Statistical modelling of multichannel blind system identification errors

It is well known that blind system identification (BSI) algorithms misconverge in the presence of noise and that applications relying on such channel estimates must be designed to be robust to these blind system identification errors (BSIEs). However, there is currently no generalized model of BSIEs in the literature and instead, white Gaussian noise (WGN) is commonly assumed. This paper investigates the statistics of BSIEs based on a robust state-of-the-art BSI algorithm using both simulated and real impulse responses. A BSIE model is proposed based on Gaussian mixture models (GMMs) and a method for generating artificial BSIEs based on this model for simulations is given. Comparisons against alternative assumptions used in the literature are given and it is shown through experimental results that the proposed model gives BSIEs that are most statistically similar to the ground truth.