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As an alternative to quantum error correction, quantum error mitigation methods, including Zero-Noise Extrapolation (ZNE), have been proposed to alleviate run-time errors in current noisy quantum devices. In this work, we propose a modified version of ZNE that provides for a significant performance enhancement on current noisy devices. Our modified ZNE method extrapolates to zero-noise data by evaluating groups of noisy data obtained from noise-scaled circuits and selecting extrapolation functions for each group with the assistance of estimated noisy simulation results. To quantify enhancement in a real-world quantum application, we embed our modified ZNE in Quantum Random Access Memory (QRAM) - a memory system important for future quantum networks and computers. Our new ZNE-enhanced QRAM designs are experimentally implemented on a 27-qubit noisy superconducting quantum device, the results of which demonstrate that with reasonable estimated simulation results, QRAM fidelity is improved significantly relative to traditional ZNE usage. Our results demonstrate the critical role the extrapolation function plays in ZNE - judicious choice of that function on a per-measurement basis can make the difference between a quantum application being functional or non-functional.

We design statistical hypothesis tests 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 first design a test procedure based on the generalized likelihood ratio test, which we show through simulations to offer appreciable leak detection performance gain over conventional approaches designed in an analogous context (for radar detection). Our proposed method requires estimation of the noise covariance matrix, which can become inaccurate under high-dimensional settings, and when the measurement data is scarce. To deal with this, we present a second leak detection method, 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. This second proposed approach is shown to yield improved performance in leak detection compared with the first approach, at the expense of requiring higher computational complexity.

The channel estimation overhead of reconfigurable intelligent surface (RIS) assisted communication systems can be prohibitive. Prior works have demonstrated via simulations that grouping neighbouring RIS elements can help to reduce the pilot overhead and improve achievable rate. In this paper, we present an analytical study of RIS element grouping. We derive a tight closed-form upper bound for the achievable rate and then maximize it with respect to the group size. Our analysis reveals that more coarse-grained grouping is important-when the channel coherence time is low (high mobility scenarios) or the transmit power is large. We also demonstrate that optimal grouping can yield significant performance improvements over simple `On-Off' RIS element switching schemes that have been recently considered., Comment: Submitted to IEEE Wireless Communications Letters

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., Comment: Submitted to IEEE Transactions on Communications

We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space displacement and squeezing parameter estimation, this is achieved by introducing Expectation-Maximization (EM) based algorithms, while for phase parameter estimation an empirical Bayes method is applied. The estimated prior distribution parameters along with the observed data are used for finding the optimal Bayesian estimate of the unknown displacement, squeezing and phase parameters. Our simulation results show that the proposed algorithms have estimation performance that is very close to that of Genie Aided Bayesian estimators, that assume perfect knowledge of the prior parameters. Our proposed methods can be utilized by experimentalists to find the optimum Bayesian estimate of parameters of Gaussian quantum states by using only the observed measurements without requiring any knowledge about the prior distribution parameters., Comment: Submitted to IEEE Transactions on Quantum Engineering

We propose a multiple-input multiple-output (MIMO) quantum key distribution (QKD) scheme for terahertz (THz) frequency applications operating at room temperature. Motivated by classical MIMO communications, a transmit-receive beamforming scheme is proposed that converts the rank-$r$ MIMO channel between Alice and Bob into $r$ parallel lossy quantum channels. Compared with existing single-antenna QKD schemes, we demonstrate that the MIMO QKD scheme leads to performance improvements by increasing the secret key rate and extending the transmission distance. Our simulation results show that multiple antennas are necessary to overcome the high free-space path loss at THz frequencies. We demonstrate a non-monotonic relation between performance and frequency, and reveal that positive key rates are achievable in the $10-30$ THz frequency range. The proposed scheme can be used for both indoor and outdoor QKD applications for beyond fifth-generation ultra-secure wireless communications systems., Comment: Revisions submitted to IEEE Communications Letters

