Bi-iterative least squares algorithms for blind channel identification and equalization with second-order statistics

We present an adaptive algorithm for blind identification and equalization of single-input multiple-output (SIMO) FIR channels with second-order statistics. We first reformulate the blind channel identification problem into a low-rank matrix approximation solution based on the QR decomposition of the received data matrix. Then, a fast recursive algorithm is developed based on the bi-iterative least squares (Bi-LS) subspace tracking method. The new algorithm requires only a computational complexity of O(md2) at each iteration, or even as low as O(md) if only equalization is necessary, where m is the dimension of the received data vector (or the row rank of channel matrix) and d is the dimension of the signal subspace (or the column rank of channel matrix). To overcome the shortcoming of the back substitution, an inverse QR iteration algorithm for subspace tracking and channel equalization is also developed. The inverse QR iteration algorithm is well suited for the parallel implementation in the systolic array. Simulation results are presented to illustrate the effectiveness of the proposed algorithms for the channel identification and equalization.