Gross-coupled LMS for quadratic constrained filter design

Quadratic constrained maximization appears as the central problem in many filter design methods and signal processing applications, whenever the processing or filtering entails the maximization of a signal to noise ratio. Furthermore, self reference systems for MSE filters, beamformers and equalizers which manage either time or frequency diversity of the desired signal, give rise to the same mathematical problem. This work reports an adaptive algorithm based on two coupled LMS-like algorithms. It is shown how the Lagrange multiplier, involved in constrained minimization problems, plays the role of gain control in forming the error signal for the filter updates. This gain is power controlled by the output signals keeping the proper equilibrium between the outputs of the two LMS loops.