We consider multi-antenna wireless systems aided by large intelligent surfaces (LIS). LIS presents a new physical layer technology for improving coverage and energy efficiency by intelligently controlling the propagation environment. In practice however, achieving the anticipated gains of LIS requires accurate channel estimation. Recent attempts to solve this problem have considered the least-squares (LS) approach, which is simple but also sub-optimal. The optimal channel estimator, based on the minimum mean-squared-error (MMSE) criterion, is challenging to obtain and is non-linear due to the non-Gaussianity of the effective channel seen at the receiver. Here we present approaches to approximate the optimal MMSE channel estimator. As a first approach, we analytically develop the best linear estimator, the LMMSE, together with a corresponding majorization-minimization based algorithm designed to optimize the LIS phase shift matrix during the training phase. This estimator is shown to yield improved accuracy over the LS approach by exploiting second-order statistical properties of the wireless channel and the noise. To further improve performance and better approximate the globally-optimal MMSE channel estimator, we propose data-driven non-linear solutions based on deep learning. Specifically, by posing the MMSE channel estimation problem as an image denoising problem, we propose two convolutional neural network (CNN) based methods to perform the denoising and approximate the optimal MMSE channel estimation solution. Our numerical results show that these CNN-based estimators give superior performance compared with linear estimation approaches. They also have low computational complexity requirements, thereby motivating their potential use in future LIS-aided wireless communication systems., Comment: Submitted to IEEE OJCS for possible publication

Large intelligent surfaces (LIS) present a promising new technology for enhancing the performance of wireless communication systems. Realizing the gains of LIS requires accurate channel knowledge, and in practice the channel estimation overhead can be large due to the passive nature of LIS. Here, we study the achievable rate of a LIS-assisted single-input single-output communication system, accounting for the pilot overhead of a least-squares channel estimator. We demonstrate that there exists an optimal $K^{*}$, which maximizes achievable rate by balancing the power gains offered by LIS and the channel estimation overhead. We present analytical approximations for $K^{*}$, based on maximizing an analytical upper bound on average achievable rate that we derive, and study the dependencies of $K^*$ on statistical channel and system parameters., Comment: Published in IEEE Wireless Communications Letters

We study a multiple-input single-output (MISO) communication system assisted by a reconfigurable intelligent surface (RIS). A base station (BS) having multiple antennas is assumed to be communicating to a single-antenna user equipment (UE), with the help of a RIS. We assume that the system operates in an environment with line-of-sight (LoS) between the BS and RIS, whereas the RIS-UE link experiences Rayleigh fading. We present a closed form expression for the optimal active and passive beamforming vectors at the BS and RIS respectively. Then, by characterizing the statistical properties of the received SNR at the UE, we apply them to derive analytical approximations for different system performance measures, including the outage probability, average achievable rate and average symbol error probability (SEP). Our results, in general, demonstrate that the gain due to RIS can be substantial, and can be significantly greater than the gains reaped by using multiple BS antennas., Comment: Accepted for publication in IEEE GlobeCom-2020

Let $\mathbf{W}_1$ and $\mathbf{W}_2$ be independent $n\times n$ complex central Wishart matrices with $m_1$ and $m_2$ degrees of freedom respectively. This paper is concerned with the extreme eigenvalue distributions of double-Wishart matrices $(\mathbf{W}_1+\mathbf{W}_2)^{-1}\mathbf{W}_1$, which are analogous to those of F matrices ${\bf W}_1 {\bf W}_2^{-1}$ and those of the Jacobi unitary ensemble (JUE). Defining $\alpha_1=m_1-n$ and $\alpha_2=m_2-n$, we derive new exact distribution formulas in terms of $(\alpha_1+\alpha_2)$-dimensional matrix determinants, with elements involving derivatives of Legendre polynomials. This provides a convenient exact representation, while facilitating a direct large-$n$ analysis with $\alpha_1$ and $\alpha_2$ fixed (i.e., under the so-called "hard-edge" scaling limit); the analysis is based on new asymptotic properties of Legendre polynomials and their relation with Bessel functions that are here established. Specifically, we present limiting formulas for the smallest and largest eigenvalue distributions as $n \to \infty$ in terms of $\alpha_1$- and $\alpha_2$-dimensional determinants respectively, which agrees with expectations from known universality results involving the JUE and the Laguerre unitary ensemble (LUE). We also derive finite-$n$ corrections for the asymptotic extreme eigenvalue distributions under hard-edge scaling, giving new insights on universality by comparing with corresponding correction terms derived recently for the LUE. Our derivations are based on elementary algebraic manipulations, differing from existing results on double-Wishart and related models which often involve Fredholm determinants, Painlev\'e differential equations, or hypergeometric functions of matrix arguments., Comment: This work was supported by the HKTIIT (HKTIIT16EG01) and the General Research Fund of the Hong Kong Research Grants Council (16202918)

Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which the data is assumed independent. Here, considering the popular class of spiked models, we apply random matrix theory to derive asymptotic first-order and distributional results for both the leading eigenvalues and eigenvectors of sample correlation matrices. These results are obtained under high-dimensional settings for which the number of samples n and variables p approach infinity, with p/n tending to a constant. To first order, the spectral properties of sample correlation matrices are seen to coincide with those of sample covariance matrices; however their asymptotic distributions can differ significantly, with fluctuations of both the sample eigenvalues and eigenvectors often being remarkably smaller than those of their sample covariance counterparts., Comment: 32 pages, 4 figures

Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. These estimators provide robustness to outliers, while simultaneously being well-defined when the number of samples does not exceed the number of variables. By applying tools from random matrix theory, we characterize the asymptotic performance of such estimators when the numbers of samples and variables grow large together. In particular, our results show that, when outliers are absent, many estimators of the regularized-Maronna type share the same asymptotic performance, and for these estimators we present a data-driven method for choosing the asymptotically optimal regularization parameter with respect to a quadratic loss. Robustness in the presence of outliers is then studied: in the non-regularized case, a large-dimensional robustness metric is proposed, and explicitly computed for two particular types of estimators, exhibiting interesting differences depending on the underlying contamination model. The impact of outliers in regularized estimators is then studied, with interesting differences with respect to the non-regularized case, leading to new practical insights on the choice of particular estimators., Comment: 15 pages, 6 figures

We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of available market returns is often of similar order to the number of assets, so that the sample covariance matrix performs poorly as a covariance estimator. Additionally, financial market data often contain outliers which, if not correctly handled, may further corrupt the covariance estimation. We address these shortcomings by studying the performance of a hybrid covariance matrix estimator based on Tyler's robust M-estimator and on Ledoit-Wolf's shrinkage estimator while assuming samples with heavy-tailed distribution. Employing recent results from random matrix theory, we develop a consistent estimator of (a scaled version of) the realized portfolio risk, which is minimized by optimizing online the shrinkage intensity. Our portfolio optimization method is shown via simulations to outperform existing methods both for synthetic and real market data.

A large dimensional characterization of robust M-estimators of covariance (or scatter) is provided under the assumption that the dataset comprises independent (essentially Gaussian) legitimate samples as well as arbitrary deterministic samples, referred to as outliers. Building upon recent random matrix advances in the area of robust statistics, we specifically show that the so-called Maronna M-estimator of scatter asymptotically behaves similar to well-known random matrices when the population and sample sizes grow together to infinity. The introduction of outliers leads the robust estimator to behave asymptotically as the weighted sum of the sample outer products, with a constant weight for all legitimate samples and different weights for the outliers. A fine analysis of this structure reveals importantly that the propensity of the M-estimator to attenuate (or enhance) the impact of outliers is mostly dictated by the alignment of the outliers with the inverse population covariance matrix of the legitimate samples. Thus, robust M-estimators can bring substantial benefits over more simplistic estimators such as the per-sample normalized version of the sample covariance matrix, which is not capable of differentiating the outlying samples. The analysis shows that, within the class of Maronna's estimators of scatter, the Huber estimator is most favorable for rejecting outliers. On the contrary, estimators more similar to Tyler's scale invariant estimator (often preferred in the literature) run the risk of inadvertently enhancing some outliers., Comment: Submitted to IEEE Transactions on Signal Processing

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., Comment: to appear in IEEE Transactions on Wireless Communications

This paper studies the sum rate performance of a low complexity quantized CSI-based Tomlinson-Harashima (TH) precoding scheme for downlink multiuser MIMO tansmission, employing greedy user selection. The asymptotic distribution of the output signal to interference plus noise ratio of each selected user and the asymptotic sum rate as the number of users K grows large are derived by using extreme value theory. For fixed finite signal to noise ratios and a finite number of transmit antennas $n_T$, we prove that as K grows large, the proposed approach can achieve the optimal sum rate scaling of the MIMO broadcast channel. We also prove that, if we ignore the precoding loss, the average sum rate of this approach converges to the average sum capacity of the MIMO broadcast channel. Our results provide insights into the effect of multiuser interference caused by quantized CSI on the multiuser diversity gain., Comment: 13 pages, 4 figures, IEEE Trans. Signal Process., Aug. 2014

