On conditions for the rank restoration in forward/backward spatial smoothing

The forward/backward spatial smoothing is an efficient technique for obtaining a modified covariance matrix of full rank in the presence of coherent sources. The condition for the full-rank restoration was presented in an earlier paper by Pillai and Kwon (1989). It, however, is incorrect. We present the exact condition. It is shown that the forward/backward spatial smoothing results in the full-rank restoration with probability 1.