Stationary points of a kurtosis maximization algorithm for blind signal separation and antenna beamforming

Blind source separation has been the subject of extensive research. In particular, blind antenna beamforming is an effective signal separation technique for communication systems to combat co-channel interference. Among many potential candidate approaches, the simple constant modulus algorithm (CMA) has been widely studied and used in practice. The CMA is designed to capture and separate signals with negative kurtosis. However, when some signals have positive kurtoses, the CMA is unable to capture and separate these sources. We show that the kurtosis maximum algorithm (KMA) can capture signals with both the positive and negative kurtoses. Its global convergence proof is presented for noiseless systems with multiple signals sources and for systems with a single source and zero-kurtosis (such as Gaussian) additive noise.