This paper studies intelligent reflecting surface (IRS)-assisted free space optical (FSO) quantum communication systems. An IRS can relax the requirement of a line-of-sight (LoS) link between Alice and Bob for FSO quantum key distribution (QKD) applications. The IRS focuses the laser beam toward Bob by introducing a phase shift to the incoming incident beam from Alice. Both discrete variable QKD (DV-QKD) and continuous variable QKD (CV-QKD) protocols for IRS-assisted QKD systems are studied. For DV-QKD, we characterize the average quantum bit error rate (QBER) and the achievable secret key rate (SKR) under a log-normal fading turbulence model. For CV-QKD, we present the ultimate quantum information-theoretic bounds for the SKR and entanglement distribution rates. We also characterize the achievable SKR of a practical CV-QKD protocol implemented using Gaussian coherent states. Our results reveal that Alice and Bob can generate a quantum secure key even if the LoS link between them is blocked by utilizing the IRS. Furthermore, with a quadratic phase shift profile, the IRS-assisted link achieves a higher SKR as compared to the direct LoS link and a relay-assisted link for large transmission distances.

We design a statistical hypothesis test for performing leak detection in water pipeline channels. By applying an appropriate model for signal propagation, we show that the detection problem becomes one of distinguishing signal from noise, with the noise being described by a multivariate Gaussian distribution with unknown covariance matrix. We present a detection method for high dimensional settings, which employs a regularized covariance matrix estimate. The regularization parameter is optimized for the leak detection application by applying results from large dimensional random matrix theory. The proposed approach is shown to yield improved performance in leak detection under high dimensional settings.

We study the secret key rate (SKR) of a multiple-input multiple-output (MIMO) continuous variable quantum key distribution (CVQKD) system operating at terahertz (THz) frequencies, accounting for the effects of channel estimation. We propose a practical channel estimation scheme for the THz MIMO CVQKD system which is necessary to realize transmit-receive beamforming between Alice and Bob. We characterize the input-output relation between Alice and Bob during the key generation phase, by incorporating the effects of additional noise terms arising due to the channel estimation error and detector noise. Furthermore, we analyze the SKR of the system and study the effect of channel estimation error and overhead. Our simulation results reveal that the SKR may degrade significantly as compared to the SKR upper bound that assumes perfect channel state information, particularly at large transmission distances.

We consider multi-antenna wireless systems employing large intelligent surfaces (LIS); a new physical layer technology for improving coverage and energy efficiency by intelligently controlling the propagation environment. In practice, achieving the promised gains of LIS requires accurate channel estimation. Recent solutions have been presented based on the simple, but sub-optimal, least-squares (LS) approach. Here, we propose an improved channel estimator based on the minimum mean-squared-error (MMSE) criterion. While a closed-form MMSE solution is intractable, we obtain an approximate MMSE solution by employing a deep learning-based denoising convolutional neural network (DnCNN) that takes as input the noisy LS channel estimate, and produces a cleaned channel matrix at its output. Simulation results show that the proposed DnCNN-based estimator achieves a 3 dB improvement in mean squared error compared with the existing LS approach.

SUMMARY: Learning underlying correlation patterns in data is a central problem across scientific fields. Maximum entropy models present an important class of statistical approaches for addressing this problem. However, accurately and efficiently inferring model parameters are a major challenge, particularly for modern high-dimensional applications such as in biology, for which the number of parameters is enormous. Previously, we developed a statistical method, minimum probability flow-Boltzmann Machine Learning (MPF-BML), for performing fast and accurate inference of maximum entropy model parameters, which was applied to genetic sequence data to estimate the fitness landscape for the surface proteins of human immunodeficiency virus and hepatitis C virus. To facilitate seamless use of MPF-BML and encourage more widespread application to data in diverse fields, we present a standalone cross-platform package of MPF-BML which features an easy-to-use graphical user interface. The package only requires the input data (protein sequence data or data of multiple configurations of a complex system with large number of variables) and returns the maximum entropy model parameters. AVAILABILITY AND IMPLEMENTATION: The MPF-BML software is publicly available under the MIT License at https://github.com/ahmedaq/MPF-BML-GUI. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

SUMMARY: Patterns of mutational correlations, learnt from protein sequences, have been shown to be informative of co-evolutionary sectors that are tightly linked to functional and/or structural properties of proteins. Previously, we developed a statistical inference method, robust co-evolutionary analysis (RoCA), to reliably predict co-evolutionary sectors of proteins, while controlling for statistical errors caused by limited data. RoCA was demonstrated on multiple viral proteins, with the inferred sectors showing close correspondences with experimentally-known biochemical domains. To facilitate seamless use of RoCA and promote more widespread application to protein data, here we present a standalone cross-platform package 'RocaSec' which features an easy-to-use GUI. The package only requires the multiple sequence alignment of a protein for inferring the co-evolutionary sectors. In addition, when information on the protein biochemical domains is provided, RocaSec returns the corresponding statistical association between the inferred sectors and biochemical domains. AVAILABILITY AND IMPLEMENTATION: The RocaSec software is publicly available under the MIT License at https://github.com/ahmedaq/RocaSec. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

A new digital modulation scheme, termed frequency-phase keying (FPK), that combines frequency-shift keying (FSK) and phase-shift keying (PSK), is presented. Optimized signal designs for $M$ -ary FPK that jointly select the phase and frequency of the modulating signal in order to minimize the union bound on the symbol error probability with maximum likelihood reception are obtained. Solutions for baseband communication in additive white Gaussian noise channels and for passband communication in Rayleigh fading with receive diversity are derived. In contrast to conventional FSK and PSK, and to existing hybrid FSK/PSK schemes, the designed FPK signal constellations have the desirable property that the maximum correlation coefficient between any two signals is negative. We demonstrate that the proposed FPK solutions yield improved error performance for both baseband and passband communication.

We consider a robust version of regularized discriminant analysis (RDA) classifiers to account for potential spurious or mislabeled observations in the training data set. To build a robust discriminant rule, a robust estimation of the covariance matrix is essential. In this work, we propose to use a regularized version of Tyler's covariance estimator, in the regime where both the number of variables and the number of training samples are large and of similar order. Building upon fundamental results from random matrix theory, we show that the robust classifier is asymptotically equivalent to traditional, non-robust classifiers when the training data is free from outliers. Simulations on synthetic and real datasets confirm our theoretical observations and further attest to the benefits brought by the robust classifier when the data is corrupted by outliers.

MOTIVATION: Patterns of mutational correlations, learnt from patient-derived sequences of human immunodeficiency virus (HIV) proteins, are informative of biochemically linked networks of interacting sites that may enable viral escape from the host immune system. Accurate identification of these networks is important for rationally designing vaccines which can effectively block immune escape pathways. Previous computational methods have partly identified such networks by examining the principal components (PCs) of the mutational correlation matrix of HIV Gag proteins. However, driven by a conservative approach, these methods analyze the few dominant (strongest) PCs, potentially missing information embedded within the sub-dominant (relatively weaker) ones that may be important for vaccine design. RESULTS: By using sequence data for HIV Gag, complemented by model-based simulations, we revealed that certain networks of interacting sites that appear important for vaccine design purposes are not accurately reflected by the dominant PCs. Rather, these networks are encoded jointly by both dominant and sub-dominant PCs. By incorporating information from the sub-dominant PCs, we identified a network of interacting sites of HIV Gag that associated very strongly with viral control. Based on this network, we propose several new candidates for a potent T-cell-based HIV vaccine. AVAILABILITY AND IMPLEMENTATION: Accession numbers of all sequences used and the source code scripts for all analysis and figures reported in this work are available online at https://github.com/faraz107/HIV-Gag-Immunogens. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Mutational correlation patterns found in population-level sequence data for the Human Immunodeficiency Virus (HIV) and the Hepatitis C Virus (HCV) have been demonstrated to be informative of viral fitness.Such patterns can be seen as footprints of the intrinsic functional constraints placed on viral evolution under diverse selective pressures.Here, considering multiple HIV and HCV proteins, we demonstrate that these mutational correlations encode a modular co-evolutionary structure that is tightly linked to the structural and functional properties of the respective proteins.Specifically, by introducing a robust statistical method based on sparse principal component analysis, we identify near-disjoint sets of collectively-correlated residues (sectors) having mostly a one-to-one association to largely distinct structural or functional domains.This suggests that the distinct phenotypic properties of HIV/HCV proteins often give rise to quasi-independent modes of evolution, with each mode involving a sparse and localized network of mutational interactions.Moreover, individual inferred sectors of HIV are shown to carry immunological significance, providing insight for guiding targeted vaccine strategies. Author summaryHIV and HCV cause devastating infectious diseases for which no functional vaccine exists.A key problem is that while individual mutations in viral epitopes under immune pressure may substantially compromise viral fitness, immune escape is typically facilitated by other "compensatory" mutations that restore fitness.These compensatory pathways are complicated and remain poorly understood.They do, however, leave co-evolutionary markers which may be inferred from measured sequence data.Here, by introducing a new robust statistical method, we demonstrated that the compensatory networks employed by both viruses exhibit a remarkably simple decomposition involving small and near-distinct groups of protein residues, with most groups having a clear association to

We investigate the achievable uplink rate of multi-cell massive multi-input multi-output (MIMO) systems considering pilot reuse across cells. Based on tractable approximations for the achievable rates, we derive the optimal pilot length to maximize the sum rate per cell. Interestingly, it is found that, for moderately large numbers of base station (BS) antennas, the optimal pilot length is above the minimum feasible value, and the gains brought by the extra amount of training diminish as the reuse factor grows. Simulation results confirm the accuracy of our analysis.

