Performance Analysis of Deficient-length RLS and EDS Algorithms

In practice, the length of the impulse response of the system to be identified is unknown and often infinite. When the system is modeled as an FIR filter, the length is usually shorter, and hence the name deficient-length filter. The learning rate, mean square error, and other properties of a deficient-length adaptive filter are different from that of a filter that is of sufficient length. In this paper, mean square error and convergence in the mean are analyzed for least square type deficient-length adaptive filters. In particular, we analyze recursive least square (RLS) and euclidean direction search (EDS) algorithms with deficient-length filters, and derive some mathematical properties. Simulation results agree with the theoretical analyses.