We show that the problem of analyzing the outage probability in cellular systems affected by co-channel interference and background noise is mathematically equivalent to the problem of analyzing the wireless information-theoretic security in terms of the maximum secrecy rate in fading channels. Hence, these both apparently unrelated problems can be addressed by using a common approach. We illustrate the applicability of the connection unveiled herein to provide new results for the secrecy outage probability in different scenarios., Comment: This work has been accepted for publication at IEEE Transactions on Vehicular Technology. Copyright (c) 2014 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org

We investigate the multiple-input multiple-output broadcast channel with statistical channel state information available at the transmitter. The so-called linear assignment operation is employed, and necessary conditions are derived for the optimal transmit design under general fading conditions. Based on this, we introduce an iterative algorithm to maximize the linear assignment weighted sum-rate by applying a gradient descent method. To reduce complexity, we derive an upper bound of the linear assignment achievable rate of each receiver, from which a simplified closed-form expression for a near-optimal linear assignment matrix is derived. This reveals an interesting construction analogous to that of dirty-paper coding. In light of this, a low complexity transmission scheme is provided. Numerical examples illustrate the significant performance of the proposed low complexity scheme., Comment: Accepted for IEEE Transaction on Signal Processing

This paper derives central limit theorems (CLTs) for general linear spectral statistics (LSS) of three important multi-spiked Hermitian random matrix ensembles. The first is the most common spiked scenario, proposed by Johnstone, which is a central Wishart ensemble with fixed-rank perturbation of the identity matrix, the second is a non-central Wishart ensemble with fixed-rank noncentrality parameter, and the third is a similarly defined non-central $F$ ensemble. These CLT results generalize our recent work to account for multiple spikes, which is the most common scenario met in practice. The generalization is non-trivial, as it now requires dealing with hypergeometric functions of matrix arguments. To facilitate our analysis, for a broad class of such functions, we first generalize a recent result of Onatski to present new contour integral representations, which are particularly suitable for computing large-dimensional properties of spiked matrix ensembles. Armed with such representations, our CLT formulas are derived for each of the three spiked models of interest by employing the Coulomb fluid method from random matrix theory along with saddlepoint techniques. We find that for each matrix model, and for general LSS, the individual spikes contribute additively to yield a $O(1)$ correction term to the asymptotic mean of the linear statistic, which we specify explicitly, whilst having no effect on the leading order terms of the mean or variance.

We consider multiple-antenna signal detection of primary user transmission signals by a secondary user receiver 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 user. We first derive exact expressions for the moments of the generalized likelihood ratio test (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. Further, using results from large random matrix theory, we derive expressions to compute the detection probability without explicit knowledge of the channel, and then particularize these expressions for two scenarios of practical interest: 1) a single primary user sending spatially multiplexed signals, and 2) multiple spatially distributed primary users. Our analytical results are finally used to obtain simple design rules for the signal detection threshold., Comment: Revised version (14 pages). Change in title

Using the Coulomb Fluid method, this paper derives central limit theorems (CLTs) for linear spectral statistics of three "spiked" Hermitian random matrix ensembles. These include Johnstone's spiked model (i.e., central Wishart with spiked correlation), non-central Wishart with rank-one non-centrality, and a related class of non-central $F$ matrices. For a generic linear statistic, we derive simple and explicit CLT expressions as the matrix dimensions grow large. For all three ensembles under consideration, we find that the primary effect of the spike is to introduce an $O(1)$ correction term to the asymptotic mean of the linear spectral statistic, which we characterize with simple formulas. The utility of our proposed framework is demonstrated through application to three different linear statistics problems: the classical likelihood ratio test for a population covariance, the capacity analysis of multi-antenna wireless communication systems with a line-of-sight transmission path, and a classical multiple sample significance testing problem.

This article studies two regularized robust estimators of scatter matrices proposed (and proved to be well defined) in parallel in (Chen et al., 2011) and (Pascal et al., 2013), based on Tyler's robust M-estimator (Tyler, 1987) and on Ledoit and Wolf's shrinkage covariance matrix estimator (Ledoit and Wolf, 2004). These hybrid estimators have the advantage of conveying (i) robustness to outliers or impulsive samples and (ii) small sample size adequacy to the classical sample covariance matrix estimator. We consider here the case of i.i.d. elliptical zero mean samples in the regime where both sample and population sizes are large. We demonstrate that, under this setting, the estimators under study asymptotically behave similar to well-understood random matrix models. This characterization allows us to derive optimal shrinkage strategies to estimate the population scatter matrix, improving significantly upon the empirical shrinkage method proposed in (Chen et al., 2011)., Comment: Journal of Multivariate Analysis

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 networkwide 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., Comment: to appear in IEEE Transactions on Information Forensics and Security

This letter studies information-theoretic security without knowing the eavesdropper's channel fading state. We present an alternative secrecy outage formulation to measure the probability that message transmissions fail to achieve perfect secrecy. Using this formulation, we design two transmission schemes that satisfy the given security requirement while achieving good throughput performance.

