Blind source separation based on multi-user kurtosis criteria

A novel technique for the blind source separation (BSS) of mutually independent and identically distributed i.i.d. discrete-time sequences is presented. The observed signals are assumed mixed through a narrow-band (memoryless) multiple-input-multiple-output (MIMO) noisy channel and are then processed by a linear MIMO receiver, whose outputs should ideally match the transmitted signals. In the proposed approach (called the multi-user kurtosis (MUK) algorithm), the linear receiver's matrix setting is computed adaptively based on the optimization of a constrained statistical criterion that involves only second and fourth order statistics of the receiver's output. At each iteration, the algorithm combines a stochastic gradient adaptation with a Gram-Shmidt orthogonalization that enforces its criterion's constraints. The analysis of its stationary points, reveals that it is globally convergent to a zero forcing -ZF (or decorrelating) solution, both in the absence of noise and in the presence of spatio-temporally white additive Gaussian noise.