MMSE Signal Detection for MIMO Systems based on Ordinary Differential Equation

TL;DR

This paper introduces a continuous-time MMSE signal detection method for MIMO systems using an ordinary differential equation, providing analytical MSE formulas and improved convergence with a time-dependent regularization parameter.

Contribution

It develops a novel continuous-time MMSE estimation approach for MIMO systems based on ODEs, with analytical MSE expressions and enhanced convergence via a time-dependent regularization.

Findings

Analytical MSE formula derived for the proposed method.

Excellent agreement between numerical experiments and theoretical MSE.

Improved convergence performance with time-dependent regularization parameter.

Abstract

Motivated by emerging technologies for energy efficient analog computing and continuous-time processing, this paper proposes continuous-time minimum mean squared error estimation for multiple-input multiple-output (MIMO) systems based on an ordinary differential equation. Mean squared error (MSE) is a principal detection performance measure of estimation methods for MIMO systems. We derive an analytical MSE formula that indicates the MSE at any time. The MSE of the proposed method depends on a regularization parameter which affects the convergence property of the MSE. Furthermore, we extend the proposed method by using a time-dependent regularization parameter to achieve better convergence performance. Numerical experiments indicated excellent agreement with the theoretical values and improvement in the convergence performance owing to the use of the time-dependent parameter.