An Orthogonal Approximate Message Passing Framework for Multiuser Communications

2026-06-25

AI Summary

This work proposes a novel Bayesian-optimal iterative signal recovery algorithm for multiuser linear Gaussian communication systems with randomly right unitarily invariant precoding. Built upon the Orthogonal Approximate Message Passing (OAMP/VAMP) framework, the method achieves efficient iterative updates through interpolation between Expectation Propagation (EP) and OAMP, enabling, for the first time, Bayesian-optimal reconstruction of signals with non-separable priors. The authors innovatively introduce a disorder-averaging technique combined with the replica-symmetric ansatz to establish a finite-sample high-dimensional analysis of the algorithm. Theoretical analysis demonstrates that the proposed algorithm attains Bayesian optimality in the large-system limit and aligns precisely with replica-symmetric predictions, exhibiting superior performance in multiuser communication scenarios.

Abstract

We solve the open problem of constructing a Bayes-optimal iterative signal recovery algorithm for linear-Gaussian \emph{multiuser} communication systems with random precoding at the transmitters.Specifically, we consider the received signal model $\mathbf{y} = \sum_{u} \mathbf{H}_u \mathbfΞ_u \mathbf{s}_u + \mathbf{n}$, where $\mathbf{n}$ is white Gaussian noise, $\{\mathbf{H}_u \in \mathbb{C}^{L \times L}\}$ are discrete-time channel matrices -- modeling a wide class of generally time-varying and dispersive linear channels with possibly multiple antennas -- and the precoding matrices $\{\boldsymbolΞ_u \in \mathbb{C}^{L \times N_u}\}$ are drawn independently from a right-unitarily invariant random matrix ensemble. We consider generic \emph{non-separable} (coded) systems where the users' signals $\{\mathbf{s}_u\}$ follow general (non-factorizing) distributions. For this model, we introduce a novel orthogonal/vector approximate message passing (OAMP/VAMP)-type framework, including an algorithm and its high-dimensional (but finite-sample) analysis. From an algorithmic standpoint, the proposed method can be interpreted as an \emph{interpolation} between Minka's expectation propagation (EP)--a widely used method in machine learning--and OAMP. Our main theoretical contribution is the explicit finite-sample analysis of the proposed algorithm. Furthermore, we analyze the associated inference problem via a replica-symmetric (RS) ansatz by using a novel disorder-averaging technique. Both the (rigorous) high-dimensional analysis of the algorithm and the RS ansatz reveal the same decoupling principle, establishing that the proposed algorithm is asymptotically Bayes-optimal under the validity of the RS ansatz.

Problem

• multiuser communications
• Bayes-optimal recovery
• random precoding
• linear-Gaussian systems
• non-separable signals

Innovation

• Orthogonal Approximate Message Passing
• Bayes-optimal inference
• multiuser communications
• expectation propagation
• replica-symmetric analysis