel-assigning strategies based on spatial multiplexing with threshold-based user selection at the uplink. Allowing multiple chosen users to access the channel, we obtain additional multiplexing gain and a reduced feedback complexity, compared to the conventional greedy approach. We prove that the proposed system outperforms the greedy approach also with respect to the degree of fairness among users, measured by the variance of the time averaged throughput. For practical uplink multiuser systems, we show that the standard greedy scheme may not be the optimal policy in terms of the minimization of average BER. The numerical results corroborate our findings.

We consider space-time-frequency (STF) coded MIMO-OFDM systems with imperfect channel estimates due to channel estimation error. We address the problem of optimal training design for acquiring the channel state information (CSI) and performance analysis using pairwise error probability (PEP) in the presence of channel estimation error. The optimal power allocation factor between the training and the information-bearing data is determined using the novel training-based PEP for MIMO-OFDM. Furthermore, the loss of coding gain due to channel estimation error is quantified to demonstrate performance benefits of power allocation optimization in MIMO-OFDM systems between the training and information symbols.

We study the parameter estimation problem over fading channels with type-based multiple access (TBMA [1], [3], [6]) sensor networks. The existing estimators in the literature require the knowledge of the mean of the channel coefficients which should be non-zero, and the number of alive sensors. In this paper, we propose a novel estimator for the non-zero mean fading channel when the mean of the channel coefficients and the number of alive sensors are unknown. We compute the asymptotic variance of our novel estimator and theoretically show that it is asymptotically optimal and its asymptotic performance is the same as the existing estimator. Furthermore, we study the estimation over a zero-mean Rayleigh fading channel, where the channel status information (CSI) is available at the sensor side [3]. We study different power control schemes over Rayleigh fading channels, and propose an algorithm to optimize the parameters for the power control scheme under both average power and peak power constraints. Simulation results corroborate our analysis.

Synchronization is a key issue for ultra-wideband (UWB) radios. Coherent UWB receivers, which correlate the received signal with a well-designed template, have very stringent requirements for synchronization accuracy, leading to a long synchronization time. Various acquisition/synchronization algorithms have been proposed to enhance the synchronization speed of UWB receivers, but many of them only focus on a partial synchronization process, and performance analysis in a practical scenario is usually not provided. In this paper, we propose acom complete acquisition algorithm for coherent UWB receivers, which includes both pulse-acquisition and symbol-level synchronization (SLS) stages. Practical error-resistant approaches are developed to combat the synchronization error. Detailed analysis based on the finite state machine and flow graph theories is carried out to evaluate its performance, and parameter selections that minimize the average acquisition time are discussed. The proposed algorithm is shown to have enhanced efficiency compared to separate pulse-acquisition and SLS algorithms. Simulations corroborate our theoretical results.

Non-coherent ultra-wideband (UWB) receivers require no channel state information for demodulating the received signal. The primary non-coherent receiver in the UWB literature is the autocorrelation receiver, which autocorrelates the received signal at specific time lags, circumventing problems of template signal design and multipath energy combining. A unique advantage of the UWB autocorrelation receiver is its robustness to synchronization errors, which has not been explored yet to date. This paper investigates two major UWB schemes employing autocorrelation receivers: the transmitted reference (TR) scheme (R. Hoctor and H. Tomlinson, 2002) and the differential (DF) scheme (M. Ho et al., 2002). Performance is analyzed for TR and DF receivers at different synchronization accuracy levels, their robustness to synchronization errors is shown, and the existence of a tradeoff between performance and synchronization complexity for non-coherent UWB receivers is revealed. As a result of our analysis, comparisons of TR and DF schemes are also made in the presence of synchronization errors, which have not been addressed before. Simulations corroborate our findings

Abstract-Channel state information (CSI) at the transmitter can be used to adapt transmission rate or antenna gains in multi-antenna systems. We propose a rate-adaptive M-QAM scheme equipped with orthogonal space-time block coding with simple outdated, finite-rate feedback over independent flat fading channels. We obtain closed-form expressions for the average BER and throughput for our scheme, and analyze the effects of possibly delayed feedback on the performance gains. We derive optimal switching thresholds maximizing the average throughput under average and outage BER constraints with outdated feedback. Our numerical results illustrate the immunity of our optimal thresholds to delayed feedback.

