Scaling up MIMO: Opportunities and Challenges with Very Large Arrays

This paper surveys recent advances in the area of very large MIMO systems. With very large MIMO, we think of systems that use antenna arrays with an order of magnitude more elements than in systems being built today, say a hundred antennas or more. Very large MIMO entails an unprecedented number of antennas simultaneously serving a much smaller number of terminals. The disparity in number emerges as a desirable operating condition and a practical one as well. The number of terminals that can be simultaneously served is limited, not by the number of antennas, but rather by our inability to acquire channel-state information for an unlimited number of terminals. Larger numbers of terminals can always be accommodated by combining very large MIMO technology with conventional time- and frequency-division multiplexing via OFDM. Very large MIMO arrays is a new research field both in communication theory, propagation, and electronics and represents a paradigm shift in the way of thinking both with regards to theory, systems and implementation. The ultimate vision of very large MIMO systems is that the antenna array would consist of small active antenna units, plugged into an (optical) fieldbus.Comment: Accepted for publication in the IEEE Signal Processing Magazine, October 201

Joint Unitary Triangularization for MIMO Networks

This work considers communication networks where individual links can be described as MIMO channels. Unlike orthogonal modulation methods (such as the singular-value decomposition), we allow interference between sub-channels, which can be removed by the receivers via successive cancellation. The degrees of freedom earned by this relaxation are used for obtaining a basis which is simultaneously good for more than one link. Specifically, we derive necessary and sufficient conditions for shaping the ratio vector of sub-channel gains of two broadcast-channel receivers. We then apply this to two scenarios: First, in digital multicasting we present a practical capacity-achieving scheme which only uses scalar codes and linear processing. Then, we consider the joint source-channel problem of transmitting a Gaussian source over a two-user MIMO channel, where we show the existence of non-trivial cases, where the optimal distortion pair (which for high signal-to-noise ratios equals the optimal point-to-point distortions of the individual users) may be achieved by employing a hybrid digital-analog scheme over the induced equivalent channel. These scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network, thus we coin the approach "network modulation".Comment: Submitted to IEEE Tran. Signal Processing. Revised versio

A compressed sensing approach to block-iterative equalization: connections and applications to radar imaging reconstruction

The widespread of underdetermined systems has brought forth a variety of new algorithmic solutions, which capitalize on the Compressed Sensing (CS) of sparse data. While well known greedy or iterative threshold type of CS recursions take the form of an adaptive filter followed by a proximal operator, this is no different in spirit from the role of block iterative decision-feedback equalizers (BI-DFE), where structure is roughly exploited by the signal constellation slicer. By taking advantage of the intrinsic sparsity of signal modulations in a communications scenario, the concept of interblock interference (IBI) can be approached more cunningly in light of CS concepts, whereby the optimal feedback of detected symbols is devised adaptively. The new DFE takes the form of a more efficient re-estimation scheme, proposed under recursive-least-squares based adaptations. Whenever suitable, these recursions are derived under a reduced-complexity, widely-linear formulation, which further reduces the minimum-mean-square-error (MMSE) in comparison with traditional strictly-linear approaches. Besides maximizing system throughput, the new algorithms exhibit significantly higher performance when compared to existing methods. Our reasoning will also show that a properly formulated BI-DFE turns out to be a powerful CS algorithm itself. A new algorithm, referred to as CS-Block DFE (CS-BDFE) exhibits improved convergence and detection when compared to first order methods, thus outperforming the state-of-the-art Complex Approximate Message Passing (CAMP) recursions. The merits of the new recursions are illustrated under a novel 3D MIMO Radar formulation, where the CAMP algorithm is shown to fail with respect to important performance measures.A proliferação de sistemas sub-determinados trouxe a tona uma gama de novas soluções algorítmicas, baseadas no sensoriamento compressivo (CS) de dados esparsos. As recursões do tipo greedy e de limitação iterativa para CS se apresentam comumente como um filtro adaptativo seguido de um operador proximal, não muito diferente dos equalizadores de realimentação de decisão iterativos em blocos (BI-DFE), em que um decisor explora a estrutura do sinal de constelação. A partir da esparsidade intrínseca presente na modulação de sinais no contexto de comunicações, a interferência entre blocos (IBI) pode ser abordada utilizando-se o conceito de CS, onde a realimentação ótima de símbolos detectados é realizada de forma adaptativa. O novo DFE se apresenta como um esquema mais eficiente de reestimação, baseado na atualização por mínimos quadrados recursivos (RLS). Sempre que possível estas recursões são propostas via formulação linear no sentido amplo, o que reduz ainda mais o erro médio quadrático mínimo (MMSE) em comparação com abordagens tradicionais. Além de maximizar a taxa de transferência de informação, o novo algoritmo exibe um desempenho significativamente superior quando comparado aos métodos existentes. Também mostraremos que um equalizador BI-DFE formulado adequadamente se torna um poderoso algoritmo de CS. O novo algoritmo CS-BDFE apresenta convergência e detecção aprimoradas, quando comparado a métodos de primeira ordem, superando as recursões de Passagem de Mensagem Aproximada para Complexos (CAMP). Os méritos das novas recursões são ilustrados através de um modelo tridimensional para radares MIMO recentemente proposto, onde o algoritmo CAMP falha em aspectos importantes de medidas de desempenho

Joint Unitary Triangularization for Gaussian Multi-User MIMO Networks

The problem of transmitting a common message to multiple users over the Gaussian multiple-input multiple-output broadcast channel is considered, where each user is equipped with an arbitrary number of antennas. A closed-loop scenario is assumed, for which a practical capacity-approaching scheme is developed. By applying judiciously chosen unitary operations at the transmit and receive nodes, the channel matrices are triangularized so that the resulting matrices have equal diagonals, up to a possible multiplicative scalar factor. This, along with the utilization of successive interference cancellation, reduces the coding and decoding tasks to those of coding and decoding over the single-antenna additive white Gaussian noise channel. Over the resulting effective channel, any off-the-shelf code may be used. For the two-user case, it was recently shown that such joint unitary triangularization is always possible. In this paper, it is shown that for more than two users, it is necessary to carry out the unitary linear processing jointly over multiple channel uses, i.e., space-time processing is employed. It is further shown that exact triangularization, where all resulting diagonals are equal, is still not always possible, and appropriate conditions for the existence of such are established for certain cases. When exact triangularization is not possible, an asymptotic construction is proposed, that achieves the desired property of equal diagonals up to edge effects that can be made arbitrarily small, at the price of processing a sufficiently large number of channel uses together.Comment: Extended version of published paper in IEEE Transactions on Information Theory, vol. 61, no. 5, pp. 2662-2692, May 201

Space-Time Coding: an Overview

This work provides an overview of the fundamental aspects and of some recent advances in space-time coding (STC). Basic information theoretic results on Multiple-Input Multiple-Output (MIMO) fading channels, pertaining to capacity, diversity, and to the optimal Diversity-Multiplexing Tradeoff (DMT), are reviewed. The code design for the quasi-static, outage limited, fading channel is recognized as the most challenging and innovative with respect to traditional “Gaussian” coding. Then, a survey of STC constructions is presented. This culminates with the description of families of codes that are optimal with respect to the DMT criterion and have error performance that is very close to the information theoretic limits. The paper concludes with some important recent topics, including open problems in STC design