We derive an asymptotic outage probability expression for multiple-input multiple-output maximum-ratiocombining (MIMO-MRC) systems considering Rician fading channels with both transmit and receive spatial correlation. This result is facilitated by a new asymptotic expression which we obtain for the cumulative distribution function of the maximum eigenvalue of a noncentral quadratic form in complex Gaussian matrices. Based on our analysis, we demonstrate that for a rank-1 line-of-sight (LoS) path, the interaction with the correlation matrices may yield improved or degraded performance. The relative effect depends largely on the geometric alignment of the LoS path with the eigenvectors of the correlation matrices. Generally speaking, when the LoS path aligns with the weak eigenvectors (i.e., those corresponding to the smallest eigenvalues), both a stronger LoS component, characterized by a higher Rician K factor, and a higher correlation lead to improved performance. In contrast, when the LoS path aligns with the strong eigenvectors, we demonstrate that there exists distinct regions for which increasing the Rician K factor has a beneficial or deleterious effect. Our results, in general, provide novel insight into how the mutual interactions of LoS and spatial correlation components impact the performance of MIMO-MRC systems.

Building on recent results in the random matrix analysis of robust estimators of scatter, we show that a certain class of such estimators obtained from samples containing outliers behaves similar to a well-known random matrix model in the limiting regime where both the population and sample sizes grow to infinity at the same speed. This result allows us to understand the structure of such estimators when a certain fraction of the samples is corrupted by outliers and, in particular, to derive their asymptotic eigenvalue distributions. This analysis is a first step towards an improved usage of robust estimation methods under the presence of outliers when the number of independent observations is not too large compared to the size of the population.

This paper investigates the sum-rate gains brought by power allocation strategies in multicell massive multiple-input- multiple-output systems, assuming time-division duplex transmission. For both uplink and downlink, we derive tractable expressions for the achievable rate with zero-forcing receivers and precoders, respectively. To avoid high-complexity joint optimization across the network, we propose a scheduling mechanism for power allocation, where, in a single time slot, only cells that do not interfere with each other adjust their transmit powers. Based on this, corresponding transmit power allocation strategies are derived, aimed at maximizing the sum rate per cell. These schemes are shown to bring considerable gains over equal power allocation for practical antenna configurations (e.g., up to a few hundred). However, with fixed number of users N, these gains diminish as M → ∞, and equal power allocation becomes optimal. A different conclusion is drawn for the case where both M and N grow large together, in which case improved rates are achieved as M grows with fixed M/N ratio, and the relative gains over the equal power allocation diminish as M/N grows. Moreover, we also provide applicable values of M/N under an acceptable power allocation gain threshold, which can be used to determine when the proposed power allocation schemes yield appreciable gains and when they do not. From the network point of view, the proposed scheduling approach can achieve almost the same performance as the joint power allocation after one scheduling round, with much reduced complexity.

We present an optimized secure multi-antenna transmission approach based on artificial-noise-aided beamforming, with limited feedback from a desired single-antenna receiver. To deal with beamformer quantization errors as well as unknown eavesdropper channel characteristics, our approach is aimed at maximizing throughput under dual performance constraints-a connection outage constraint on the desired communication channel and a secrecy outage constraint to guard against eavesdropping. We propose an adaptive transmission strategy that judiciously selects the wiretap coding parameters, as well as the power allocation between the artificial noise and the information signal. This optimized solution reveals several important differences with respect to solutions designed previously under the assumption of perfect feedback. We also investigate the problem of how to most efficiently utilize the feedback bits. The simulation results indicate that a good design strategy is to use approximately 20% of these bits to quantize the channel gain information, with the remainder to quantize the channel direction, and this allocation is largely insensitive to the secrecy outage constraint imposed. In addition, we find that 8 feedback bits per transmit antenna is sufficient to achieve approximately 90% of the throughput attainable with perfect feedback.

We study secure multi-antenna transmission with limited feedback from the intended receiver and no feedback from the malicious eavesdropper. Our system uses the artificial-noise-aided beamforming approach to enhance secrecy, considering slow fading channels with outage constraints on the reliability performance of legitimate communication and the secrecy performance against eavesdropping. Our analytical results provide conditions on the minimum number of feedback bits and the minimum strength of the intended channel for making secure transmission possible. We observe that strengthening the secrecy outage constraint puts higher requirements on the number of feedback bits and the strength of the intended channel. To maximize the achievable secrecy rate, the optimal transmit power allocation between the information signal and the artificial noise is also derived in closed form.

We consider multiple-antenna signal detection of primary user transmission signals by secondary user receivers in cognitive radio networks. The optimal detector is analyzed for the scenario where the number of primary user signals is no less than the number of receive antennas at the secondary users. We first derive exact expressions for the moments of the generalized likelihood ratio (GLRT) statistic, yielding approximations for the false alarm and detection probabilities. We then show that the normalized GLRT statistic converges in distribution to a Gaussian random variable when the number of antennas and observations grow large at the same rate, which is used to obtain a simple design rule for the signal detection threshold.

In this paper, the impact of interferers that are not synchronized in frequency is investigated in multi-antenna OFDM systems. Exact closed-form expressions for the outage probabilities are derived for two spatial linear receivers: the matched-filter (MF) receiver and the linear minimum-mean-square-error (LMMSE) receiver, assuming correlated frequency-selective Rayleigh fading channels and carrier frequency offsets (CFOs) between each interferer and the receiver. It is found that the CFOs have a negligible impact on the performance of the MF receiver, but a non-negligible impact on the performance of the LMMSE receiver for a range of realistic parameters. This theoretical analysis reveals valuable insights into practical implementation of such systems, and enables system designers to quantify the impact of the CFOs on the performance of the MF receiver and the LMMSE receiver.

We investigate the impact of channel estimation on the performance of downlink random cellular networks. First, we derive a new closed-form expression for the coverage probability under certain practical conditions. We show that the coverage probability is dependent on the user and base station (BS) densities solely through their ratio for arbitrary pilot-training length. Next, we derive the optimal pilot-training length that maximizes the area spectral efficiency (ASE) in several asymptotic regimes, and capture the dependence of this optimal length on the ratio between the user and BS densities. The ASE loss due to training is shown to be less significant in small cell networks with a larger base station density.

We investigate the asset allocation optimization under the time-varying high frequency global minimum variance portfolio framework. The overall performance strongly relies on the estimate of the portfolio covariance matrix. However, for such applications, the sample size is often of similar order to the number of assets and in this case, the performance of the conventional covariance estimators are not very satisfactory. Additionally, the time variation effects will further amplify the estimation error and thus lead to inaccurate and high-risk investment decisions. In this paper, we propose to use the recently developed time variation adjusted realized covariance (TVARCV) estimator in a shrinkage structure, in order to address the above-mentioned problems. For this shrinkage TVARCV estimator, we provide a deterministic characterization of the portfolio realized risk in terms of the shrinkage parameter and the covariance matrix. At last, aiming to minimize the portfolio risk with respect to the shrinkage parameter, we also provide a consistent estimator for the realized variance, which depends only on the observable returns. Numerical results show that the proposed estimator is robust to time variation and has smaller portfolio risk.

The performance of single-cell distributed multiple-input multiple-output (D-MIMO) systems is not only affected by small-scale Rayleigh fading but also from large-scale fading and path-loss. In this paper, we elaborate on the sum rate of D-MIMO systems employing linear zero-forcing receivers, accounting for both large and small-scale fading effects, as well as spatial correlation at the transmit side. In particular, we consider the classical lognormal model and propose closed-form upper and lower bounds on the achievable sum rate. Using these bounds as a starting point, we pursue a "large-system" analysis and provide asymptotic expressions when the number of antennas at the base station (BS) grow large, and when the number of antennas at both ends grow large with a fixed and finite ratio. A detailed characterization in the asymptotically high and low signal to noise ratio regimes is also provided. An interesting observation from our results is that in order to maximize the sum rate, the RPs should be placed at unequal distances to the BS when they experience the same level of shadowing. The resulting closed-form expressions are compared with the corresponding results on MIMO optimal receivers.

We study physical-layer security in wireless ad hoc networks and investigate two types of multi-antenna transmission schemes for providing secrecy enhancements. To establish secure transmission against malicious eavesdroppers, we consider the generation of artificial noise with either sectoring or beamforming. For both approaches, we provide a statistical characterization and tradeoff analysis of the outage performance of the legitimate communication and the eavesdropping links. We then investigate the network-wide secrecy throughput performance of both schemes in terms of the secrecy transmission capacity, and study the optimal power allocation between the information signal and the artificial noise. Our analysis indicates that, under transmit power optimization, the beamforming scheme outperforms the sectoring scheme, except for the case where the number of transmit antennas are sufficiently large. Our study also reveals some interesting differences between the optimal power allocation for the sectoring and beamforming schemes.

