Fast recursive eigensubspace adaptive filters

A class of adaptive filters based on sequential eigen-decomposition of the data covariance matrix is introduced. These new algorithms are completely rank revealing and hence they can perfectly handle the following two relevant data cases where conventional RLS methods fail to provide satisfactory results: 1) highly oversampled “smooth” data with rank deficient or almost rank deficient covariance matrix. 2) Noise-corrupted data where a signal must be separated effectively from superimposed noise. The paper corrects the widely held belief that eigenbased algorithms must be computationally more demanding than conventional RLS techniques. A spatial RLS adaptive filter has a principal complexity of O(N²) operations per time step, where N is the filter order. Somewhat ironically, though, the corresponding new eigensubspace or low rank adaptive filter requires only O(Nr) operations per time step where r⩽N denotes the numerical rank of the data covariance matrix. Thus eigensubspace adaptive filters can be computationally less or even much less demanding depending on the rank/order ratio r/N or the “compressibility” of the signal. Some high-performance subspace trackers are obtained as by-products of this research. Simulation results confirm the present claims