A fast algorithm for conditional maximum likelihood blind identification of SIMO/MIMO FIR systems

Blind system identification is important for a wide range of applications. The conditional maximum likelihood (CML) method is one of the most effective ones recently developed for blind system identification. In particular, the CML method is statistically most efficient at relatively high signal-to-noise ratios (SNR). Unfortunately, the original implementation of the CML method via the two-step maximum likelihood (TSML) algorithm is computationally too expensive [1]. In this paper, a computationally attractive implementation of the TSML algorithm based on the Cholesky decomposition is proposed. This leads to a new fast TSML (FTSML) algorithm that has a linear complexity, i.e., O(N) flops as compared to O(N³) flops in [1], N being the data size. In a second part of the paper, we generalize the FTSML algorithm from the single-source case to the multiple-sources case.