Convergence of the SMI and the diagonally loaded SMI algorithms with weak interference (adaptive array)

Approximations for the power levels at the output of an adaptive array that uses the diagonally loaded sample matrix inversion (SMI) algorithm are derived. Diagonal loading is a technique where the diagonal of the covariance matrix is augmented with a positive or negative constant prior to inversion. The authors examine how the signal-to-interference-plus-noise ratio (SINR) and signal-to-interference ratio (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 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 which verify the theoretical procedure are given.>