CANONICAL CORRELATION ANALYSIS (CCA) ALGORITHMS FOR MULTIPLE DATA SETS: APPLICATION TO BLIND SIMO EQUALIZATION

Canonical Correlation Analysis (CCA) is a classical tool in statisti-cal analysis that measures the linear relationship between two or several data sets. In [1] it was shown that CCA of M = 2 data sets can be reformulated as a pair of coupled least squares (LS) problems. Here, we generalize this idea to M> 2 data sets. First, we present a batch algorithm to extract all the canonical vectors through an iterative regression procedure, which at each iteration uses as desired output the mean of the outputs obtained in the pre-vious iteration. Furthermore, this alternative formulation of CCA as M coupled regression problems allows us to derive in a straight-forward manner a recursive least squares (RLS) algorithm for on-line CCA. The proposed batch and on-line algorithms are applied to blind equalization of single-input multiple-output (SIMO) channels. Some simulation results show that the CCA-based algorithms out-perform other techniques based on second-order statistics for this particular application. 1