In this review, we investigate a key information-theoretic performance metric in multiple-antenna wireless communications, the so-called outage probability. This quantity may be expressed in terms of a moment generating function, for which we present two separate integral representations, one involving a particular $\sigma$-form of Painlev\'e V. We also present a representation involving a non-linear second order difference equation., Comment: arXiv admin note: text overlap with arXiv:1007.0496

This paper builds upon our recent work which computed the moment generating function of the MIMO mutual information exactly in terms of a Painlev\'{e} 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 SNR for the case of unequal antenna arrays, whilst 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., Comment: Submitted to IEEE Transaction on Information Theory (under revision)

This paper gives an in-depth study of a multiple-antenna wireless communication scenario in which a weak signal received at an intermediate relay station is amplified and then forwarded to the final destination. The key quantity determining system performance is the statistical properties of the signal-to-noise ratio (SNR) \gamma\ at the destination. Under certain assumptions on the encoding structure, recent work has characterized the SNR distribution through its moment generating function, in terms of a certain Hankel determinant generated via a deformed Laguerre weight. Here, we employ two different methods to describe the Hankel determinant. First, we make use of ladder operators satisfied by orthogonal polynomials to give an exact characterization in terms of a "double-time" Painlev\'e differential equation, which reduces to Painlev\'e V under certain limits. Second, we employ Dyson's Coulomb Fluid method to derive a closed form approximation for the Hankel determinant. The two characterizations are used to derive closed-form expressions for the cumulants of \gamma, and to compute performance quantities of engineering interest., Comment: 72 pages, 6 figures; Minor typos corrected; Two additional lemmas added in Appendix A

In this paper, we investigate the design of artificial-noise-aided secure multi-antenna transmission in slow fading channels. The primary design concerns include the transmit power allocation and the rate parameters of the wiretap code. We consider two scenarios with different complexity levels: i) the design parameters are chosen to be fixed for all transmissions, ii) they are adaptively adjusted based on the instantaneous channel feedback from the intended receiver. In both scenarios, we provide explicit design solutions for achieving the maximal throughput subject to a secrecy constraint, given by a maximum allowable secrecy outage probability. We then derive accurate approximations for the maximal throughput in both scenarios in the high signal-to-noise ratio region, and give new insights into the additional power cost for achieving a higher security level, whilst maintaining a specified target throughput. In the end, the throughput gain of adaptive transmission over non-adaptive transmission is also quantified and analyzed., Comment: to appear in IEEE Transactions on Vehicular Technology

Let $\mathbf{W}$ be a correlated complex non-central Wishart matrix defined through $\mathbf{W}=\mathbf{X}^H\mathbf{X}$, where $\mathbf{X}$ is $n\times m \, (n\geq m)$ complex Gaussian with non-zero mean $\boldsymbol{\Upsilon}$ and non-trivial covariance $\boldsymbol{\Sigma}$. We derive exact expressions for the cumulative distribution functions (c.d.f.s) of the extreme eigenvalues (i.e., maximum and minimum) of $\mathbf{W}$ for some particular cases. These results are quite simple, involving rapidly converging infinite series, and apply for the practically important case where $\boldsymbol{\Upsilon}$ has rank one. We also derive analogous results for a certain class of gamma-Wishart random matrices, for which $\boldsymbol{\Upsilon}^H\boldsymbol{\Upsilon}$ follows a matrix-variate gamma distribution. The eigenvalue distributions in this paper have various applications to wireless communication systems, and arise in other fields such as econometrics, statistical physics, and multivariate statistics., Comment: Accepted for publication in Journal of Multivariate Analysis

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., Comment: 51 pages, 19 figures, submitted to IEEE Transactions on Information Theory