We propose a closed-loop spatial multiplexing system with limited feedback and rate control over MIMO fading channels. The transmitter adaptation is designed to maximize spectral efficiency subject to an average bit error rate (BER) constraint by adapting the number of substreams based on a given threshold, and a fixed constellation, which determines the instantaneous rate. The proposed system chooses the substream selection threshold as a function of the slowly changing average SNR. We analyze the performance of the proposed system by deriving closed-form expressions for spectral efficiency, average transmit power, and BER. Compared with the rate adaptive orthogonal STBC requiring highly complex constellation adaptation, the proposed rate control method achieves 5 dB power gain for a spectral efficiency of 7 bits/s/Hz at average BER of 10/sup -4/, with 2 transmit antennas.

Without channel state information (CSI) at the receiver, we study receive antenna selection (AS) for multi-antenna systems that employ differential unitary space-time signals. We perform AS only at the receiver and a subset of receive antennas that have the largest received signal power is chosen. Selecting a single antenna at the receiver, it is proved in Q. Mia and C. Tepedelenlioglu (2005) that with no CSI at the receiver, the diversity gain with AS is preserved for differential unitary space-time codes with full spatial diversity. In this paper, we generalize the performance analysis to the case of selecting more than one antenna at the receiver. As an immediate consequence of performance analysis, based on the derived diversity gain and coding gain expressions, we develop code design principles for the differential ST codes suitable for maximum-power based AS systems. In particular, for 2/spl times/2 differential AS systems, we have devised new excellent-performing parametric codes, which outperform known differential codes when AS is employed. Simulation results are presented to validate our analysis and code design.

In this paper, we characterize the diversity properties of linear equalizers for block transmission systems, which unify preceded OFDM systems and zero-padded block transmissions. Fundamental results are proven to show that the diversity order of linear equalizers over fading channels can be the minimum (one) or the maximum diversity the channel offers. By exploiting the structure of the channel matrix, an alternative closed form expression for the pseudo-inverse is derived to reduce the complexity of the equalizer. Also, by quantifying the computational complexity, we demonstrate the complexity-performance tradeoff among the design for various linear equalizers. When the conditional error rate is known in closed form, a novel efficient approach is proposed to calculate the performance of linear zero-forcing equalizers. Corroborating simulations confirm that even with linear equalization, the block transmission systems perform better over channels with more taps at practical high SNRs.

In this paper, PEP (pairwise error probability) is derived for MIMO systems in the presence of channel estimation error, where the channel is estimated using training insertion and linear channel estimation. This training-based PEP expression is utilized to design the training sequence and for optimal power allocation between the training and data symbols. The loss of coding gain due to the training is quantified at high SNR. It is shown that both the proposed PEP-based and the existing capacity-based optimal training approach of B. Hassibi and B. Hochwald (IEEE Trans. Inform. Theory, vol. 49, no. 4, pp. 951-963, 2003) reveal the same power allocation for constant modulus (CM) constellations. The performance of our optimal power allocation scheme falls between the nonoptimized equal power allocation and perfectly known channel cases, and converges to the latter for larger data transmission intervals. Numerical and simulation results are presented to justify the usefulness of our analytical findings.

Impulsive, nonGaussian noise is prevalent in wireless environments. We adopt an impulsive noise model over multi-input-multi-output (MIMO) channels and discuss receiver design and code design over MIMO channels with impulsive noise. We derive the code design criterion for the so-called genie-aided receiver and suboptimal receiver, both of which yield criteria identical to Tarokh et al. (1998) when the noise is not impulsive. We propose a maximum a posteriori (MAP) receiver, whose performance can be tightly lower bounded by the genie-aided receiver. We simplify the optimal MAP receiver by an approximation and show that for all cases of practical interest, only 2 terms in the approximation is enough to get near-optimal performance.

