A Bayesian Framework for Collaborative Multi-Source Signal Detection

This paper introduces a Bayesian framework to detect multiple signals embedded in noisy observations from a sensor array. For various states of knowledge on the communication channel and the noise at the receiving sensors, a marginalization procedure based on recent tools of finite random matrix theory, in conjunction with the maximum entropy principle, is used to compute the hypothesis selection criterion. Quite remarkably, explicit expressions for the Bayesian detector are derived which enable to decide on the presence of signal sources in a noisy wireless environment. The proposed Bayesian detector is shown to outperform the classical power detector when the noise power is known and provides very good performance for limited knowledge on the noise power. Simulations corroborate the theoretical results and quantify the gain achieved using the proposed Bayesian framework.Comment: 15 pages, 9 pictures, Submitted to IEEE Trans. on Signal Processin

Asymptotic Analysis of Double-Scattering Channels

We consider a multiple-input multiple-output (MIMO) multiple access channel (MAC), where the channel between each transmitter and the receiver is modeled by the doubly-scattering channel model. Based on novel techniques from random matrix theory, we derive deterministic approximations of the mutual information, the signal-to-noise-plus-interference-ratio (SINR) at the output of the minimum-mean-square-error (MMSE) detector and the sum-rate with MMSE detection which are almost surely tight in the large system limit. Moreover, we derive the asymptotically optimal transmit covariance matrices. Our simulation results show that the asymptotic analysis provides very close approximations for realistic system dimensions.Comment: 5 pages, 2 figures, submitted to the Annual Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, 201

Asymptotic Moments for Interference Mitigation in Correlated Fading Channels

We consider a certain class of large random matrices, composed of independent column vectors with zero mean and different covariance matrices, and derive asymptotically tight deterministic approximations of their moments. This random matrix model arises in several wireless communication systems of recent interest, such as distributed antenna systems or large antenna arrays. Computing the linear minimum mean square error (LMMSE) detector in such systems requires the inversion of a large covariance matrix which becomes prohibitively complex as the number of antennas and users grows. We apply the derived moment results to the design of a low-complexity polynomial expansion detector which approximates the matrix inverse by a matrix polynomial and study its asymptotic performance. Simulation results corroborate the analysis and evaluate the performance for finite system dimensions.Comment: 7 pages, 2 figures, to be presented at IEEE International Symposium on Information Theory (ISIT), Saint Petersburg, Russia, July 31 - August 5, 201

Iterative Deterministic Equivalents for the Performance Analysis of Communication Systems

In this article, we introduce iterative deterministic equivalents as a novel technique for the performance analysis of communication systems whose channels are modeled by complex combinations of independent random matrices. This technique extends the deterministic equivalent approach for the study of functionals of large random matrices to a broader class of random matrix models which naturally arise as channel models in wireless communications. We present two specific applications: First, we consider a multi-hop amplify-and-forward (AF) MIMO relay channel with noise at each stage and derive deterministic approximations of the mutual information after the Kth hop. Second, we study a MIMO multiple access channel (MAC) where the channel between each transmitter and the receiver is represented by the double-scattering channel model. We provide deterministic approximations of the mutual information, the signal-to-interference-plus-noise ratio (SINR) and sum-rate with minimum-mean-square-error (MMSE) detection and derive the asymptotically optimal precoding matrices. In both scenarios, the approximations can be computed by simple and provably converging fixed-point algorithms and are shown to be almost surely tight in the limit when the number of antennas at each node grows infinitely large. Simulations suggest that the approximations are accurate for realistic system dimensions. The technique of iterative deterministic equivalents can be easily extended to other channel models of interest and is, therefore, also a new contribution to the field of random matrix theory.Comment: submitted to the IEEE Transactions on Information Theory, 43 pages, 4 figure

Random Beamforming over Quasi-Static and Fading Channels: A Deterministic Equivalent Approach

