Gradient-based joint block diagonalization algorithms: Application to blind separation of FIR convolutive mixtures

This article addresses the problem of the non-unitary joint block diagonalization of a given set of complex matrices. Two new algorithms are provided: the first is based on a classical gradient approach and the second is based on a relative gradient approach. For each algorithm, two versions are provided: the fixed stepsize and the optimal stepsize version. Computer simulations are provided to illustrate the behavior of both algorithms in different contexts. Finally, it is shown that these algorithms enable solving the problem of the blind separation of finite impulse response (FIRFIR) convolutive mixtures of (non-stationary correlated) sources. We focus on methods based on the use of spatial quadratic time–frequency spectra or distributions. The suggested approach main advantage is to enable the elimination of the spatial whitening of the observations which has been proven to establish a bound with regard to the best reachable performances in the blind sources separation context.