Convergence properties of the multistage constant modulus array for correlated sources

Abstract

A steady-state analysis of the multistage constant modulus (CM) array is presented for the case of correlated source signals. Using a Wiener model for the converged adaptive algorithms, it is demonstrated that because of the cascade structure, signal cross-correlation causes "phantom" sources to be present. The resulting signal leakage in the adaptive cancellers between stages causes an increase in the minimum mean-square error. A parallel implementation that overcomes this loss in performance is described; it requires an initialization strategy to ensure that each stage captures a different source. Computer simulations are presented to illustrate the convergence properties of the cascade and parallel CM array systems and to verify the theoretical results.