Asymptotic Performance of Linear Receivers in MIMO Fading Channels

Linear receivers are an attractive low-complexity alternative to optimal processing for multi-antenna MIMO communications. In this paper we characterize the information-theoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the high-SNR regime in terms of the Diversity-Multiplexing Tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas. As far as the DMT is concerned, we report a negative result: we show that both linear Zero-Forcing (ZF) and linear Minimum Mean-Square Error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and decoding is performed across the antennas. We also provide an approximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and non-asymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information at the output of a MMSE or ZF linear receiver has fluctuations that converge in distribution to a Gaussian random variable, whose mean and variance can be characterized in closed form. This analysis extends to the linear receiver case a well-known result previously obtained for the optimal receiver. Simulations reveal that the asymptotic analysis captures accurately the outage behavior of systems even with a moderate number of antennas.Comment: 48 pages, Submitted to IEEE Transactions on Information Theor

Living at the Edge: A Large Deviations Approach to the Outage MIMO Capacity

Using a large deviations approach we calculate the probability distribution of the mutual information of MIMO channels in the limit of large antenna numbers. In contrast to previous methods that only focused at the distribution close to its mean (thus obtaining an asymptotically Gaussian distribution), we calculate the full distribution, including its tails which strongly deviate from the Gaussian behavior near the mean. The resulting distribution interpolates seamlessly between the Gaussian approximation for rates $R$ close to the ergodic value of the mutual information and the approach of Zheng and Tse for large signal to noise ratios $\rho$. This calculation provides us with a tool to obtain outage probabilities analytically at any point in the $(R, \rho, N)$ parameter space, as long as the number of antennas $N$ is not too small. In addition, this method also yields the probability distribution of eigenvalues constrained in the subspace where the mutual information per antenna is fixed to $R$ for a given $\rho$. Quite remarkably, this eigenvalue density is of the form of the Marcenko-Pastur distribution with square-root singularities, and it depends on the values of $R$ and $\rho$.Comment: Accepted for publication, IEEE Transactions on Information Theory (2010). Part of this work appears in the Proc. IEEE Information Theory Workshop, June 2009, Volos, Greec

A Repair Framework for Scalar MDS Codes

Several works have developed vector-linear maximum-distance separable (MDS) storage codes that min- imize the total communication cost required to repair a single coded symbol after an erasure, referred to as repair bandwidth (BW). Vector codes allow communicating fewer sub-symbols per node, instead of the entire content. This allows non trivial savings in repair BW. In sharp contrast, classic codes, like Reed- Solomon (RS), used in current storage systems, are deemed to suffer from naive repair, i.e. downloading the entire stored message to repair one failed node. This mainly happens because they are scalar-linear. In this work, we present a simple framework that treats scalar codes as vector-linear. In some cases, this allows significant savings in repair BW. We show that vectorized scalar codes exhibit properties that simplify the design of repair schemes. Our framework can be seen as a finite field analogue of real interference alignment. Using our simplified framework, we design a scheme that we call clique-repair which provably identifies the best linear repair strategy for any scalar 2-parity MDS code, under some conditions on the sub-field chosen for vectorization. We specify optimal repair schemes for specific (5,3)- and (6,4)-Reed- Solomon (RS) codes. Further, we present a repair strategy for the RS code currently deployed in the Facebook Analytics Hadoop cluster that leads to 20% of repair BW savings over naive repair which is the repair scheme currently used for this code.Comment: 10 Pages; accepted to IEEE JSAC -Distributed Storage 201

Bit-Interleaved Coded Modulation Revisited: A Mismatched Decoding Perspective

We revisit the information-theoretic analysis of bit-interleaved coded modulation (BICM) by modeling the BICM decoder as a mismatched decoder. The mismatched decoding model is well-defined for finite, yet arbitrary, block lengths, and naturally captures the channel memory among the bits belonging to the same symbol. We give two independent proofs of the achievability of the BICM capacity calculated by Caire et al. where BICM was modeled as a set of independent parallel binary-input channels whose output is the bitwise log-likelihood ratio. Our first achievability proof uses typical sequences, and shows that due to the random coding construction, the interleaver is not required. The second proof is based on the random coding error exponents with mismatched decoding, where the largest achievable rate is the generalized mutual information. We show that the generalized mutual information of the mismatched decoder coincides with the infinite-interleaver BICM capacity. We also show that the error exponent -and hence the cutoff rate- of the BICM mismatched decoder is upper bounded by that of coded modulation and may thus be lower than in the infinite-interleaved model. We also consider the mutual information appearing in the analysis of iterative decoding of BICM with EXIT charts. We show that the corresponding symbol metric has knowledge of the transmitted symbol and the EXIT mutual information admits a representation as a pseudo-generalized mutual information, which is in general not achievable. A different symbol decoding metric, for which the extrinsic side information refers to the hypothesized symbol, induces a generalized mutual information lower than the coded modulation capacity.Comment: submitted to the IEEE Transactions on Information Theory. Conference version in 2008 IEEE International Symposium on Information Theory, Toronto, Canada, July 200

