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Inspired by the emerging technologies for energy-efficient analog computingand continuous-time processing, this paper proposes a continuous-time minimummean squared error (MMSE) estimation for multiple-input multiple-output (MIMO)systems based on an ordinary differential equation (ODE). We derive ananalytical formula for the mean squared error (MSE) at any given time, which isa primary performance measure for estimation methods in MIMO systems. The MSEof the proposed method depends on the regularization parameter, which affectsthe convergence properties. In addition, this method is extended byincorporating a time-dependent regularization parameter to enhance convergenceperformance. Numerical experiments demonstrate excellent consistency withtheoretical values and improved convergence performance due to the integrationof the time-dependent parameter. Other benefits of the ODE are also discussedin this paper. Discretizing the ODE for MMSE estimation using numerical methodsprovides insights into the construction and understanding of discrete-timeestimation algorithms. We present discrete-time estimation algorithms based onthe Euler and Runge-Kutta methods. The performance of the algorithms can beanalyzed using the MSE formula for continuous-time methods, and theirperformance can be improved by using theoretical results in a continuous-timedomain. These benefits can only be obtained through formulations using ODE.

Ordinary Differential Equation-based MIMO Signal Detection