Fast and low-complexity synchronization constitutes a big challenge for ultra-wideband (UWB) radio systems. Due to the ultrafine time-resolvability of the UWB signal and the difficulty of channel estimation, it is difficult to achieve synchronization with accuracy on the order of tens of picoseconds, which is required by coherent UWB receivers. Non-coherent UWB receivers, however, have less stringent requirement for the synchronization accuracy (Ning He and C. Tepedelenlioglu, Proc. GLOBECOM 2004, Nov. 2004). Thus, synchronization algorithms for non-coherent UWB receivers can be developed to achieve synchronization with higher inaccuracy but much lower implementation complexity than coherent receivers. This paper analyzes the performance of a noncoherent synchronization algorithm proposed previously by the authors (Proc. IEEE Int. Conf. on Acoustics, Speech, and Sig. Proc., vol. 4, pp. 517-520, 2004). Based on the analysis, parameter optimization to minimize the average acquisition time is pursued. Simulations corroborate our results.

For multiuser diversity systems employing adaptive modulation, we compare the spectral efficiency for space-time block coding (STBC) and transmit beamforming (BF) with outdated channel feedback. Taking into account the channel feedback delay, we derive the optimal thresholds to maximize spectral efficiency subject to an average BER constraint, and illustrate the impact of feedback delay on the achievable multiuser diversity gain with either STBC or BF. We observe that more transmit antennas bring higher spectral efficiency for BF But this becomes inverted using STBC, due to the effect of channel-hardening. With a small feedback delay, the BF scheme outperforms the STBC scheme. However, when feedback delay becomes large enough, the STBC scheme achieves higher spectral efficiency due to the reduced diversity order of BF.

This correspondence studies receive antenna selection (AS) for multiple-antenna systems that employ unitary space-time (ST) signals, where the channel state information (CSI) is known neither at the transmitter nor at the receiver. Without CSI at the receiver, we perform AS only at the receiver and the selection is based on a maximum-norm criterion, i.e., a subset of receive antennas that have the largest received signal power is chosen. Using a Chernoff bound approach, we present theoretical performance analysis based on the pairwise error probability (PEP) and quantify the asymptotic performance at high signal-to-noise ratio (SNR) by giving the diversity and coding gain expressions. We prove that with no CSI at the receiver, the diversity gain with AS is preserved for unitary ST codes with full spatial diversity, the same as the case with known CSI. As a concrete example, for differential unitary ST modulation with M=2 transmit antennas and N=2 receive antennas, we have devised new excellent-performing parametric codes based on the derived PEP bound. The new codes, which are specifically designed for differential AS systems, outperform known differential codes when AS is employed. Corroborating simulations validate our analysis and code design.

Addressing orthogonal frequency division multiplexing (OFDM) transmissions over frequency-selective Rayleigh fading channels, we propose a differential space-time-frequency (DSTF) coding scheme with maximum multipath diversity. Resorting to subcarrier grouping, we convert the system into a set of parallel DSTF systems, within which DSTF coding is considered. Through pairwise error probability (PEP) analysis, we prove that full diversity gain, which is the product of the number of transmit antennas, receive antennas, and the multipath channel length, can be achieved without channel state information (CSI) at the receiver. We analyze the performance of group DSTF coding over correlated fading channels and establish the design criteria for subcarrier selection and code selection. In addition to applying existing differential unitary diagonal codes, we propose a systematic approach to designing nondiagonal codes for DSTF systems, which are block diagonal (BD) and have the necessary unitary and full diversity properties. Based on permutation techniques, we have devised new excellent-performing BD DSTF codes, which significantly improve the coding gain as compared to their diagonal counterparts. Corroborating simulations confirm the merits of our approach.

