Low-Complexity Statistically Robust Precoder/Detector Computation for Massive MIMO Systems

Abstract

Massive MIMO is a variant of multiuser MIMO in which the number of antennas at the base station (BS) M is very large and typically much larger than the number of served users (data streams) K. Recent research has widely investigated the system-level advantages of massive MIMO and, in particular, the beneficial effect of increasing the number of antennas M . These benefits, however, come at the cost of a dramatic increase in hardware and computational complexity. This is partly due to the fact that the BS needs to compute precoding/receiving vectors in order to coherently transmit/detect data to/from each user, where the resulting complexity grows proportionally to the number of antennas M and the number of served users K. Recently, different algorithms based on tools from asymptotic random matrix theory and/or approximated message passing have been proposed to reduce such complexity. The underlying assumption in all these techniques, however, is that the exact statistics (covariance matrix) of the channel vectors of the users is a priori known. This is far from being realistic, especially taking into account that, in the high-dim regime of M ≫ 1, estimating the channel covariance matrices of the users is also challenging in terms of both computation and storage requirements. In this paper, we propose a novel technique for computing the precoder/detector in a massive MIMO system. Our method is based on the randomized Kaczmarz algorithm and does not require a priori knowledge of the statistics of the users channel vectors. We analyze the performance of our proposed algorithm theoretically and compare its performance with that of other techniques based on random matrix theory and approximate message

Randomized Kaczmarz algorithm for massive MIMO systems with channel estimation and spatial correlation

“…Note, therefore, that the more relevant a row of A , the greater the chance of this being chosen during the update schedule. The main convergence result of the rKA established in Boroujerdi et al and Strohmer and Vershynin is summarized by the following corollary.…”

“…If the rKA is applied to solve this problem, a convergence bias or residual error is eventually introduced in the solution because of the inconsistency. In Boroujerdi et al, this problem was circumvented by splitting B ϱ = y 0 with into two stages. The first strives to remodel the OD SLE to a consistent form, leading to an UD SLE; then, another OD SLE is derived on the basis of the genuine stated problem ( B ϱ = y 0 ).…”

“…This random approach of the KA obtains an expected exponential rate of convergence and is therefore much more reliable, unlike the case of classical KA convergence that depends tremendously on the way that the equations are arranged in an SLE to be solved. For M‐MIMO, Boroujerdi et al derived a mathematical framework to examine the performance of rKA applied to emulate some linear signal processing techniques. The rKA‐based schemes of Boroujerdi et al consider the resolution of the signal estimation problems, ie, they are used to estimate in the receiver/transmitter the signals sent/transmitted by/for each UE in each symbol period.…”

“…For M‐MIMO, Boroujerdi et al derived a mathematical framework to examine the performance of rKA applied to emulate some linear signal processing techniques. The rKA‐based schemes of Boroujerdi et al consider the resolution of the signal estimation problems, ie, they are used to estimate in the receiver/transmitter the signals sent/transmitted by/for each UE in each symbol period. The work, however, did not focus on deriving a notion of convergence of the rKA‐based schemes and relating it to amounts of performance and computational complexity.…”

“…In particular, our contributions in this work are threefold: We show that large‐term fading effects (pathloss and shadowing) are detrimental to the rKA functionality when this approach is applied to obtain the receive combining matrix, as revealed in a previous study by which we broadly introduced these findings in terms of performance only. This motivated us to propose modifications upon the initialization (forcing and hybridizing it) of a particular, called hereafter as parallel rKA‐based scheme, improving its convergence, its average performance, and effectively decreasing its computational cost. Once the authors in Boroujerdi et al only presented the complexity related to rKA‐based schemes in terms of big‐ notation, we enhance the computational complexity analysis considering complex scalar multiplications/divisions related to the multiplications/divisions operations of matrices and vectors (see the framework reported in Björnson et al, App.B, p.558). This enabled us to define upper bounds for the number of rKA iterations considering as basis of the computational complexity difference between the proposed and available canonical schemes.…”