A composite hypothesis test for active weight detection in sparse system identification

Adaptive sparse system identification can profit from specialized algorithms that detect and adapt only the weights corresponding to the nonzero coefficients of the unknown impulse response. This leads to adaptive identification with reduced computational complexity and faster convergence. Most real-time sparse system identification algorithms which follow this strategy neglect prior information on the adaptive weight activity. Thus, the probabilities of a given weight to be active (nonzero) or not are assumed to be equal at each detection step. This paper proposes a Bayesian composite hypothesis test for detecting active weights. The prior probabilities of the active and non-active weights are adjusted from previous decisions and used to evaluate the decision threshold. The proposed hypothesis test is employed on a well known sparse system identification algorithm. The results indicate the improvements that can be achieved using the proposed Bayesian approach.