CONVERGENCE OF THE SMI AND THE DIAGONALLY LOADED SMI ALGORITHMS WITH WEAK INTERFERENCE

The sample matrix inversion (SMI) algorithm is commonly used in adaptive arrays since it offers rapid convergence to the maximum signal-to-interference-plus-noise ratio (SINR) solution. However, in some applications, such as digital communications or satellite television communications, other measures of performance such as the signal-to-interference ratio (SIR) may be equally important. In this paper approximations are derived for the power levels at the output of an adaptive array that uses the diagonally loaded SMI algorithm. Diagonal loading is a technique where the diagonal of the covariance matrix is augmented with a positive or negative constant prior to inversion. We examine how SINR and SIR at the array output vary with the number of samples taken when the input signals are continuous wave. It is shown that positive loading produces more rapid convergence with a reduction in output SIR. Negative loading provides an improved SIR level, but it is shown that the output power levels are erratic and slow to converge. Simulation results are given which verify the theoretical predictions. © 1990 IEEE