A DISCRETE-TIME MMSE FRAMEWORK FOR CONVERGENT MIMO SIGNAL DETECTION

Abstract

Multiple-input multiple-output (MIMO) technology plays a crucial role in modern wireless communication systems by improving spectral efficiency and link reliability. Accurate signal detection in MIMO receivers, however, remains a challenging task due to inter-antenna interference and noise. This work presents a mathematical framework for MIMO signal detection using linear minimum mean squared error (MMSE) principles, with particular emphasis on difference equation modeling and convergence analysis. The discrete-time MIMO system is formulated as a vector difference equation, enabling the application of linear systems theory to study detector stability and performance. A convergence theorem for an MMSE-based iterative detection algorithm is established under a spectral radius condition on the residual coupling matrix. To validate the theoretical findings, a MATLAB-based simulation is developed, demonstrating monotonic decay of estimation error across iterations. The results confirm that the proposed MMSE-based iterative detector converges to a unique fixed point, thereby providing a computationally efficient and stable solution for MIMO signal detection in noisy environments.