In an Uncertain World: Distributed Optimization in MIMO Systems with Imperfect Information

TL;DR

This paper presents a distributed matrix exponential learning algorithm for optimizing MIMO system signal covariance matrices under imperfect, delayed, and changing channel information, ensuring convergence and robustness.

Contribution

It introduces a novel matrix exponential learning method that converges under mild conditions and handles asynchronous updates, delays, and channel variations in MIMO systems.

Findings

Algorithm converges quickly even with many users and antennas.

Proven robustness to delays, asynchrony, and channel changes.

Numerical simulations confirm scalability and effectiveness.

Abstract

In this paper, we introduce a distributed algorithm that optimizes the Gaussian signal covariance matrices of multi-antenna users transmitting to a common multi-antenna receiver under imperfect and possibly delayed channel state information. The algorithm is based on an extension of exponential learning techniques to a semidefinite setting and it requires the same information as distributed water-filling methods. Unlike water-filling however, the proposed matrix exponential learning (MXL) algorithm converges to the system's optimum signal covariance profile under very mild conditions on the channel uncertainty statistics; moreover, the algorithm retains its convergence properties even in the presence of user update asynchronicities, random delays and/or ergodically changing channel conditions. In particular, by properly tuning the algorithm's learning rate (or step size), the algorithm converges within a few iterations, even for large numbers of users and/or antennas per user. Our theoretical analysis is complemented by numerical simulations which illustrate the algorithm's robustness and scalability in realistic network conditions.