The Nakagami-m parameter is known to capture the envelope distribution of various fading channel conditions in wireless communications. The value of m is indicative of the severity of fading, and is a measure of channel quality, making its estimation necessary in many applications. In this paper, we summarize the existing estimators for the Nakagami-m parameter and propose a new class of estimators, whose performance is analyzed by deriving the asymptotic variance and comparing with the Cramer-Rao bound (CRB). Moreover, we develop a novel estimator robust to the presence of additive white Gaussian noise (AWGN) or any other additive noise with a symmetrical distribution. We also discuss practical issues not previously addressed in the literature including adaptation and computational complexity of these estimators. We conclude that our novel integer-moment based estimators are the best choice from a computational complexity and performance point of view. Simulation results corroborate our analysis.

We analyze the performance of an uncoded orthogonal frequency-division multiplexing (OFDM) system in a quasistatic fading channel where optimal training is being employed for the acquisition of channel state information (CSI). A bit-error probability (BEP) expression is obtained for the linear minimum mean-square error (LMMSE) based channel estimator where the mean-square error (MSE) of the channel estimator is minimized by equispaced, equipowered training with the number of training tones equal to the channel length. Optimal power allocation is obtained by minimizing the BEP expressions. The performances of BPSK, QPSK and 16-QAM schemes are considered. It is shown that while equal power training performs around 3 dB worse than the known channel case, our optimal power channel estimator performance varies between these two, depending on the number of subcarrier to channel length ratio. Numerical examples are presented to further clarify and confirm the analytical findings.

Transmitted reference (TR) (Hoctor, R. and Tomlinson, H., Proc. IEEE Conf. on Ultra Wideband Systems and Technologies, p.265-9, 2002) and differential (DF) (Ho, M. et al., Proc. 55th IEEE Vehicular Technology Conf., vol.4, p.1896-1900, 2002) schemes are alternatives for ultra-wideband (UWB) communication systems. They both employ non-coherent autocorrelation receivers, circumventing problems of template signal design and multipath energy combining. Their receivers can also operate at different synchronization accuracy levels, being more robust to synchronization inaccuracy than coherent receivers. The BER performance of TR and DF receivers at different synchronization levels is derived. Comparisons of TR and DF schemes are made, and the tradeoff between performance and synchronization complexity for autocorrelation receivers is discussed. Simulations corroborate our findings.

The prevalence of impulsive electromagnetic interference, atmospheric or ignition noise necessitates thorough analysis of their effects on the performance of diversity combining schemes. In this paper, we adopt Middleton's class A model for the noise distribution, and analyze the performance of different diversity combining techniques over fading channels with statistically dependent impulsive noise on each branch. We systematically analyze the performance of maximum ratio combining (MRC), equal gain combining (EGC), selection combining (SC), and post-detection combining (PDC) under the impulsive noise model, and derive insightful upper bounds. We show that even under impulsive noise, the diversity order is retained for each combining scheme. However, there is a fundamental tradeoff between diversity gain and coding gain. Our simulation results corroborate our analysis.

Pair-wise error probability (PEP) is analyzed in the presence of channel estimation error (CEE) for orthogonal frequency division multiplexing (OFDM) in a quasi-static Rayleigh fading channel. Subcarriers in OFDM are grouped in an equi-spaced manner with the number of subcarriers in a group equal to the number of channel taps. One group is dedicated for training and the rest are for data transmission. A linear minimum mean square error (LMMSE) based channel estimation for coherent detection is considered in this paper. This enables the signal dependent CEE to be uncorrelated to the data. Since ML decoding employed with perfect CSI becomes suboptimal in the presence of CEE, an optimal ML decoding is derived. It is observed from our training-based PEP expression that the CEE does not reduce the diversity order but contributes to a loss of coding gain. Moreover, a code design criterion is established. To reduce the loss of coding gain, an optimal training scheme is developed, based on the PEP expression. Loss of performance due to an imperfect channel estimate is quantified in terms of bounds on bit error probability (BEP) for high SNR. Our analytical findings are corroborated by simulation examples.

