Steady-state analysis of the multistage constant modulus array

The multistage constant modulus (CM) array is a cascade adaptive beamforming system that can recover several narrowband cochannel signals without training. We examine its steady-state properties at convergence using a stochastic analysis and computer simulations. Based on a Wiener model of convergence for the gradient adaptive algorithms, closed-form expressions are derived for the CM array and canceller weight vectors, as well as the effective source direction vectors at all stages along the cascade system. The signal-capture and direction-finding capabilities of the system are also discussed. Computer simulations for stationary and fading sources are presented to confirm the theoretical results and to illustrate the rapid convergence behavior of the adaptive algorithms.