Blind system identification using fourth order spectral analysis of complex signals

In this paper we give an analytic optimal solution to the identification problem of non minimum phase systems using the fourth order spectra. We show that this solution is in first approximation equivalent to the solution given by the well-known kurtosis maximization method. The proposed solution gives the phase of the system transfer function, the modulus can be obtained from the second order statistics. However this solution requires trispectrum phase unwrapping as the trispectrum phase is known in the interval [-π,π] but needs to be unwrapped in the interval [-4π,4π] in order to obtain the optimal solution. Therefore, we present different phase unwrapping solutions. Next, we propose a method to improve the trispectrum phase estimation using a factorizability condition. Simulation results are given and the algorithm shows good behavior even with few data