This paper builds upon our recent work which computed the moment generating function of the multiple-input multiple-output mutual information exactly in terms of a Painlevé V differential equation. By exploiting this key analytical tool, we provide an in-depth characterization of the mutual information distribution for sufficiently large (but finite) antenna numbers. In particular, we derive systematic closed-form expansions for the high-order cumulants. These results yield considerable new insight, such as providing a technical explanation as to why the well-known Gaussian approximation is quite robust to large signal-to-noise ratio for the case of unequal antenna arrays, while it deviates strongly for equal antenna arrays. In addition, by drawing upon our high-order cumulant expansions, we employ the Edgeworth expansion technique to propose a refined Gaussian approximation which is shown to give a very accurate closed-form characterization of the mutual information distribution, both around the mean and for moderate deviations into the tails (where the Gaussian approximation fails remarkably). For stronger deviations where the Edgeworth expansion becomes unwieldy, we employ the saddle point method and asymptotic integration tools to establish new analytical characterizations which are shown to be very simple and accurate. Based on these results, we also recover key well-established properties of the tail distribution, including the diversity-multiplexing-tradeoff.

We investigate the impact of channel estimation (CE) on the performance of point-to-point transmission schemes in wireless ad hoc networks. We first derive a new closed-form expression for the outage probability when the minimum mean square error estimator is utilized for CE, and show that the training-pilot length should increase as a linear function of the network intensity to maintain a fixed CE quality. Next, we derive the optimal training-pilot length which maximizes the transmission capacity under interference-limited conditions, and show that this optimal length increases with the frame length according to a square-root law.

This paper presents a detailed sum rate characterization of distributed multiple-input multiple-output systems operating over composite fading channels and employing linear zero-forcing receivers. We consider the Rayleigh/Lognormal fading model and also take into account the effects of path-loss and spatial correlation at the transmit side. New closed-form upper and lower bounds on the achievable sum rate are proposed that apply for arbitrary numbers of antennas. Moreover, we investigate the concept of large-scale multiple-antenna systems when the number of receive antennas grow large. In this asymptotic regime, it is shown that the effects of Rayleigh fading are averaged out and the channel is dominated by the much more slowly varying shadowing. An interesting observation from our results is that in order to maximize capacity, the radio ports should be placed at unequal distances to the base station when they experience the same level of shadowing.

In this paper we study the distribution of the scaled largest eigenvalue of complex Wishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have been derived for the probability density function and the cumulative distribution function. The derived results involve only finite sums of polynomials. These results are obtained by taking advantage of properties of the Mellin transform for products of independent random variables.

This paper investigates the finite signal-to-noise ratio (SNR) diversity-multiplexing trade-off (DMT) of point-to-point wireless channels assisted by multiple relays. Results are derived for both amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. For the AF protocol, we derive accurate approximations for the system outage probability when the relays are clustered between the source and destination. For the case where all the relays are clustered near the destination, an exact closed-form expression for the system outage probability is obtained. For the DF protocol, under general multiple relaying configurations, we derive an exact closed-form expression for the system outage probability. The outage results for AF and DF are used subsequently to yield expressions for the finite-SNR DMT. We also extract the conventional asymptotic DMTs as special cases of the finite-SNR results, and demonstrate that the asymptotic DMTs can significantly overestimate the level of diversity that is achievable for practical error rates and SNRs.

In this paper, we compute two important information-theoretic quantities which arise in the application of multiple-input multiple-output (MIMO) antenna wireless communication systems: the distribution of the mutual information of multiantenna Gaussian channels, and the Gallager random coding upper bound on the error probability achievable by finite-length channel codes. We show that the mathematical problem underpinning both quantities is the computation of certain Hankel determinants generated by deformed versions of classical weight functions. For single-user MIMO systems, it is a deformed Laguerre weight; for multiuser MIMO systems, it is a deformed Jacobi weight. We apply two different methods to characterize each of these Hankel determinants. First, we employ the ladder operators of the corresponding monic rthogonal polynomials to give an exact characterization of the Hankel determinants in terms of Painlevé differential equations. This turns out to be a Painlevé V for the single-user MIMO scenario and a Painlevé VI for the multiuser scenario. We then introduce Coulomb fluid linear statistics methods to derive closed-form approximations for the MIMO mutual information distribution and the error probability which, although formally valid for large matrix dimensions, are shown to give accurate results even when the matrix dimensions are small. Focusing on the single-user mutual information distribution, we then employ the exact Painlevé V representation with the help of the Coulomb fluid linear statistics approximation to yield deeper insights into the scaling behavior in terms of the number of antennas and signal-to-noise ratio (SNR). Among other things, these results allow us to study the asymptotic Gaussianity of the distribution as the number of antennas increase, and to investigate when and why such approximations break down as the SNR increases. Based on the Painlevé, we also derive recursive formulas for explicitly computing in closed form any desired number of correction terms to the asymptotic mean and variance, as well as closed-form asymptotic expressions for any desired number of higher order cumulants. Using these cumulants, we propose new closed-form approximations to the mutual information distribution which are shown to be very accurate, not only in the bulk but also in the tail region of interest for the outage probability.

This paper investigates the following general problem relating to ordered random processes: givennindependent but not necessarily identical random processes, how frequently, on average, does any given process become one of thepth (p=1,2,...,n-1) largest processes? This is a fundamental problem arising in the design and analysis of contemporary multidimensional wireless communication systems (e.g., multiantenna, multiuser) employing opportunistic selection. We formulate this problem as one involving the level crossing rate (LCR) of a carefully defined ordered random process across the zero threshold, which we solve by developing a new mathematical framework based on the theory of permanents. For the case where the processes correspond to time-varying Rayleigh fading channels, we present exact closed-form formulas for the LCR, simplified tight upper bounds, as well as asymptotic results fornandpapproaching infinity but with fixed ratio. These results reveal interesting fundamental limits for the LCR, and are shown to given meaningful insight even for small values ofnandp. We further use our mathematical framework to characterize the required per-branch and overall switching rate of a generalized selection combining diversity receiver, allowing for different average powers for each branch. With the aid of majorization theory, we demonstrate that the overall switching rate is maximized when the power delay profile is uniform.

This paper investigates communication over multiple-input multiple-output Rayleigh-product channels in the presence of both co-channel interference and thermal noise. We first present exact expressions for the marginal ordered eigenvalue distributions of the channel Gram matrix when multichannel beamforming is employed, from which we obtain exact results on the outage probability on each eigenmode. Our results are applicable to an extensive class of multichannel systems with generic system configurations. For particular scenarios of single-input multiple-output, keyhole, and multiple-input single-output channels, simplified closed-form expressions for the asymptotic distributions of the non-zero eigenvalue of the channel Gram matrix are derived. These results indicate that the diversity order is only determined by the second largest value among the number of transmit antennas, scatterers, and receive antennas. For these scenarios, we also derive concise closed-form expressions for the moments of the output signal-to-interference-plus-noise ratio, from which an explicit relationship to the moments in Rayleigh fading channels is revealed. These results are also used to investigate the impact of the number of channel scatterers on the bandwidth requirements for a given transmission rate and power, at low signal-to-noise ratios.

We develop a general framework for the analysis of a broad class of point-to-point linear multiple-input multiple-output (MIMO) transmission schemes in decentralized wireless ad hoc networks. New general closed-form expressions are derived for the outage probability, throughput and transmission capacity. For the throughput, we investigate the optimal number of data streams in various asymptotic regimes, which is shown to be dependent on different network parameters. For the transmission capacity, we prove that it scales linearly with the number of antennas, provided that the number of data streams also scales linearly with the number of antennas, in addition to meeting some mild technical conditions. We also characterize the optimal number of data streams for maximizing the transmission capacity. To make our discussion concrete, we apply our general framework to investigate three popular MIMO schemes, each requiring different levels of feedback. In particular, we consider eigenmode selection with MIMO singular value decomposition, multiple transmit antenna selection, and open-loop spatial multiplexing. Our analysis of these schemes reveals that significant performance gains are achieved by utilizing feedback under a range of network conditions.

This paper studies the eigenvalue distributions of multiple-input multiple-output (MIMO) Rayleigh-product channels in the presence of both co-channel interference and thermal noise. We first present exact expressions for the marginal ordered eigenvalue distributions of the channel Gram matrix when multichannel beamforming is employed, from which we obtain exact results of the outage probability on each eigenmode. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel, allowing for transmission on any numbers of eigensubchannels, with any numbers of antennas, any numbers of scatterers in the environment, and any numbers of interferers with arbitrary powers. Also, for the particular case of keyhole channels, simplified closed-form expressions for the asymptotic distributions of the non-zero eigenvalue of the channel Gram matrix are derived, which indicate that the diversity order is only determined by the minimum of the number of transmit and receive antennas.