Ultra-wideband (UWB) radio transmits data using sub-nanosecond pulses with a very low duty-cycle. It is a promising candidate for short-range communications in dense multipath environments. However, UWB systems have to cope with great design challenges, including difficulties on synchronization, template signal design, and multipath energy combining. The UWB differential scheme with a non-coherent receiver offers a way to solve these problems, but may experience performance degradation due to inadequate synchronization knowledge. In this paper a novel adaptive synchronization algorithm for UWB non-coherent receivers is proposed, which adaptively improves on partial synchronization information until frame-level synchronization is achieved. The algorithm requires only tens of symbol durations, which is orders of magnitude less than that of the coherent receiver. Performance enhancement is observed through both theoretical analysis and simulations.

Channel state information (CSI) at the transmitter can be used to adapt transmission rate or antenna gains to time-varying fading channels in multi-antenna systems. However, the CSI that is fed back will get outdated if the channel is changing rapidly. We have developed a rate-adaptive M-QAM technique equipped with space-time block coding for multi-input multi-output (MIMO) systems and imperfect signal to noise ratio (SNR) feedback as opposed to the more complex full channel feedback in Ko et al. (2003). Based on the closed-form expressions for the average BER and average throughput derived in Ko et al, we derive herein optimal switching thresholds which maximize the average throughput under average BER constraint for MIMO fading channels. Our numerical results illustrate the immunity of our optimal thresholds to error due to time-delayed feedback.

Inspired by the information theoretic results concerning multiuser diversity, we address practical issues in implementing multiuser diversity in a realistic multiple access wireless setting. The users are allowed to have different average channel powers and the important issue of fairness is investigated. Using a fair channel assignment strategy that assigns the channel to only the user with the greatest instantaneous SNR-to-average-SNR ratio, our emphasis is on the effect of channel feedback delay in downlink transmissions. A novel optimization criterion based on an outage probability constraint is proposed. Applying the outdated channel feedback model, we illustrate the impact of channel feedback delay on the achievable multiuser diversity gain with the number of users. A robust, constant power, variable rate M-QAM scheme that is less sensitive to feedback delay is proposed using the optimal set of switching thresholds, which is derived to maximize the average throughput, subject to an outage probability constraint.

We derive the performance of post-detection-combining (PDC) over Rayleigh fading channels with impulsive noise and compare it with maximum-ratio-combining (MRC). The bit error rates (BER) and simple upper and lower bounds are derived in closed form for the first time in the literature for these two techniques over impulsive noise channels. We show how the impulsive noise deteriorates the performance compared with Gaussian noise. PDC is shown to be more robust to impulsive noise than MRC, especially when the number of antennas is large. Simulation results corroborate our analysis.

We propose a new technique to estimate the signal-to-noise ratio (SNR) over the flat-fading channel. This is a non-data-aided, envelope-based estimator that can be applied to non-constant modulus constellations which is a feature not found in the existing approaches. We also analyze the performance of our estimators for both PSK and non-PSK constellations by deriving their asymptotic variances and comparing it with the Cramer-Rao bounds (CRBs). Moreover, we discuss how the SNR estimates can be used to approximate the bit error rate (BER) and how the accuracy of the SNR estimate is related to that of the BER estimate, which justifies the necessity for the accurate estimation of SNR. The analytical performance is shown for both PSK and non-PSK constellations, such as 8 QAM. and 16 QAM. Monte Carlo simulation results corroborate our analysis.

Inspired by the information theoretic results concerning multiuser diversity, we address practical issues in implementing multiuser diversity in a realistic multiple access wireless setting. Using the optimal channel-assigning policy that assigns the channel to only one user with the best channel gain (R Knopp et al., 1995), our emphasis is on the effects of channel feedback delay in downlink transmissions. A finite set of M-QAM constellations is adopted and a constant transmit power is assumed in this practical scenario. Based on the closed-form expressions for exact and approximate average BER and sum throughput we derive under the outdated channel feedback model, we illustrate the impact of channel feedback delay on the achievable multiuser diversity gain with the number of users. Simple and accurate asymptotic approximations are also provided in the limit of large number of users. A novel robust constant power, variable rate M-QAM scheme that is less sensitive to feedback delay is proposed using the optimal set of switching thresholds, which is derived to maximize the average sum throughput subject to an average BER constraint.

