Fast adaptive algorithms using eigenspace projections

Although adaptive gradient algorithms are simple and relatively robust, they generally have poor performance in the absence of “rich” excitation. In particular, it is well known that the convergence speed of the LMS algorithm deteriorates when the condition number of the input autocorrelation matrix is large. This problem has been previously addressed using weighted RLS or normalized frequency-domain algorithms. We present a new approach that employs gradient projections in selected eigenvector sub-spaces to improve the convergence properties of LMS algorithms for colored inputs. We also introduce an efficient method to iteratively update an “eigen subspace” of the autocorrelation matrix. The proposed algorithm is more efficient in terms of computational complexity, than the WRLS and its convergence speed approaches that of the WRLS even for highly correlated inputs