Asymptotic properties of the algebraic constant modulus algorithm

The algebraic constant modulus algorithm (ACMA) is a noniterative blind source separation algorithm. It computes jointly beamforming vectors for all constant modulus sources as the solution of a joint diagonalization problem. We analyze its asymptotic properties and show that (unlike CMA) it converges to the Wiener beamformer when the number of samples or the signal-to-noise ratio (SNR) goes to infinity. We also sketch its connection to the related JADE algorithm and derive a version of ACMA that converges to a zero-forcing beamformer. This gives improved performance in applications that use the estimated mixing matrix, such as in direction finding.