Householder-transform constrained LMS algorithms with reduced-rank updating

This paper proposes a new approach to linearly-constrained adaptive filtering, where successive Householder transformations are incorporated in the algorithm update equation in order to reduce computational complexity and coefficient-error norm. We show the derivation of two new algorithms, namely the unnormalized and the normalized Householder-transform constrained LMS algorithms (HCLMS and NHCLMS, respectively). Although the derivation is carried out based on the constrained LMS (CLMS) algorithm, the technique can be applied to other constrained algorithms as well. Simulation results of a linearly-constrained minimum-variance problem show that in finite-precision implementation the coefficient-error norms obtained with the new algorithms are smaller than those obtained with the CLMS and the normalized CLMS algorithms