This paper derives analytical expressions for the eigenvalues of so-called gamma-Wishart random matrices, which arise in the context of multiple-input multiple-output (MIMO) transmission over land-mobile-satellite (LMS) communication channels. Such matrices are representative of complex noncentral Wishart matrices, but with randomly varying noncentrality parameter following a distribution closely related to the matrix-variate gamma. For these matrices, we derive exact closed form expressions for the distribution functions of the extreme eigenvalues (i.e., the maximum and minimum). These results are remarkably simple, and are useful for the performance analysis of MIMO transmission techniques over LMS channels.

Given n independent but not necessarily identical random processes, this paper investigates the general problem of determining how frequently, on average, any given process becomes at least the p-th (p = 1, 2, . . . , n - 1) largest among all processes. This problem requires determining the level crossing rate (LCR) of a carefully defined ordered process, which we solve by developing a general mathematical framework based on the theory of permanents. Our results are very general and may be applicable for a wide range of engineering applications which involve ordered random processes. To demonstrate the applicability to wireless communications, we present closed-form formulas for the LCR for the case where the processes correspond to time-varying Rayleigh fading channels, and use these to characterize the required switching rate for a particular branch of a generalized selection combining diversity receiver.

The performance of spatial multiplexing systems with linear minimum-mean-squared-error receivers is investigated in ad hoc networks. We present new exact closed-form expressions for the outage probability and transmission capacity. These expressions reveal that from a transmission capacity perspective, single-stream transmission is preferable over multi-stream transmission.

We investigate the multiple-input multiple-output broadcast channel with channel distribution information available at the transmitter. The so-called fading-paper model is considered with Nttransmit antennas, and each user having Nrreceive antennas. Near-optimal designs are proposed for the inflation factor matrix under general fading conditions, based on maximizing the approximation of linear assignment capacity. It is proved that for Nt≤ Nr, this matrix has a similar structure and achieves a similar interference elimination effect as dirty-paper coding. Also, low complexity iterative algorithms are proposed for Nt>; Nrcase, which yield a good choice for the inflation factor matrix numerically. Based on the obtained inflation factor matrix, we provide efficient approaches to evaluate the linear assignment achievable rate region for some popular statistical channel models.

We investigate the capacity and beamforming optimality of multi-antenna relaying systems, given access to statistical channel information at the relay and source. Multi-antenna relay configurations are considered, for which the source as well as either the relay or destination have multiple antennas, and the relay operates with amplify-and-forward. We first compute the optimal transmission strategies at both the source and relay, and derive necessary and sufficient conditions for which beamforming achieves capacity. To gain more insight, we then employ tools from stochastic majorization theory to characterize the impact of the destination correlation and the relay gain on the capacity and beamforming optimality range. These results demonstrate some intriguing behavior, which arises due to the joint interplay between the transmit power, relay gain, and level of correlation at the destination. It is shown, among other things, that for certain transmit powers and relay gains, the beamforming optimality region becomes independent of the destination correlation. By relaxing the beamforming optimality condition, we also derive a simple explicit upper bound which gives further insights into the joint effect of the SNR and the transmit correlation on the beamforming optimality range.

The diamond relay network is an efficient cooperative networking configuration in which the source node cooperates with two selected neighbors. For such networks, we investigate the impact of the relay positioning on the performance. In particular, considering an opportunistic protocol based on the use of relaying buffers, we provide sets of constraints which, when satisfied, give sufficient conditions for simultaneously guaranteeing network stability and throughput improvement. These results are given for both symmetric and asymmetric relay locations. In contrast to prior work dealing with the diamond relay network, we also break the strong hypothesis of no interlink interference between the source and relay transmissions. Our results provide design guidelines for relay selection by establishing areas of feasible relay locations, whilst also identifying optimal positions which lead to maximum throughput gain.

This paper investigates the symbol error rate (SER) performance of the multiple-input multiple-output (MIMO) multi-channel beamforming (MB) in the general double-scattering channel. We derive an asymptotic expansion on the marginal eigenvalue distribution of the MIMO channel matrix, and apply the result to get an approximate expression on the average SER at high signal-to-noise ratio (SNR). Two parameters pertaining to the SER, i.e., the diversity gain and the array gain, are analyzed. Our results show that it suffices for the double-scattering channel to have only limited scatterers, if the same diversity gain as the Rayleigh channel is desired; however, once the number of scatterers is below a certain level, the array gain in the double-scattering channel will vary with the SNR logarithmically.

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

This paper investigates the performance of open-loop multi-antenna point-to-point links in ad hoc networks with slotted ALOHA medium access control (MAC). We consider spatial multiplexing transmission with linear maximum ratio combining and zero forcing receivers, as well as orthogonal space time block coded transmission. New closed-form expressions are derived for the outage probability, throughput and transmission capacity. Our results demonstrate that both the best performing scheme and the optimum number of transmit antennas depend on different network parameters, such as the node intensity and the signal-to-interference-and-noise ratio operating value. We then compare the performance to a network consisting of single-antenna devices and an idealized fully centrally coordinated MAC. These results show that multi-antenna schemes with a simple decentralized slotted ALOHA MAC can outperform even idealized single-antenna networks in various practical scenarios.

We propose new low complexity opportunistic relaying strategies for multiple-antenna relay networks. Assuming that a source communicates with a destination, both equipped with M antennas, assisted by K single-antenna relay terminals using an amplify-and-forward half-duplex protocol, we propose a new transmission strategy which employs linear zero-forcing transmission and reception. Integrated with this transmission strategy, we propose two low complexity opportunistic relay selection algorithms, referred to as the Maximum Sum Rate Relay Selection (MSR) and Greedy Semi-Orthogonal Relay Selection (GSO) algorithms, which select only a few very important relays to share the total power. For the GSO algorithm, we present a theoretical analysis of the sum capacity as K grows large, which is shown to be M/2 log log K + O(1). This result is also shown to coincide with a fundamental cut-set upper bound on the sum capacity of MIMO networks with opportunistic relaying which we derive; thereby establishing a new exact scaling law for such networks, as well as demonstrating the asymptotic optimality of our proposed low complexity approach. Our numerical studies also indicate that our proposed opportunistic relaying techniques yield significant capacity benefits over the conventional approach without opportunistic selection, even when the number of relays is not large.

We use non-asymptotic random matrix theory to obtain new expressions for certain statistical properties of spatially uncorrelated multi-keyhole multiple-input multiple-output (MIMO) channels. These include closed-form expressions for the distribution and moments of an unordered eigenvalue, as well as solutions for the expected log-determinant and expected characteristic polynomial. Our results are general for arbitrary numbers of transmit and receive antennas, and arbitrary number of keyholes with possibly differing powers. Based on these, we derive exact closed-form expressions and simplified upper and lower bounds for the ergodic mutual information, assuming that channel state information (CSI) is only known at the receiver. Results show that the capacity of multi-keyhole channels is typically worse than that for rich-scattering MIMO Rayleigh channels.

In this paper, we investigate the benefits of providing limited-feedback and using transmit antenna selection (TAS) in ad hoc networks. We find that the TAS scheme can provide throughput gains of up to 50% compared to the non-feedback scheme. We also find that the performance gains of the TAS scheme are more significant for low path loss exponents and single-antenna transmission. Our results are obtained by deriving new closed-form expressions for the network throughput and transmission capacity. Moreover, we also propose design guidelines for TAS to determine the optimal number of antennas used for transmission.

In this paper, we study the statistical distribution of the Demmel condition number of complex Wishart matrices, a quantity which has found numerous applications to wireless communications, such as adaptive switching, link adaptation, and spectrum sensing. We give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF).

We analyze the optimality of beamforming in multiple-input single-output relay channels without a direct link between the source and the destination. Assuming that the source has access to the channel correlation information, and that the relay operates in amplify and forward mode with a long term power constraint, we first show that the optimal transmission strategy is to transmit along the eigen-vectors of the transmit correlation matrix. The optimality of beamforming is then studied via the power allocation problem at the source. In particular, we derive a necessary and sufficient condition under which beamforming achieves the capacity. Our results demonstrate that the finite relay gain decreases the range at which beamforming is optimal.

The standard condition number (SCN) is a fundamental metric in the context of multiple-input multiple-output communication systems, linear detection and classical linear algebra. Hence, in this paper we propose a novel generic framework for the SCN distribution of three different classes of Wishart matrices which leads to new results and insights. In particular, our analysis covers both central and non-central Wishart distributions of arbitrary dimension and therefore is applicable to uncorrelated/semi-correlated Rayleigh fading and Ricean fading scenarios. For the special case of dual semi-correlated central Wishart matrices, we derive exact and asymptotic polynomial expressions for the SCN distributions. All analytical results are validated via Monte-Carlo simulations with the attained accuracy being excellent in all cases. The impact of the model parameters on channel conditioning is also investigated in detail.

