Accelerated Randomized Methods for Receiver Design in Extra-Large Scale MIMO Arrays

Recent interest has been cast on accelerated versions of the randomized Kaczmarz (RK) algorithm due to the increase in applications that consider sparse linear systems. In particular, considering the context of massive multiple-input-multiple-output (M-MIMO) communication systems, a low complexity naive RK-based receiver has recently been proposed. This method can take advantage of non-stationarities emerging from extra-large M-MIMO systems, but it performs poorly on highly spatially correlated channels. To address this problem, in this paper, we propose a new class of accelerated RK-based receiver designs, where convergence acceleration is based on the residual information. However, we show that the cost of obtaining this knowledge on an iteration basis is not worth it due to the lousy convergence effects caused by system and channel parameters. Inspired by this observation, we further propose a RK-based receiver with sampling without replacement, referred to as RK-RZF. This simple technique is more effective in performing signal detection under reduced complexity. Future works suggest advantage of RK-based receivers to improve current 5G commercial systems and solve the problem of signal detection in other paradigms beyond 5G.