Bit-interleaved coded modulation in the wideband regime

The wideband regime of bit-interleaved coded modulation (BICM) in Gaussian channels is studied. The Taylor expansion of the coded modulation capacity for generic signal constellations at low signal-to-noise ratio (SNR) is derived and used to determine the corresponding expansion for the BICM capacity. Simple formulas for the minimum energy per bit and the wideband slope are given. BICM is found to be suboptimal in the sense that its minimum energy per bit can be larger than the corresponding value for coded modulation schemes. The minimum energy per bit using standard Gray mapping on M-PAM or M^2-QAM is given by a simple formula and shown to approach -0.34 dB as M increases. Using the low SNR expansion, a general trade-off between power and bandwidth in the wideband regime is used to show how a power loss can be traded off against a bandwidth gain.Comment: Submitted to IEEE Transactions on Information Theor

Game theory-based resource allocation for secure WPCN multiantenna multicasting systems

This paper investigates a secure wireless-powered multiantenna multicasting system, where multiple power beacons (PBs) supply power to a transmitter in order to establish a reliable communication link with multiple legitimate users in the presence of multiple eavesdroppers. The transmitter has to harvest radio frequency (RF) energy from multiple PBs due to the shortage of embedded power supply before establishing its secure com- munication. We exploit a novel and practical scenario that the PBs and the transmitter may belong to different operators and a hierarchical energy interaction between the PBs and the transmitter is considered. Specifically, the monetary incentives are required for the PBs to assist the transmitter for secure communications. This leads to the formulation of a Stackelberg game for the secure wireless-powered multiantenna multicasting system, where the transmitter and the PB are modelled as leader and follower, respectively, each maximizing their own utility function. The closed-form Stackelberg equilibrium of the formulated game is then derived where we study various scenarios of eavesdroppers and legitimate users that can have impact on the optimality of the derived solutions. Finally, numerical results are provided to validate our proposed schemes

Closed-form performance analysis of linear MIMO receivers in general fading scenarios

Linear precoding and post-processing schemes are ubiquitous in wireless multi-input-multi-output (MIMO) settings, due to their reduced complexity with respect to optimal strategies. Despite their popularity, the performance analysis of linear MIMO receivers is mostly not available in closed form, apart for the canonical (uncorrelated Rayleigh fading) case, while for more general fading conditions only bounds are provided. This lack of results is motivated by the complex dependence of the output signal-to-interference and noise ratio (SINR) at each branch of the receiving filter on both the squared singular values as well as the (typically right) singular vectors of the channel matrix. While the explicit knowledge of the statistics of the SINR can be circumvented for some fading types in the analysis of the linear Minimum Mean-Squared Error (MMSE) receiver, this does not apply to the less complex and widely adopted Zero-Forcing (ZF) scheme. This work provides the first-to-date closed-form expression of the probability density function (pdf) of the output ZF and MMSE SINR, for a wide range of fading laws, encompassing, in particular, correlations and multiple scattering effects typical of practically relevant channel models.Comment: 16 pages, 2 figures, contents submitted to IEEE/VDE WSA 201

Achievable Region of the K-User MAC Wiretap Channel Under Strong Secrecy

This paper investigates the information-theoretic secrecy problem for a K-user discrete memoryless (DM) multiple-access wiretap (MAC-WT) channel. Instead of using the weak secrecy criterion characterized by information leakage rate, we adopt the strong secrecy metric defined by information leakage to better protect the confidential information. We provide an achievable rate region and prove its achievability by providing a coding scheme and analyzing the output statistics in terms of (average) variational distance. We show that the rate region obtained in previous works on the subject is a special case of ours. We also show that the achievability proof in such works is incomplete, because it is assumed that certain inequalities hold while they may not in some cases. We solve this problem by constructing an inequality structure for the rates of all users' secret and redundant messages, and analyzing the conditions required to maintain this structure

On the Effectiveness of OTFS for Joint Radar Parameter Estimation and Communication

We consider a joint radar parameter estimation and communication system using orthogonal time frequency space (OTFS) modulation. The scenario is motivated by vehicular applications where a vehicle (or the infrastructure) equipped with a mono-static radar wishes to communicate data to its target receiver, while estimating parameters of interest related to this receiver. Provided that the radar-equipped transmitter is ready to send data to its target receiver, this setting naturally assumes that the receiver has been already detected. In a point-to-point communication setting over multipath time-frequency selective channels, we study the joint radar and communication system from two perspectives, i.e., the radar parameter estimation at the transmitter as well as the data detection at the receiver. For the radar parameter estimation part, we derive an efficient approximated Maximum Likelihood algorithm and the corresponding Cramér-Rao lower bound for range and velocity estimation. Numerical examples demonstrate that multi-carrier digital formats such as OTFS can achieve as accurate radar estimation as state-of-the-art radar waveforms such as frequency-modulated continuous wave (FMCW). For the data detection part, we focus on separate detection and decoding and consider a soft-output detector that exploits efficiently the channel sparsity in the Doppler-delay domain. We quantify the detector performance in terms of its pragmatic capacity, i.e., the achievable rate of the channel induced by the signal constellation and the detector soft-output. Simulations show that the proposed scheme outperforms concurrent state-of-the-art solutions. Overall, our work shows that a suitable digitally modulated waveform enables to efficiently operate joint radar parameter estimation and communication by achieving full information rate of the modulation and near-optimal radar estimation performance. Furthermore, OTFS appears to be particularly suited to the scope