Max-Min SINR in Large-Scale Single-Cell MU-MIMO: Asymptotic Analysis and Low Complexity Transceivers

This work focuses on the downlink and uplink of large-scale single-cell MU-MIMO systems in which the base station (BS) endowed with $M$ antennas communicates with $K$ single-antenna user equipments (UEs). Particularly, we aim at reducing the complexity of the linear precoder and receiver that maximize the minimum signal-to-interference-plus-noise ratio subject to a given power constraint. To this end, we consider the asymptotic regime in which $M$ and $K$ grow large with a given ratio. Tools from random matrix theory (RMT) are then used to compute, in closed form, accurate approximations for the parameters of the optimal precoder and receiver, when imperfect channel state information (modeled by the generic Gauss-Markov formulation form) is available at the BS. The asymptotic analysis allows us to derive the asymptotically optimal linear precoder and receiver that are characterized by a lower complexity (due to the dependence on the large scale components of the channel) and, possibly, by a better resilience to imperfect channel state information. However, the implementation of both is still challenging as it requires fast inversions of large matrices in every coherence period. To overcome this issue, we apply the truncated polynomial expansion (TPE) technique to the precoding and receiving vector of each UE and make use of RMT to determine the optimal weighting coefficients on a per-UE basis that asymptotically solve the max-min SINR problem. Numerical results are used to validate the asymptotic analysis in the finite system regime and to show that the proposed TPE transceivers efficiently mimic the optimal ones, while requiring much lower computational complexity.Comment: 13 pages, 4 figures, submitted to IEEE Transactions on Signal Processin

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

Linear Precoding Based on Polynomial Expansion: Large-Scale Multi-Cell MIMO Systems

Large-scale MIMO systems can yield a substantial improvement in spectral efficiency for future communication systems. Due to the finer spatial resolution achieved by a huge number of antennas at the base stations, these systems have shown to be robust to inter-user interference and the use of linear precoding is asymptotically optimal. However, most precoding schemes exhibit high computational complexity as the system dimensions increase. For example, the near-optimal RZF requires the inversion of a large matrix. This motivated our companion paper, where we proposed to solve the issue in single-cell multi-user systems by approximating the matrix inverse by a truncated polynomial expansion (TPE), where the polynomial coefficients are optimized to maximize the system performance. We have shown that the proposed TPE precoding with a small number of coefficients reaches almost the performance of RZF but never exceeds it. In a realistic multi-cell scenario involving large-scale multi-user MIMO systems, the optimization of RZF precoding has thus far not been feasible. This is mainly attributed to the high complexity of the scenario and the non-linear impact of the necessary regularizing parameters. On the other hand, the scalar weights in TPE precoding give hope for possible throughput optimization. Following the same methodology as in the companion paper, we exploit random matrix theory to derive a deterministic expression for the asymptotic SINR for each user. We also provide an optimization algorithm to approximate the weights that maximize the network-wide weighted max-min fairness. The optimization weights can be used to mimic the user throughput distribution of RZF precoding. Using simulations, we compare the network throughput of the TPE precoding with that of the suboptimal RZF scheme and show that our scheme can achieve higher throughput using a TPE order of only 3