Constrained adaptation algorithms employing Householder transformation

This paper presents a tutorial-like detailed explanation of linearly constrained minimum-variance filtering in order to introduce an efficient implementation that utilizes Householder transformation (HT). Through a graphical description of the algorithms, further insight on linearly constrained adaptive filters was made possible, and the main differences among several algorithms were highlighted. The method proposed herein, based on HT, allows direct application of any unconstrained adaptation algorithm as in a generalized sidelobe canceller (GSC), but unlike the GSC, the HT-based approach always renders efficient implementations. A complete and detailed comparison with the GSC model and a thorough discussion of the advantages of the HT-based approach are also given. Simulations were run in a beamforming application where a linear array of 12 sensors was used. It was verified that not only the HT approach yields efficient implementation of constrained adaptive filters, but in addition, the beampatterns achieved with this method were much closer to the optimal solution than the beampatterns obtained with GSC models with similar computational complexity.