Multichannel recursive least squares adaptive filtering without a desired signal

The author presents a pair of adaptive QR decomposition-based algorithms for the adaptive mixed filter in which no desired signal is available, but the signal-to-data cross-correlation vector is known. The algorithms are derived by formulating the recursive mixed filter as a least-squares problem and then applying orthogonal QR-based techniques in its solution. This leads to algorithms with the performance, numerical, and structural advantages of the RLS/ QR algorithm, but without the requirement of a desired signal. Both Givens and square-root-free Givens rotations are used in implementing the recursive QR decomposition. Because of their structural regularity, the algorithms are easily implemented by triangular systolic array structures. Simulations show that these algorithms require fewer computations and less precision than recursive sample matrix inversion approaches