An adaptive RLS solution to the optimal minimum power filtering problem with a max/min formulation

In signal processing, there are problems where the processed signal output energy is maximized while the noise component is minimized. This gives rise to a max/min problem, which is equivalent to a generalized eigenvalue problem. Exemplary applications of the max/min formulation have been seen in Capon's blind beamforming method and the blind minimum output energy (MOE) detection in CDMA wireless communications. The solution to such a problem involves eigen-decomposition of a transformed data covariance matrix inverse, which is computationally expensive to implement. This paper offers an adaptive RLS solution to the optimal minimum power filtering problem without involving eigen-decompositions. It is based on a new recursive least square updating procedure that works for multiple linear constraints, and uses a one-dimensional subspace tracking method to update the filter weights. The performance is comparable with that of using the direct eigen-decomposition and matrix inversion.