In wireless communications, the fading multipath channel attenuates and distorts the transmitted signal. To decode the transmitted symbols and take advantage of the full multipath diversity that the channel has to offer, computationally complex maximum-likelihood (ML) decoding is often employed. We show that a linear equalizer followed by a hard decision is capable of benefiting from maximum multipath diversity in linearly precoded orthogonal frequency-division multiplexing (OFDM) systems, where the information symbols are mapped through a matrix transformation before the inverse fast Fourier transform (IFFT) at the OFDM transmitter. As far as we are aware, this is the first proof of a linear equalization scheme achieving maximum multipath diversity over single-input single-output wireless links. We can conclude from this result that at sufficiently high signal-to-noise ratios (SNR), precoded OFDM systems will perform better over channels with more taps even with linear equalization, due to the increase in diversity order.

Focusing on orthogonal frequency division multiplexing (OFDM) transmissions over frequency selective Rayleigh fading channels, we consider full diversity block diagonal codes for differential space-time-frequency (DSTF) coded OFDM with no channel state information (CSI). Resorting to subcarrier grouping, we convert the system into a set of DSTF systems, within which DSTF coding is considered. Through pairwise error probability (PEP) analysis, the code design criteria are derived over correlated channels and shown to be not dependent on the channel correlations. In [Q. Ma, et al. (2003)], it is proved that full diversity gain can be achieved by appropriately using the existing unitary diagonal space-time (ST) codes without CSI over the frequency selective channels. We show here that, at higher data rates there exist fuller nondiagonal matrices that have the necessary unitary and full diversity properties, and outperform the diagonal codes in [Q. Ma, et al., (2003)], Two design methods are proposed for block diagonal codes with full diversity which are based on existing designs for flat fading channels.

The Nakagami m parameter is known to capture the envelope distribution of various fading channel conditions in wireless communications. The value of m is indicative of the severity of fading, and is a measure of channel quality, making its estimation necessary. We discuss some practical issues not addressed in the literature including presence of additive noise, adaptation and computational complexity. Moreover, we propose new estimators which are robust to any symmetrically distributed noise with the best performance and lowest complexity among the existing estimators designed for noise immunity. Simulation results corroborate our analysis.

In wireless communications the fading multipath channel attenuates and distorts the transmitted signal. This makes equalization of the frequency selective channel of utmost importance. To exploit the full diversity provided by the multipath channel, maximum likelihood (ML) decoding is usually employed, which is computationally complex. In this paper we show that a specific linear zero-forcing equalizer is capable of benefitting from maximum multipath diversity in systems where the transmitted blocks are separated by zero guard intervals of length greater than the channel length (the well-known trailing zeros approach (Wang et al. (2000))). Furthermore, we exploit the banded Toeplitz structure of the channel matrix to reduce the complexity of the equalization process, and quantify the reduction in complexity. Simulations corroborate our results.

In wireless communications, the relative strength of the direct and scattered components of the received signal, as expressed by the Ricean K factor, provides an indication of link quality. Accordingly, efficient and accurate methods for estimating K are of considerable interest. In this paper, we propose a general class of moment-based estimators which use the signal envelope. This class of estimators unifies many of the previous estimators, and introduces new ones. We derive, for the first time, the asymptotic variance (AsV) of these estimators and compare them with the Cramer-Rao bound (CRB). We then tackle the problem of estimating K from the in-phase and quadrature-phase (I/Q) components of the received signal and illustrate the improvement in performance as compared with the envelope-based estimators. We derive the CRBs for the I/Q data model, which, unlike the envelope CRB, is tractable for correlated samples. Furthermore, we introduce a novel estimator that relies on the I/Q components, and derive its AsV even when the channel samples are correlated. We corroborate our analytical findings by simulations.