We consider a setup where a source communicates with a destination, both equipped with M antennas, assisted by K single-antenna relays using an amplify-and-forward half-duplex protocol. In contrast to conventional approaches where all relays in the network participate, we propose a new opportunistic relaying protocol in which only a few very important relays (VIRs) are selected to share the total power. Assuming perfect channel state information (CSI) at the destination and CSI of the backward channels for the selected VIRs at the source node, we show that the network capacity scales as M/2 log log K + O(1) for fixed M, fixed signal-to-noise ratio, and K → ∞. We also propose two low complexity algorithms for selecting the VIRs, and show that our proposed opportunistic relaying protocol can achieve the optimal capacity scaling, and also yield significant capacity gains compared with the conventional approach.

The paper establishes connections between orthogonal space-time block codes (OSTBC) and multiple-input multiple-output beamforming (MIMO BF). Different from previous work, where the two schemes were studied independently and under specific fading conditions, we consider a framework which unifies the analysis of both schemes in arbitrary fading. In particular, we demonstrate that the diversity gains of OSTBC and MIMO BF are equivalent, regardless of the underlying channel fading distribution. We also derive bounds on the difference in transmit power required for the two schemes to achieve the same outage probability. This result, which again applies for arbitrary fading, quantifies the gain of MIMO BF over OSTBC due to the presence of transmitter channel knowledge.

For multiple-input multiple-output wireless systems, we investigate the important question of how many antennas to place in fixed-length arrays, accounting for both spatial correlation and mutual coupling at the transmitter and receiver. We show that there is an optimal antenna configuration yielding the highest capacity which depends strongly on the array length and the transmission wavelength, but does not depend strongly on the signal to noise ratio (SNR). Moreover, we show that ignoring the effect of mutual coupling gives misleading results, yielding unbounded capacity growth. As another key finding, we demonstrate the surprising result that if the optimal antenna configuration is employed, then further optimizing the transmission based on the channel statistics gives very little benefit over simple equal-power spatial multiplexing. By deriving an expression for the capacity at low SNR, we provide a straightforward method for estimating the optimal number of antennas.

Diamond relay network is a kind of efficient cooperative network, in which the source user selects two neighbors as relays and cooperates with both of them. In our previous work, we have studied its transmission rates for different coding and relaying schemes and proved that the performance of SRP scheme (Spatial Reuse Pattern) is better than others. To further improve the performance, we incorporated the opportunistic scheduling and studied how to use buffers adapted to the time varying Rayleigh fading channel. However, the position information of users has not been considered yet which actually has a great influence on the performance of the diamond relay channel. Thus, in this paper, it is the first time that we study how to select the position of two relays to guarantee the performance of the throughput and delay constraint. This study facilitates the practical application of diamond relay networks since the source user knows that from where selecting neighbors as relays will bring nice performance. Finally, the simulation results confirm our analysis and some interesting illustrations show much novelty.

In this paper, we consider optimal power allocation (OPA) for distributed space-time coded two-way relay networks. Each relay transmits a scaled version of the linear combinations of the received symbols and their conjugates, and the scaling factor is based on automatic gain control (AGC) at the relays. We show that solving the OPA across relays to minimize the average conditional PEP of the destination terminals is a generalized linear fractional programming problem, which can be resolved by the Dinkelbach-type procedure. We also prove that at most two relays are active while the others keep silent if the sum power constraint is made across the relays. This motivates us to propose a new low-complexity relaying scheme that uses distributed Alamouti codes on the selected two-best relay nodes. Simulation results show that the distributed space-time codes (DSTC) with the OPA and the proposed scheme have significant performance gains over the DSTC with the equal power allocation.

This paper considers orthogonal space-time block coded transmission for a multiple-input multiple-output channel (MIMO) with non-coherent amplify-and-forward (AF) relaying in Rayleigh fading. We first characterize the statistical properties of the instantaneous signal-to-noise ratio (SNR) at the destination, by deriving new exact closed form expressions for the moment generating function, cumulants, and first and second moments. These results show a reciprocity relationship between the number of antennas at the relay and destination. The probability density function and cumulative distribution function of the SNR are also derived for certain system configurations, and for various asymptotic regimes. We then investigate the system performance by presenting new analytical expressions for the symbol error rate, outage probability, amount of fading, as well as the diversity order and array gain. Our results indicate that the proposed scheme can achieve the maximum diversity order of the non-coherent AF MIMO relay channel.

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multiple-output (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading.

This paper presents an analytical characterization of the ergodic capacity of amplify-and-forward (AF) MIMO dual-hop relay channels, assuming that the channel state information is available at the destination terminal only. In contrast to prior results, our expressions apply for arbitrary numbers of antennas and arbitrary relay configurations. We derive an expression for the exact ergodic capacity, simplified closed-form expressions for the high SNR regime, and tight closed-form upper and lower bounds. These results are made possible by employing recent tools from finite-dimensional random matrix theory, which are used to derive new closed-form expressions for various statistical properties of the equivalent AF MIMO dual-hop relay channel, such as the distribution of an unordered eigenvalue and certain random determinant properties. Based on the analytical capacity expressions, we investigate the impact of the system and channel characteristics, such as the antenna configuration and the relay power gain. We also demonstrate a number of interesting relationships between the dual-hop AF MIMO relay channel and conventional point-to-point MIMO channels in various asymptotic regimes.

This paper investigates the achievable sum rate of multiple-input multiple-output (MIMO) wireless systems employing linear minimum mean-squared error (MMSE) receivers. We present a new analytic framework which exploits an interesting connection between the achievable sum rate with MMSE receivers and the ergodic mutual information achieved with optimal receivers. This simple but powerful result enables the vast prior literature on ergodic MIMO mutual information to be directly applied to the analysis of MMSE receivers. The framework is particularized to various Rayleigh and Rician channel scenarios to yield new exact closed-form expressions for the achievable sum rate, as well as simplified expressions in the asymptotic regimes of high and low signal-to-noise ratios (SNRs). These expressions lead to the discovery of key insights into the performance of MIMO MMSE receivers under practical channel conditions.

We study the sum capacity of the uplink multiuser multiple-input multiple-output (MIMO) multiple-access channel (MAC) in the low signal-to-noise ratio (SNR) regime under double-scattering and Rician fading scenarios. The receiver is assumed to have perfect channel state information (CSI), while each transmitter knows only its statistical CSI. We first derive analytical expressions for the minimum ¿b/N0and the wideband slope of MIMO systems employing statistical beamforming, based on which we then present new analytical approximations for the sum capacity of the MIMO-MAC at low SNRs, and investigate the effects of transmit, receive and scatterer correlation, as well as Rician K-factor.

This paper investigates a low complexity zero-forcing dirty paper coding based transmission approach for the MIMO broadcast channel, employing eigenmode transmission with greedy semi-orthogonal user selection (SUS). We prove that as the number of users K grows large, our scheme achieves the optimal sum rate scaling of the MIMO broadcast channel (i.e. linear scaling with the number of transmit antennas, and double-logarithmic scaling with K). In addition, we show that whilst the number of receive antennas only affects the asymptotic sum rate scaling via the second-order behavior of the multiuser diversity gain; for finite K, the benefit due to multiple receive antennas can be very significant. Finally, we show the interesting result that the semi-orthogonality constraint imposed by the SUS algorithm, whilst facilitating a very low complexity user selection procedure, does not reduce the multiuser diversity gain in either first or second-order.

We investigate the sum capacity of the uplink multiuser multiple-input multiple-output (MIMO) multiple-access channel (MAC) in the low signal-to-noise ratio (SNR) regime. For each user, the MIMO channel is modeled according to a general class of stochastic channel matrices, known as double-scattering. Assuming that each user knows only their own spatial correlation matrices and employs optimal statistical beamforming transmission, we present new analytical approximations for the sum capacity of the MIMO-MAC for low SNR values. Our approximations are accurate, and lead to key insights into the effect of correlation.

In this paper, we investigate the performance of multiple-input multiple-output (MIMO) multi-channel beamforming (MB) systems in double-scattering channels. In particular, we first derive new expressions for the marginal ordered eigen-value distributions of the double-scattering channel matrices. Based on these results, we present analytical expressions for the symbol error rate of MIMO MB. It is demonstrated that MB sub-channels can achieve full spatial diversity even in the presence of double scattering, if the number of effective scatterers is greater than or equal to the maximum number of transmit and receive antennas.

This paper considers orthogonal space-time block coded (OSTBC) transmission for non-regenerative multiple- input multiple-output dual-hop channels. We focus on scenarios where the relay does not have access to instantaneous channel state information, and as such operates according to a noncoherent amplify-and-forward protocol based on a long-term power constraint. We investigate the performance of the proposed OSTBC approach by employing tools from finite-dimensional random matrix theory. In particular, we derive exact closed-form expressions for the moment generating function, high order cumulants, and first and second moments of the signal-to-noise ratio at the destination. Based on these results, we also derive analytical expressions for the symbol error rate with M-ary phase-shift keying, and the amount of fading.

This paper presents an ergodic capacity analysis of an amplify-and-forward multiple-input, multiple-output two-hop system including the source to destination (direct) link. We first derive an expression for the probability density function of an unordered eigenvalue of the system. Then, using this result, a closed form expression for the ergodic capacity of the system is derived. The ergodic capacity expression has one integral that needs to be evaluated numerically. The results produced are valid for all SNR values and for arbitrary numbers of antennas at the source, relay and destination. We also present simulation results to validate our analysis. The results show that the analysis exactly matches the simulations and quantifies the improvements in capacity due to the diversity offered by the direct link.

