Analysis of the linear GSIC multiuser detector using a matrix iterative approach

In this work, we use a new approach that relies on the theory of matrix iterative analysis to study the convergence behavior of the linear group-wise successive interference cancellation (GSIC) detector. Particularly, we show that the linear GSIC detector is in fact a realization of a modified block successive over-relaxation (BSOR) iterative method where the relaxation factor is a matrix instead of scalar. Consequently, to study the convergence behavior of the GSIC detector, we propose two new corollaries that extend the famous work of Kahan (Varga, Matrix iterative analysis, 2000) to the case where the relaxation factor is a matrix instead of a scalar. Using the two new corollaries we develop two new conditions of convergence for the linear GSIC detector. Simulation results are in excellent agreement with theory.