A low-complexity Gaussian message passing iterative detector for massive MU-MIMO systems

Abstract

This paper considers a low-complexity Gaussian Message Passing Iterative Detection (GMPID) method over a pairwise graph for a massive Multiuser Multiple-Input Multiple-Output (MU-MIMO) system, in which a base station with M antennas serves K Gaussian sources simultaneously. Both K and M are large numbers and we consider the cases that K < M in this paper. The GMPID is a message passing algorithm based on a fully connected loopy graph, which is well known that it is not convergent in some cases. In this paper, we first analyse the convergence of GMPID. Two sufficient conditions that the GMPID converges to the Minimum Mean Square Error (MMSE) detection are proposed. However, the GMPID may still not converge when K/M > ( √ 2 − 1) 2 . Therefore, a new convergent GMPID with equally low complexity called SA-GMPID is proposed, which converges to the MMSE detection for any K < M with a faster convergence speed. Finally, numerical results are provided to verify the validity and accuracy of the proposed theoretical results.

Capacity-Achieving MIMO-NOMA: Iterative LMMSE Detection

“…1) Uncoded Low-Complexity Detection: Many lowcomplexity linear detections such as Matched Filter (MF), Zero-Forcing (ZF) receiver, Minimum Mean Square Error (MMSE), and Message Passing Detector (MPD) [7], [27] are proposed for the practical systems. In addition, some iterative methods such as Jacobi method, Richardson method [28]- [30], Belief Propagation (BP) method, and iterative MPD [5], [6], [31], [32] are put forward to further reduce the computational complexity by avoiding the unfavorable matrix inversion in the linear detections. Although being attractive from the complexity view point, these individual detectors are regarded to be sub-optimal MUDs, where decoding results are not fed back to the detector.…”

“…• The decoding order of SIC changes with the different channel state and different Quality of Service (QoS), which brings a higher overhead cost. 3) Coded PIC Detection: PIC, where users are parallelly recovered and messages exchanged between the detector and decoders are soft, is another promising technique for the practical MIMO-NOMA systems [6], [30], [32], [37]. This technique has been commonly used for the non-orthogonal MAC like the Code Division Multiple Access (CDMA) systems [7], [35] and the Interleave Division Multiple Access (IDMA) systems [39], [40].…”

“…Proposition 3: The achievable rate R i of user i and an upper bound of R i are given by From (4), (6) and Proposition 1, we have snr dec pri,i = ρ i , snr est ext,i = φ i (vx), mmse dec ap,i (snr dec,i pri ) = ρ i + ψ i (ρ i ) −1 −1 and mmse est ap,i (snr est ext,i ) = vx i (vx). Therefore, we have the following corollary from Proposition 3.…”

Message Passing in C-RAN: Joint User Activity and Signal Detection

“…1) Gaussian message update for g k ∼N (e m k→n (t + 1), v m k→n (t + 1)): According to the update rules of Gaussian message [9]- [11], PDF of the output Gaussian message from a variable node is the normalized product of PDFs of the input Gaussian messages. Therefore, we can obtain v m…”

Gaussian Message Passing Iterative Detection for MIMO-NOMA Systems with Massive Access

“…Another promising detection for MIMO-NOMA is message passing algorithm (MPA) [19], [20]. There are two MPAs, one of which is the Gaussian Belief Propagation (GaBP) algorithm based on a graph consisted of variable nodes [21], [22], the other one is the Gaussian Message Passing Iterative Detection (GMPID) based on a pairwise graph consisted of variable nodes and sum nodes [10], [23]- [25].…”