This paper investigates the capacity of double-scattering multiple-input multiple-output (MIMO) channels in the low signal to noise ratio (SNR) regime. We first derive analytical expressions for the two key low SNR parameters; namely, the minimum required Eb/N0and wideband slope, assuming statistical channel state information (CSI) at the transmitter. Based on these results, we investigate the effect of transmit, scatter, and receive correlation. For the case of the double-scattering MIMO keyhole channel, we then analyze the low SNR capacity for different levels of transmit CSI. We show that increased transmit CSI leads to a reduced minimum required Eb/N0.

This paper investigates the performance of point-to-point spatial multiplexing with stream control and slotted ALOHA in ad hoc networks. In particular, we derive new closed-form outage probability, network throughput and transmission capacity expressions for spatial multiplexing with maximum-ratio-combining (MRC) and zero forcing (ZF) receivers. From these expressions, we show that the relative throughput of MRC and ZF receivers is dependent on node intensity and SINR threshold levels. In addition, we present a new transmission capacity scaling law for ZF receivers, which shows that increasing the number of transmitted data streams can either increase or decrease the transmission capacity depending on the path loss exponent and number of receive antennas. We also present conditions such that the transmission capacity using spatial multiplexing with ZF receivers is greater than orthogonal space time block codes.

We present an interesting and powerful new framework connecting the achievable sum rate of multiple-input multiple-output (MIMO) wireless systems employing linear minimum mean-squared error (MMSE) receivers, and the ergodic MIMO mutual information. This allows the vast literature on ergodic MIMO mutual information to be directly applied to the analysis of MMSE receivers. As an example, the framework is particularized to spatially-correlated Rayleigh fading to yield new exact closed-form expressions for the achievable sum rate, as well as simplified expressions for high and low signal to noise ratios.

This paper presents an analytical performance analysis for a multi-keyhole multiple-input multiple-output (MIMO) fading channel. Our main contribution is a set of new statistical results for the maximum eigenvalue of the random multi-keyhole channel matrix, which includes closed-form expressions for the cumulative distribution function and probability density function, as well as asymptotic expansions. Based on the results, we analyze the outage performance of the optimal joint beamforming system in multi-keyhole MIMO channels. Our results illustrate that the outage performance of the multi-keyhole channels is generally worse than that of rich-scattering MIMO Rayleigh channels.

This paper analyzes the performance of multiuser optimum combining systems. We consider the practical scenario where the desired user undergoes Rician fading, and the received signals are corrupted by Rayleigh-faded interference and noise. We derive new closed-form expressions for the symbol error rate, ergodic capacity, level crossing rate, and average fade duration. These results are given as either accurate approximations or asymptotic (eg. high signal-to-noise ratio (SNR)) expressions, and are based on new closed-form statistical properties which we derive for the signal-to-interference noise ratio (SINR). Specifically, we derive exact first order expansions and accurate gamma approximations for the SINR distribution, as well as simplified exact expressions for the moments. We also present closed-form expressions for key performance parameters such as the diversity order and array gain, wideband slope, and high SNR power offset, and analyze the impact of the Rician K-factor, which is shown in all cases to yield a performance improvement.

We analyze scheduling algorithms for multiuser communication systems with users having multiple antennas and linear receivers. When there is no feedback of channel information, we consider a common round robin scheduling algorithm, and derive new exact and high signal-to-noise ratio (SNR) maximum sum-rate results for the maximum ratio combining (MRC) and minimum mean squared error (MMSE) receivers. We also present new analysis of MRC, zero forcing (ZF) and MMSE receivers in the low SNR regime. When there are limited feedback capabilities in the system, we consider a common practical scheduling scheme based on signal-to-interference- and-noise ratio (SINR) feedback at the transmitter. We derive new accurate approximations for the maximum sum-rate, for the cases of MRC, ZF and MMSE receivers. We also derive maximum sum-rate scaling laws, which reveal that the maximum sum-rate of all three linear receivers converge to the same value for a large number of users, but at different rates.

This paper considers the analysis of optimum combining systems in the presence of both co-channel interference and thermal noise. We address the cases where either the desired-user or the interferers undergo Rician fading. Exact expressions are derived for the moment generating function of the SINR which apply for arbitrary numbers of antennas and interferers. Based on these, we obtain expressions for the symbol error probability with M-PSK. For the case where the desired-user undergoes Rician fading, we also derive exact closed-form expressions for the moments of the SINR. We show that these moments are directly related to the corresponding moments of a Rayleigh system via a simple scaling parameter, which is investigated in detail. Numerical results are presented to validate the analysis and to examine the impact of Rician fading on performance.

We investigate multiple-input multiple-output (MIMO) eigenmode transmission using statistical channel state information at the transmitter. We consider a general jointly correlated MIMO channel model, which does not require separable spatial correlations at the transmitter and receiver. For this model, we first derive a closed-form tight upper bound for the ergodic capacity, which reveals a simple and interesting relationship in terms of the matrix permanent of the eigenmode channel coupling matrix and embraces many existing results in the literature as special cases. Based on this closed-form and tractable upper bound expression, we then employ convex optimization techniques to develop low-complexity power allocation solutions involving only the channel statistics. Necessary and sufficient optimality conditions are derived, from which we develop an iterative water-filling algorithm with guaranteed convergence. Simulations demonstrate the tightness of the capacity upper bound and the near-optimal performance of the proposed low-complexity transmitter optimization approach.

We derive the exact cumulative distribution function (c.d.f.) of the minimum eigenvalue of a correlated complex non-central Wishart matrix. This result is in the form of a simple infinite series with fast convergence, and applies for the important case where the non-centrality matrix has rank one. Simplified asymptotic expressions for the c.d.f. are given for large matrix dimensions, as well as first-order expansions around the origin. The eigenvalue distributions in this paper have various important applications to multiple-input multiple-output (MIMO) communication systems, as well other scientific areas such as econometrics and multivariate statistics.

This paper investigates the performance of multiple- input multiple-output (MIMO) multichannel beamforming systems in interference-limited Ricean fading channels. We derive new expressions for the exact symbol error rate, as well as the diversity order and array gain. Our results are based on new exact closed-form expressions which we derive for the marginal ordered eigenvalue distributions of finite-dimensional complex noncentral F-distributed random matrices. Numerical results are presented to validate the theoretical analysis.

We analyze the sum capacity achieved by linear receivers in a multiple-input multiple-output broadcast channel. We consider a simple and practical opportunistic scheduling algorithm, based on the signal to interference noise ratio (SINR) feedback from each user. Each transmit antenna sends data to a particular user, selected based on SINR. Under this scheduling scheme, we derive new accurate approximations for the sum capacity, for the cases of maximum ratio combining, zero forcing, and minimum mean-squared error receivers. We also derive capacity scaling laws, which reveal that the capacity of all three linear receivers converge to the same value for a large number of users. Our results are confirmed through comparison with Monte Carlo simulations.

This paper studies the performance of MIMO multichannel beamforming systems in the presence of unequal-power co-channel interference and noise. We present exact expressions for the symbol error rate, and investigate the high signal to noise ratio regime by deriving explicit closed-form expressions for the diversity order and array gain. Our results are based on new exact and asymptotic marginal ordered eigenvalue distributions which we derive for a certain class of finite-dimensional complex random matrices.

This paper analyzes the performance of adaptive antenna arrays employing linear combining techniques designed to maximize the SINR. In the communications literature, these systems are referred to as optimum combining (OC) systems. We consider the practical case where the desired signal undergoes Rician fading, and is corrupted by Rayleigh-faded interfering signals and noise. We first propose new closed-form gamma approximations for the SINR distribution at the output of the OC combiner, which we show to be remarkably accurate. We then employ these approximations to derive new closed-form expressions for the ergodic capacity and simplified expressions for the high-SNR regime. These results reveal that the capacity improves monotonically with Rician K-factor.

This paper presents an analytical performance investigation of a Rayleigh-product multiple-input multiple-output (MIMO) channel using optimum transmit-receive beamforming. By deriving the closed-form expressions for the cumulative distribution function (C.D.F.), and the probability density function (P.D.F.), we provide a complete statistical characterization of the received signal-to-noise ratio (SNR) of the Rayleigh-product MIMO channel. These new statistical results further permit the analysis for the outage probability and the symbol-error-rate (SER), which are important performance indications of MIMO systems. In addition, we examine, in detail, an important special case corresponding to the degenerate keyhole scenario, for which we present insightful closed-form expressions for the diversity order and array gain.

This paper analyzes the performance of multiuser optimum combining (OC) systems where the desired user undergoes Rician fading, and the received signals are corrupted by Rayleigh-faded interference and noise. We consider the SER and ergodic capacity in asymptotic SNR regimes, and derive new closed-form expressions for key performance parameters such as the diversity order, array gain, and wideband slope. These results clearly reveal the impact of the Rician if-factor, which is shown to be advantageous to performance in all cases.

