New Kurtosis Optimization Schemes for MISO Equalization

This paper deals with efficient optimization of cumulant based contrast functions. Such a problem occurs in the blind source separation framework, where contrast functions are criteria to be maximized in order to retrieve the sources. More precisely, we focus on the extraction of one source signal and our method applies in deflation approaches, where the sources are extracted one by one. We propose new methods to maximize the kurtosis contrast function. These methods are intermediate between a gradient and an iterative “fixed-point” optimization of so-called reference contrasts. They rely on iterative updates of the parameters which monotonically increase the contrast function value: we point out the strong similarity with the Expectation-Maximization (EM) method and with recent generalizations referred to as Minimization-Maximization (MM). We also prove the global convergence of the algorithm to a stationary point. Simulations confirm the convergence of our methods to a separating solution. They also show experimentally that our methods have a much lower computational cost than former classical optimization methods. Finally, simulations suggest that the methods remain valid under weaker conditions than those required for proving convergence.