The Strong Uncorrelating Projection Approximation (SUPA) Algorithm for Decorrelating Complex Non-Circular Data

The second order statistics of stationary complex random vector signals are not completely specified by the data covariance matrix. Hence, conventional decorrelation methods may not suffice in removing dependencies within complex-valued signals; instead, strong-uncorrelation is required (J. Eriksson and V. Koivunen, 2006). In this paper, we develop a procedure for adaptively estimating the strong uncorrelating transform (SUT) by recasting this task as a series of one-dimensional signal approximation problems using a novel prewhitened cost and applying a modified version of the projection approximation subspace tracking with deflation (PASTd) algorithm to solve each problem. The algorithm updates with prewhitening are of O(n²) complexity per n-element snapshot, and unlike other SUT algorithms, the technique can be used in a sequential fashion to identify any portion of the complex signal subspace by degree of signal non-circularity