This paper investigates an important tradeoff in wireless ad hoc networks concerning the allocation of resources to the PHY and MAC layers. We compare two approaches: One which employs a non-coordinated slotted ALOHA MAC with multi-antenna PHY, and one which employs a tightly coordinated MAC and single-antenna PHY. For both cases, we derive new closed-form throughput expressions. Based on these, we show that using simple slotted ALOHA in conjunction with multiple antennas can provide a higher throughput than fully coordinated access protocols in various practical scenarios. Our results are confirmed through comparison with Monte Carlo simulations.

This paper derives the joint density of the diagonal elements of a 3 times 3 complex non-central Wishart matrix. This distribution arises in a number of applications including synthetic aperture radar, extra-solar planet detection, and multi-antenna wireless communications. The density expression is in the form of an infinite series representation which converges rapidly and is easy to compute.

This paper analyzes the ergodic capacity of dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay channels, assuming that the channel state information is available only at the destination terminal. We first present a new expression for the unordered eigenvalue density of a certain product of independent complex matrices, which is used to derive an exact expression for ergodic capacity. We then employ results from multivariate statistics to derive new closed-form upper and lower bounds of the ergodic capacity. In contrast to prior work, our results apply for arbitrary numbers of antennas and arbitrary relay configurations. Numerical results are provided to validate the theoretical analysis.

We investigate the sum capacity of a fading multiple-input multiple-output (MIMO) multiple access channel (MAC) under a general class of fading, known as double-scattering. We assume the receiver has perfect channel state information (CSI), while the transmitters only have access to statistical CSI. We show that the optimum transmit directions for each user coincide with the eigenvectors of the user’s own transmit spatial correlation matrix. We also derive new closed-form upper bounds on the sum capacity of the MIMO-MAC under double-scattering, which we employ to obtain suboptimal power allocation policies. These policies are easy to compute, and require each user to know only their own channel statistics.

This paper analyzes MIMO systems with multichannel beamforming in Ricean fading. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel. We first present new closed-form expressions for the marginal ordered eigenvalue distributions of complex noncentral Wishart matrices. These are used to characterize the statistics of the signal to noise ratio (SNR) on each eigenmode. Based on this, we present exact symbol error rate (SER) expressions. We also derive closed-form expressions for the diversity order, array gain, and outage probability. We show that the global SER performance is dominated by the subchannel corresponding to the minimum channel singular value. We also show that, at low outage levels, the outage probability varies inversely with the Ricean A*-factor for cases where transmission is only on the most dominant subchannel (i.e. a singlechannel beamforming system). Numerical results are presented to validate the theoretical analysis.

This communication considers the distribution of the mutual information of frequency-selective spatially uncorrelated Rayleigh fading multiple-input–multiple-output (MIMO) channels. Results are presented for orthogonal frequency-division multiplexing (OFDM)-based spatial multiplexing. New exact closed-form expressions are derived for the variance of the mutual information. In contrast to previous results, our new expressions apply for systems with both arbitrary numbers of antennas and arbitrary-length channels. Simplified expressions are also presented for high and low signal-to-noise ratio (SNR) regimes. The analytical variance results are used to provide accurate analytical approximations for the distribution of the mutual information, and the outage capacity.

This paper analyzes bit error rate (BER) and outage probability of singular value decomposition-based multiple-input multiple-output systems with channel estimation error and feedback delay over uncorrelated Ricean fading channels. By utilizing marginal unordered and ordered eigenvalue distributions of complex noncentral Wishart matrices, we derive exact closed-form expressions on the average system performance and high signal- to-interference-plus-noise ratio (SINR) approximations on the individual eigen-subchannels, respectively, under the assumption of equal power allocation. Our expressions apply for various modulation formats and arbitrary numbers of transmit and receive antennas. Our results show that in low-to-moderate SINR regimes, both the BER and the outage probability increase with channel estimation error, feedback delay and the Ricean K-factor at a polynomial rate that is inversely proportional to the difference between the numbers of transmit and receive antennas. We also show that, with channel estimation error and feedback delay, the diversity orders of the BER and outage probability are zero and an irreducible error floor exists at high SINR.

We investigate the capacity of a general class of MIMO channels, known as double-scattering channels. Our results assume perfect channel state information (CSI) at the receiver and statistical CSI at the transmitter. We first derive the optimal capacity-achieving signaling directions, and show that they correspond to the eigenvectors of the transmit spatial correlation matrix. We then derive new simple closed-form power allocation policies which are shown to yield negligible capacity loss compared with the optimal power allocation policy, without requiring complicated numerical optimization methods to compute. Finally we derive a necessary and sufficient condition for which a beamforming approach (i.e. rank-1 transmission) achieves the ergodic capacity.

This paper investigates the capacity of multiple- access and broadcast channels with MIMO-MRC systems in spatially correlated environments. We present new capacity approximations which are shown to be accurate. The approximations are based on new simple expansions which we derive for the maximum eigenvalue distribution of correlated Wishart matrices. We then proceed to analyze the affects of correlation and show it is beneficial for capacity. Our results are confirmed through comparison with Monte Carlo simulations.

In this paper, we consider a general family of MIMO channels known asdoublescatteringchannels, which encompass a variety of propagation environments from independent and identically distributed Rayleigh to degenerate Keyhole or pinhole cases by embracing both rank-deficiency and spatial correlation effects. We investigate the optimal transmit strategy of a single-user MIMO systems with channel statistical information feedback in the presence of double scattering. We show that transmitting in the direction of the eigenvectors of the transmit correlation matrix is the optimal transmission strategy under the criteria of maximizing the ergodic capacity. In addition to this, the power allocation problem is studied and a necessary and sufficient condition for optimality of beamforming is derived.

This paper investigates the performance of spatial diversity techniques in dense ad hoc networks. We derive analytical expressions for the contention density in systems employing MIMO-MRC or OSTBC. In the case of MIMO- MRC the expressions are based on new expansions for the SIR distribution in the high interference regime typical in dense networks. Our results are confirmed through comparison with Monte Carlo simulations.

This paper analyzes the average bit error rate (BER) performance of singular value decomposition-based multiple-input multiple-output systems with channel estimation error and feedback delay over uncorrelated Ricean fading channels. By utilizing marginal unordered eigenvalue distributions of complex noncentral Wishart matrices, we derive exact closed- form BER expression under the assumption of equal power allocation. Our results apply for various modulation formats and arbitrary numbers of transmit and receive antennas. Our results show the average BER increases with channel estimation error, feedback delay and Ricean A'-factor at a polynomial rate that is inversely proportional to the difference between the numbers of transmit and receive antennas. We also show that the achievable BER performance is limited by the presence of an irreducible error floor as the signal-to-interference-plus-noise ratio increases.

This paper investigates the capacity of multiuser MIMO-MRC systems in spatially correlated environments. We present new capacity approximations which are shown to be accurate. The approximations are based on new simple expansions which we derive for the maximum eigenvalue of correlated Wishart matrices. We show that for a large number of users there is a capacity offset due to correlation. Through this, we show that correlation is beneficial for capacity. Our results are confirmed through comparison with Monte-Carlo simulations.

We derive new analytic approximations to the capacity distribution of frequency-selective Rayleigh fading MIMO channels. The results apply specifically to OFDM-based spatial multiplexing. In particular, we present a new closed-form Gaussian approximation which yields very high accuracy in many scenarios. For the low SNR regime, we also present a new simpler closed-form Gamma approximation, which we show to be even more accurate than Gaussian in this case. Our approximations are based on new exact closed-form expressions which we derive for the variance of the mutual information which, in contrast to previous results, apply for systems with both arbitrary numbers of antennas and arbitrary-length channel delay profiles.

This paper analyzes the performance of optimum combining systems in the presence of both co-channel interference and thermal noise, addressing the case where the desired- user undergoes Rician fading. Exact expressions are derived for the moment generating function of the SINR which apply for arbitrary numbers of antennas and interferers. Based on these, we obtain expressions for the symbol error probability with M-PSK. We also derive exact closed-form expressions for the moments of the SINR, and show that they are directly related to the corresponding moments of a Rayleigh system via a simple scaling parameter. Numerical results are presented to validate the analysis, and to examine the impact of Rician fading.

In this paper, we investigate the performance of optimum combining multiple antenna systems in the presence of Rician-faded interferers. We assume that the desired user is subjected to Rayleigh fading but interferers undergo Rician fading. Unlike other approaches addressing optimum combining with Rician fading, we consider the effect of both interference and thermal noise. Our methodology is based on the evaluation of the moment generating function of the signal-to-interference-plus-noise (SINR) ratio at the output of the combiner. Our results are exact, and allow the calculation of the symbol error probability (SEP) for M-PSK signals with arbitrary number of antennas and interferers.