In this work, we study the performance of random isometric precoders over quasi-static and correlated fading channels. We derive deterministic approximations of the mutual information and the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum-mean-square-error (MMSE) receiver and provide simple provably converging fixed-point algorithms for their computation. Although these approximations are only proven exact in the asymptotic regime with infinitely many antennas at the transmitters and receivers, simulations suggest that they closely match the performance of small-dimensional systems. We exemplarily apply our results to the performance analysis of multi-cellular communication systems, multiple-input multiple-output multiple-access channels (MIMO-MAC), and MIMO interference channels. The mathematical analysis is based on the Stieltjes transform method. This enables the derivation of deterministic equivalents of functionals of large-dimensional random matrices. In contrast to previous works, our analysis does not rely on arguments from free probability theory which enables the consideration of random matrix models for which asymptotic freeness does not hold. Thus, the results of this work are also a novel contribution to the field of random matrix theory and applicable to a wide spectrum of practical systems.Comment: to appear in IEEE Transactions on Information Theory, 201

Transmit Power Minimization in Small Cell Networks Under Time Average QoS Constraints

We consider a small cell network (SCN) consisting of N cells, with the small cell base stations (SCBSs) equipped with Nt \geq 1 antennas each, serving K single antenna user terminals (UTs) per cell. Under this set up, we address the following question: given certain time average quality of service (QoS) targets for the UTs, what is the minimum transmit power expenditure with which they can be met? Our motivation to consider time average QoS constraint comes from the fact that modern wireless applications such as file sharing, multi-media etc. allow some flexibility in terms of their delay tolerance. Time average QoS constraints can lead to greater transmit power savings as compared to instantaneous QoS constraints since it provides the flexibility to dynamically allocate resources over the fading channel states. We formulate the problem as a stochastic optimization problem whose solution is the design of the downlink beamforming vectors during each time slot. We solve this problem using the approach of Lyapunov optimization and characterize the performance of the proposed algorithm. With this algorithm as the reference, we present two main contributions that incorporate practical design considerations in SCNs. First, we analyze the impact of delays incurred in information exchange between the SCBSs. Second, we impose channel state information (CSI) feedback constraints, and formulate a joint CSI feedback and beamforming strategy. In both cases, we provide performance bounds of the algorithm in terms of satisfying the QoS constraints and the time average power expenditure. Our simulation results show that solving the problem with time average QoS constraints provide greater savings in the transmit power as compared to the instantaneous QoS constraints.Comment: in Journal on Selected Areas of Communications (JSAC), 201

When Network Coding and Dirty Paper Coding meet in a Cooperative Ad Hoc Network

We develop and analyze new cooperative strategies for ad hoc networks that are more spectrally efficient than classical DF cooperative protocols. Using analog network coding, our strategies preserve the practical half-duplex assumption but relax the orthogonality constraint. The introduction of interference due to non-orthogonality is mitigated thanks to precoding, in particular Dirty Paper coding. Combined with smart power allocation, our cooperation strategies allow to save time and lead to more efficient use of bandwidth and to improved network throughput with respect to classical RDF/PDF.Comment: 7 pages, 7 figure

A Distributed Approach to Interference Alignment in OFDM-based Two-tiered Networks

In this contribution, we consider a two-tiered network and focus on the coexistence between the two tiers at physical layer. We target our efforts on a long term evolution advanced (LTE-A) orthogonal frequency division multiple access (OFDMA) macro-cell sharing the spectrum with a randomly deployed second tier of small-cells. In such networks, high levels of co-channel interference between the macro and small base stations (MBS/SBS) may largely limit the potential spectral efficiency gains provided by the frequency reuse 1. To address this issue, we propose a novel cognitive interference alignment based scheme to protect the macro-cell from the cross-tier interference, while mitigating the co-tier interference in the second tier. Remarkably, only local channel state information (CSI) and autonomous operations are required in the second tier, resulting in a completely self-organizing approach for the SBSs. The optimal precoder that maximizes the spectral efficiency of the link between each SBS and its served user equipment is found by means of a distributed one-shot strategy. Numerical findings reveal non-negligible spectral efficiency enhancements with respect to traditional time division multiple access approaches at any signal to noise (SNR) regime. Additionally, the proposed technique exhibits significant robustness to channel estimation errors, achieving remarkable results for the imperfect CSI case and yielding consistent performance enhancements to the network.Comment: 15 pages, 10 figures, accepted and to appear in IEEE Transactions on Vehicular Technology Special Section: Self-Organizing Radio Networks, 2013. Authors' final version. Copyright transferred to IEE