Activity Detection in Distributed MIMO: Distributed AMP via Likelihood Ratio Fusion

Abstract

We develop a new algorithm for activity detection for grant-free multiple access in distributed multiple-input multiple-output (MIMO). The algorithm is a distributed version of the approximate message passing (AMP) based on a soft combination of likelihood ratios computed independently at multiple access points. The underpinning theoretical basis of our algorithm is a new observation that we made about the state evolution in the AMP. Specifically, with a minimum mean-square error denoiser, the state maintains a block-diagonal structure whenever the covariance matrices of the signals have such a structure. We show by numerical examples that the algorithm outperforms competing schemes from the literature.

Spatial Correlation Aware Compressed Sensing for User Activity Detection and Channel Estimation in Massive MTC

“…Rajoriya et al [15] proposed a Bayesian solution that couples AMP and SBL to provide an algorithm that enjoys the low complexity of AMP and the good performance of SBL. Bai et al [16] proposed a distributed AMP algorithm in cell-free MTC networks that aims to reduce the complexity of AMP by distributing the computation load over several access points. Moreover, we formulated the JUICE as an ℓ 2,1 -norm minimization problem [17], [18] and as a maximum a posteriori (MAP) problem in [19].…”

Convolutional Approximate Message-Passing

“…AMP was extended to distributed AMP [38]- [43] exploiting a central node. More precisely, distributed AMP in [38]- [40] utilizes feedback from the central node to refine messages in 0000-0000/00$00.00 © 2021 IEEE each remote node, like distributed IHT [30], while distributed AMP in [41], [42] exploits no feedback from the central node. Hayakawa et al [43] proposed decentralized AMP (D-AMP) for tree-structured networks with no central nodes via consensus propagation [44].…”

“…Proof: See Appendix D. The intuition of Theorem 4 is as follows: To achieve the performance of centralized GAMP, the effective signal-tonoise ratio (SNR) L −2 η2 t [l]/ Σt,t [l] in the inner denoiser has to converge toward the same fixed point as that for centralized GAMP. This convergence is realizable for consensus propagation since both signal power L −2 η2 t [l] and noise power Σt,t [l] are updated via consensus propagation, as shown in (29) and (42). However, the distributed protocol (44) results in different protocols for the signal and noise power.…”

“…Lemma 1 ( [46]): Consider the Bayes-optimal inner denoiser (46). For given t ≥ 0, assume Στ,t [l] = Σt,t [l] in (42) for all τ ∈ {0, . .…”

“…We next design the outer denoiser so as to maximize the signal-to-noise ratio (SNR) L −2 η2 t [l]/ Σt,t [l] in the measurement model (45) for the inner denoiser. Using the definitions of ηt [l] and Σt,t [l] in (29) and (42), we find that the SNR…”