This letter derives the asymptotic symbol error rate (SER) and outage probability of multiple-input multiple-output (MIMO) maximum ratio-combining (MRC) systems. We consider Rayleigh fading channels with both transmit and receive spatial correlation. Our results are based on new asymptotic expressions that we derive for the p.d.f. and c.d.f. of the maximum eigenvalue of positive-definite quadratic forms in complex Gaussian matrices. We prove that spatial correlation does not affect the diversity order but that it reduces the array gain and hence increases the SER in the high SNR regime

We consider multiple-input multiple-output (MIMO) transmit beamforming systems with maximum ratio combining (MRC) receivers. The operating environment is Rayleigh fading with both transmit and receive spatial correlation. We present exact expressions for the probability density function (pdf) of the output signal-to-noise ratio, as well as the system outage probability. The results are based on explicit closed-form expressions which we derive for the pdf and cumulative distribution function of the maximum eigenvalue of double-correlated complex Wishart matrices. For systems with two antennas at either the transmitter or the receiver, we also derive exact closed-form expressions for the symbol-error rate. The new expressions are used to prove that MIMO-MRC achieves the maximum available spatial diversity order, and to demonstrate the effect of spatial correlation. The analysis is validated through comparison with Monte Carlo simulations

In this letter we derive tight analytical expressions for the coded bit error rate of MIMO bit-interleaved coded modulation (BICM) in spatially-correlated Rayleigh fading channels. We consider the case where low complexity zero-forcing receivers are employed. The analysis is simpler and more direct than the standard BICM error event expurgation technique, and yields efficient, accurate expressions for the error probability. Based on the analytical results, we obtain the diversity order and show that it is independent of the spatial correlation. Moreover, we show that the presence of spatial correlation induces an SNR loss with respect to i.i.d. channels. We quantify this loss, and show that it is a function of the antenna configuration and the eigenvalues of the spatial correlation matrices, and is independent of the coding and modulation parameters

This paper considers multiple-input multiple-output (MIMO) antenna systems employing transmit beamforming (BF) with maximum ratio combining (MRC) receivers. Rayleigh fading environments are considered, with both transmit and receive spatial correlation. Exact expressions are presented for the probability density function (p.d.f.) of the output signal-to-noise ratio (SNR), as well as the system outage probability. The results are based on efficient closed-form expressions which we derive for the p.d.f. and c.d.f. of the maximum eigenvalue of double-correlated complex Wishart matrices. The results are validated through comparison with Monte-Carlo simulations, and used to examine the effect of spatial correlation on the SNR p.d.f. and the outage probability

This paper considers low complexity transmission for MIMO bit-interleaved coded modulation (BICM) in spatially-correlated Rayleigh channels. We consider both statistical beam-forming (SB) and spatial-multiplexing with a zero-forcing (ZF) receiver. We derive tight closed-form bit error rate (BER) expressions based on a saddlepoint approximation. We then propose a practical adaptive algorithm which selects, based on the analytical results, the combination of code-rate, modulation format, and MIMO transmission scheme (SB or ZF) that maximizes throughput whilst maintaining a pre-defined BER.

We derive closed-form expressions for the ergodic capacity and symbol error rate (SER) of MIMO beamforming with maximum ratio combining (MRC) receivers in uncorrelated and semi-correlated Rayleigh channels. Our results are exact, finite expressions, applying for arbitrary numbers of antennas, and all SNRs. Based on the analytical results, we examine the effect of spatial correlation on the capacity and SER.

We derive new closed-form expressions for the marginal cumulative distribution function (c.d.f.) and marginal probability density function (p.d.f.) of the ordered eigenvalues of complex noncentral Wishart matrices. These results are used to analyze the performance of singular value decomposition (SVD) based MIMO systems in Ricean fading channels. New expressions are derived for the exact symbol error rate (SER), as well as the diversity order and array gain. Our results show that the global SER performance is dominated by the subchannel SER corresponding to the minimum channel singular value. Numerical results are presented to validate the theoretical analysis

This paper presents new statistical properties of complex noncentral matrix-variate quadratic forms. In contrast to previous results, the expressions do not involve infinite sums over partitions, or matrix-variate polynomials, and are easily and efficiently computable. These properties are used to derive new upper and lower bounds on the ergodic mutual information of double-sided correlated Rician MIMO channels with arbitrary-rank channel mean matrices. The bounds are shown to be tighter than previous reported bounds in the literature

We present a low complexity adaptive transmission approach for spatially correlated MIMO channels. The proposed scheme adaptively switches between orthogonal space-time block codes (OSTBC) and spatial multiplexing (SM), depending of the channel correlation and SNR. We derive an exact closed-form expression and tight upper bound on the OSTBC capacity in double-correlated channels, and examine the relative capacity of OSTBC and SM in terms of the spatial correlation. We then derive efficient closed-form BER expressions for practical OSTBC transmission employing bit-interleaved coded modulation (BICM). Based on these results, we propose a practical adaptive algorithm which selects the combination of MIMO transmission scheme (OSTBC or SM), and BICM mode, which achieves the highest spectral efficiency whilst satisfying a pre-defined BER

This paper considers the ergodic capacity of spatially-correlated Rician MIMO channels. We address the case where the Rician component has a single dominant path and where the correlation occurs at one end of the MIMO link. We derive upper bounds which are tight for all signal to noise ratios (SNR), and lower bounds which converge to the exact capacity at high SNR. For frequency-flat channels we investigate the capacity variation with Rician K-factor and correlation. For frequency-selective channels we also examine the effect of the total angle spread

In this paper we derive tight upper and lower bounds on the MIMO capacity in correlated Rician fading channels. We assume that the receiver has perfect knowledge of the channel, and the transmitter has no knowledge (instantaneous or statistical). We examine two common power normalization models, and show how the capacity changes with Rician K-factor and with the amount of correlation.

This paper presents new statistical properties of complex noncentral Wishart matrices. The properties are then used to derive bounds on the ergodic capacity of single-sided correlated Rician MIMO channels with arbitrary-rank channel mean matrices. We present upper and lower bounds which are computationally efficient and tight

We consider a low-complexity adaptive MIMO transmission approach for spatially correlated channels. The proposed scheme adaptively switches between different transmission modes depending on the changing channel conditions, as a means to enhance system capacity. Each mode is a combination of a transmission technique (i.e. statistical beamforming, double space-time transmit diversity and spatial multiplexing) and a modulation/coding scheme. We first motivate our adaptive algorithm by deriving new closed-form capacity expressions, and demonstrating significant information theoretic improvements over non-adaptive transmission. We then present a practical method to switch between different modes, based on the channel statistics. Our approach is shown to yield significant improvements in spectral efficiency for typical channel scenarios.

We consider a layered space-frequency (LSF) extension to bit-interleaved coded modulation (BICM) for MIMO-OFDM systems. We derive tight analytical bounds for the coded BER when using zero-forcing (ZF) detectors. The analysis does not rely on standard BICM expurgation techniques, and provides exact expressions for the codeword pairwise error probability at high SNR. We show that the LSF extension achieves the same diversity order as non-layered systems, while also achieving significant cant SNR gains when the number of transmit antennas is large. We quantify the SNR gain and show that it is a function of the antenna configuration only, and is independent of the modulation and coding parameters. We also present simulation results for MIMO extensions to IEEE 802.11a OFDM WLANs.

This work considers multiple-input multiple-output bit-interleaved coded modulation (MIMO-BICM) with linear zero-forcing (ZF) receivers. We derive the link-level capacity (LLC) under ideal fast-fading conditions, and show that it approaches the maximum-likelihood (ML) LLC as the number of receive antennas approach infinity. We also derive tight analytical bounds on the coded bit-error rate, and prove that with N/sub t/ transmit and N/sub r/ receive antennas, the diversity order is N/sub r/-N/sub t/+1 multiplied by the free Hamming distance of the convolutional code. For the case of a ML receiver, we show that a tight bound is not possible, in general. Our analysis provides insights to explain the relative performance of the ZF and ML receivers. Finally, we validate the analytical results and assess the performance in a practical environment with orthogonal frequency-division multiplexing and channel estimation.

This paper considers the capacity of spatially correlated Rician multiple-input multiple-output (MIMO) channels. We consider the general case with double-sided correlation and arbitrary rank channel means. We derive tight upper and lower bounds on the ergodic capacity. In the particular cases when the numbers of transmit and receive antennas are equal, or when the correlation is single sided, we derive more specific bounds which are computationally efficient. The bounds are shown to reduce to known results in cases of independent and identically distributed (i.i.d.) and correlated Rayleigh MIMO channels. We also analyze the outage characteristics of the correlated Rician MIMO channels at high signal-to-noise ratio (SNR). We derive the mean and variance of the mutual information and show that it is well approximated by a Gaussian distribution. Finally, we present numerical results which show the effect of the antenna configuration, correlation level (angle spreads), Rician K-factor, and the geometry of the dominant Rician paths.

Tight analytical bounds on the coded bit error rate are derived for a MIMO bit-interleaved coded modulation (BICM) system with a zero forcing receiver. We show that a minimal expurgated bound exists when using Gray-labelled constellations. We also show that with N/sub t/ transmit and N/sub r/ receive antennas, the diversity order is N/sub r/-N/sub t/+1 multiplied by the free distance of the code. For the maximum likelihood receiver, we demonstrate that expurgation does not lead to a tight bound. The analysis provides insight into the relative performance of the MIMO-BICM ZF and ML receivers.