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

Massive MIMO is a variant of multi-user MIMO in which the number of antennas at the base station (BS) <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> is very large and typically much larger than the number of served users (data streams) <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>. Recent research has widely investigated the system-level advantages of the massive MIMO, and in particular, the beneficial effect of increasing the number of antennas <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> and the number of served users <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">$M \gg 1$ </tex-math></inline-formula>, 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 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 passing via numerical simulations. Our results indicate that our proposed technique is computationally very competitive and yields quite a comparable performance while it does not require the knowledge of the statistics of users’ channel vectors.