Set-membership recursive least-squares adaptive filtering algorithm

A new set-membership adaptive filtering algorithm is developed based on the exponentially-weighted RLS algorithm with a time-varying forgetting factor that is optimized at each iteration by imposing a bounded-magnitude constraint on the a posteriori filter output error. The new algorithm is designed to improve the numerical behavior of the previously proposed BEACON algorithm while delivering the same convergence and tracking performance as the BEACON algorithm. Simulation results for a flat-fading MIMO channel estimation application demonstrate the superiority of the new algorithm over the BEACON algorithm in terms of numerical stability.