Randomized Iterative Algorithms for Distributed Massive MIMO Detection

Distributed detection over decentralized baseband architectures has emerged as an important problem in the uplink massive MIMO systems. In this paper, the classic Kaczmarz method is fully investigated to facilitate the distributed detection for massive MIMO. First of all, a more general iteration performance result about the traditional randomized block Kaczmarz (RBK) method is derived, which paves the way for conceiving the conditional randomized block Kaczmarz (CRBK) algorithm. By customizing RBK with the concept of conditional sampling, CRBK achieves faster convergence and smaller error bound than RBK. To further exploit the potential of conditional sampling, multi-step conditional randomized block Kaczmarz (MCRBK) algorithm is proposed, which can be readily adopted as a flexible, scalable, low-complexity distributed detection scheme to suit various decentralized baseband architectures in massive MIMO. Moreover, to eliminate the convergence error bound of MCRBK, a novel dynamic step-size mechanism is proposed for the iteration update of MCRBK. Theoretical demonstration shows that the proposed distributed MCRBK detection with the optimized dynamic step-size not only converges exponentially to the solution of linear detection schemes but also enjoys the global convergence to well suit different practical scenarios of massive MIMO.