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 multi-antenna Gaussian channels, and the Gallager random coding upper bound on the error probability achievable by finite-length channel codes. It turns out 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, whereas for multi-user 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 orthogonal polynomials to give an exact characterization of the Hankel determinants in terms of Painlev\'{e} differential equations. This turns out to be a Painlev\'{e} V for the single-user MIMO scenario and a Painlev\'{e} VI for the multi user scenario. We then employ Coulomb fluid methods to derive new closed-form approximations for the Hankel determinants which, although formally valid for large matrix dimensions, are shown to give accurate results for both the MIMO mutual information distribution and the error exponent even when the matrix dimensions are small. Focusing on the single-user mutual information distribution, we then employ both the exact Painlev\'{e} representation and the Coulomb fluid approximation to yield deeper insights into the scaling behavior in terms of the number of antennas and signal-to-noise ratio. Among other things, these results allow us to study the asymptotic Gaussianity of the distribution as the number of antennas increase, and to explicitly compute the correction terms to the mean, variance, and higher order cumulants., Comment: 77 pages; 6 figures

We consider the problem of secure communication with multi-antenna transmission in fading channels. The transmitter simultaneously transmits an information bearing signal to the intended receiver and artificial noise to the eavesdroppers. We obtain an analytical closed-form expression of an achievable secrecy rate, and use it as the objective function to optimize the transmit power allocation between the information signal and the artificial noise. Our analytical and numerical results show that equal power allocation is a simple yet near optimal strategy for the case of non-colluding eavesdroppers. When the number of colluding eavesdroppers increases, more power should be used to generate the artificial noise. We also provide an upper bound on the signal-to-noise ratio (SNR) above which the achievable secrecy rate is positive and show that the bound is tight at low SNR. Furthermore, we consider the impact of imperfect channel state information (CSI) at both the transmitter and the receiver and find that it is wise to create more artificial noise to confuse the eavesdroppers than to increase the signal strength for the intended receiver if the CSI is not accurately obtained., Comment: To appear in IEEE Transactions on Vehicular Technology

This paper studies the sum rate performance of two low complexity eigenmode-based transmission techniques for the MIMO broadcast channel, employing greedy semi-orthogonal user selection (SUS). The first approach, termed ZFDPC-SUS, is based on zero-forcing dirty paper coding; the second approach, termed ZFBF-SUS, is based on zero-forcing beamforming. We first employ new analytical methods to prove that as the number of users K grows large, the ZFDPC-SUS approach can achieve the optimal sum rate scaling of the MIMO broadcast channel. We also prove that the average sum rates of both techniques converge to the average sum capacity of the MIMO broadcast channel for large K. In addition to the asymptotic analysis, we investigate the sum rates achieved by ZFDPC-SUS and ZFBF-SUS for finite K, and show that ZFDPC-SUS has significant performance advantages. Our results also provide key insights into the benefit of multiple receive antennas, and the effect of the SUS algorithm. In particular, we show that whilst multiple receive antennas only improves the asymptotic sum rate scaling via the second-order behavior of the multi-user diversity gain; for finite K, the benefit can be very significant. We also show the interesting result that the semi-orthogonality constraint imposed by SUS, whilst facilitating a very low complexity user selection procedure, asymptotically does not reduce the multi-user diversity gain in either first (log K) or second-order (loglog K) terms., Comment: 35 pages, 3 figures, to appear in IEEE transactions on signal processing

The performance of spatial multiplexing systems with linear minimum-mean-squared-error receivers is investigated in ad hoc networks. It is shown that single-stream transmission is preferable over multi-stream transmission, due to the weaker interference powers from the strongest interferers remaining after interference-cancelation. This result is obtained by new exact closed-form expressions we derive for the outage probability and transmission capacity., Comment: 5 pages, 3 figures, submitted to IEEE Globecom 2010

We investigate 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., Comment: 32 pages, 6 figures, to appear in IEEE Transactions on Information Theory

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 unveils 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. These expressions lead to the discovery of key insights into the performance of MIMO MMSE receivers under practical channel conditions., Comment: to appear in IEEE Transactions on Information Theory

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., Comment: 25 pages, 8 figures, corrected typos, Subject to minor revision in IEEE Transactions on Communications

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 to employing recent tools from finite-dimensional random matrix theory 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., Comment: 40 pages, 9 figures, Submitted to to IEEE Transactions on Information Theory

This paper considers the distribution of the mutual information of frequency-selective spatially-uncorrelated Rayleigh fading MIMO channels. Results are presented for 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 SNR regimes. The analytical variance results are used to provide accurate analytical approximations for the distribution of the mutual information and the outage capacity., Comment: 18 pages, 10 figures, accepted for publication in IEEE Transactions on Information Theory