Convergence properties of the multistage CMA adaptive beamformer

The multistage CMA adaptive beamformer is capable of separating multiple narrowband sources without pilot or training signals. It is comprised of a cascade of CM (constant modulus) array subsections, each of which captures one of the signals impinging an the array. An adaptive signal canceller follows each CM array to remove captured signals from the input before processing by subsequent sections. Based an a stochastic analysis, we derive the steady-state convergence properties of the system, including its direction-finding capabilities. For mutually uncorrelated sources and noise, it is shown that the canceller exactly removes a captured signal, thereby reducing the rank of the effective array matrix of the next subsection by one.<>