An insight into common filtering in noisy SIMO blind system identification

The effect of additive sensor noise on single-input-multiple-output (SIMO) blind system identification (BSI) algorithms based upon cross-relation (CR) error is investigated. Previous studies have shown that additive noise in the observed signal results in systems comprising the true estimated channels convolved with an erroneous `common filter', and additionally that identification and removal of this filter significantly improves estimation error. However, the source of the common filter remained an open question. This paper explains the common filter through a first-order perturbation analysis of the CR matrix, showing that it be estimated from the perturbation and the eigenvectors of the noiseless CR matrix. The analysis given in this paper provides a new insight into the effect of noise on SIMO BSI algorithms and forms the first step towards an overall noise robust solution.