Capacity Optimal Coded Generalized MU-MIMO

TL;DR

This paper derives the capacity of generalized MU-MIMO systems with arbitrary input distributions and channel matrices, proposing a capacity-achieving receiver and practical coding schemes that approach theoretical limits.

Contribution

It introduces a capacity analysis for GMU-MIMO with fixed input distributions and develops a capacity optimal OAMP/VAMP receiver with practical MU-LDPC coding.

Findings

Achieves within 2 dB of the constrained sum capacity.

Proposes a capacity optimal multi-user OAMP/VAMP receiver.

Designs practical MU-LDPC codes that outperform existing methods.

Abstract

With the complication of future communication scenarios, most conventional signal processing technologies of multi-user multiple-input multiple-output (MU-MIMO) become unreliable, which are designed based on ideal assumptions, such as Gaussian signaling and independent identically distributed (IID) channel matrices. As a result, this paper considers a generalized MU-MIMO (GMU-MIMO) system with more general assumptions, i.e., arbitrarily fixed input distributions, and general unitarily-invariant channel matrices. However, there is still no accurate capacity analysis and capacity optimal transceiver with practical complexity for GMU-MIMO under the constraint of coding. To address these issues, inspired by the replica method, the constrained sum capacity of coded GMU-MIMO with fixed input distribution is calculated by using the celebrated mutual information and minimum mean-square error (MMSE) lemma and the MMSE optimality of orthogonal/vector approximate message passing (OAMP/VAMP). Then, a capacity optimal multiuser OAMP/VAMP receiver is proposed, whose achievable rate is proved to be equal to the constrained sum capacity. Moreover, a design principle of multi-user codes is presented for the multiuser OAMP/VAMP, based on which a kind of practical multi-user low-density parity-check (MU-LDPC) code is designed. Numerical results show that finite-length performances of the proposed MU-LDPC codes with multi-user OAMP/VAMP are about 2 dB away from the constrained sum capacity and outperform those of the existing state-of-art methods.