Steady-State Solution of the Deficient Length Constrained FBLMS Algorithm

In almost all analyses of the frequency-domain block least mean-square (FBLMS) algorithm, the length of the adaptive filter is assumed to be equal to that of the unknown system impulse response. However, in many practical situations, where the length of the system impulse response is extremely long, the adaptive filter usually works in an under-modeling situation. The analysis results for the sufficient length FBLMS algorithm are not applicable to the deficient length case. In this correspondence, the steady-state solution of the deficient length constrained FBLMS algorithm is analyzed. Simulations illustrate the accuracy of the theoretical results.