The knowledge of the maximum Doppler spread, or equivalently the vehicle velocity is of paramount importance in such diverse applications as adaptive modulation and handoff. In this paper we derive the Cramer-Rao bound for all Doppler estimators that utilize the I/Q components of the channel coefficients, which is also shown to be a bound for all estimators that utilize the envelope or the logarithm of the envelope. Furthermore, by exploiting the method of stationary phase, we show that the sample covariances of the small scale fading converge at a rate of O(log(N)/N), regardless of the angle of arrival distribution. This is used to conclude that the covariance-based estimators in the literature converge to their true values at that same rate. We compare the CRB with the variance of covariance-based Doppler estimators by Monte Carlo simulation.

In mobile communications the strength of a line of sight component measured by the K factor of the Ricean received envelope distribution has significant impact on system performance analysis and link budget calculations. In this paper, we study the performance of moment-based estimators for the Ricean K-factor as less complex alternatives to the maximum likelihood estimator. Our asymptotic analysis reveals that the estimators that rely on lower-order moments have a better asymptotic performance for moderate/large values of K. We also illustrate, by Monte Carlo simulations, that the fading correlation among the envelope samples deteriorates the estimator performance. The simplest estimator, which can be expressed in closed form in terms of the second- and fourth-order sample moments offers a good compromise between statistical performance and computational simplicity.

The ability of orthogonal frequency-division multiplexing systems to mitigate frequency-selective channels is impaired by the presence of carrier frequency offsets (CFOs). In this paper, we investigate identifiability issues involving high-resolution techniques that have been proposed for blind CFO estimation based on null subcarriers. We propose new approaches that do not suffer from the lack of identifiability and adopt adaptive algorithms that are computationally feasible. The performance of these techniques in relation to the location of the null subcarriers is also investigated via computer simulations and compared with the modified Cramer-Rao bound.

Abstract Estimation of signal strength, a measure of channel quality, and Doppler spread which is proportional to the mobile speed, are important for handoff algorithms and optimal tuning of system parameters to changing channel conditions in adaptive transmission systems. This paper provides a survey of existing techniques for estimating the statistical parameters of the mobile channel. We discuss the current state of the art in estimation of the received signal strength, mobile velocity, and other related statistical channel parameters, illustrate their performance, and compare existing techniques. The sensitivity of these schemes to modeling error owing to the presence of line of sight, directional reception, and noise is characterized analytically and illustrated by simulations. Copyright © 2001 John Wiley & Sons, Ltd.

Estimation of the maximum Doppler spread, or equivalently the vehicle velocity is useful in improving handoff algorithms, and necessary for the optimal tuning of parameters for systems that adapt to changing channel conditions. We provide a novel velocity estimator based on the spectral moments of the in-phase and the quadrature-phase components or the squared envelope of the received signal. We characterize the joint effects of the Ricean K-factor, the directivity and the angle of non-isotropic scattering, and the effects of additive white noise on our estimator and other covariance-based velocity estimators analytically. Simulations illustrate our approach and compare with existing techniques.

The time-varying impulse response of rapidly fading mobile communication channels is expanded over a basis of complex exponentials that arise due to Doppler effects encountered with multipath propagation. Blind methods are reviewed for estimating the bases' parameters and the model orders. Existing second-order methods are critiqued and novel algorithms are developed for blind identification, direct, zero-forcing equalization and minimum mean square error (MMSE) equalization by combining channel diversity with temporal (fractional sampling) and/or spatial diversity which becomes available with multiple receivers. Illustrative simulations are also presented.

In mobile communications, often time-varying multipath is too rapid for a conventional adaptive algorithm to track. This motivates expansion of the time varying channel impulse response over a basis. Rather than estimating the time-invariant coefficients of this basis expansion, it is possible to equalize the channel output directly even when the input is not known. This requires multichannel data as well as a minimal persistence of the excitation condition on the input and a coprimeness condition on the multiple channels obtained via fractional sampling and/or multiple antennas. Since the coefficients of the basis expansion will not be constant due to noise and unmodelled dynamics, the equalizer coefficients may also change slowly with time. Adaptive algorithms to track this change are proposed and basis mismatch problems are also investigated.