Performance analysis of unconstrained partitioned-block frequency-domain adaptive filters in under-modeling scenarios

The unconstrained partitioned-block frequency-domain adaptive filter (PBFDAF) offers superior computational efficiency over its constrained counterpart. However, the correlation matrix governing the natural modes of the unconstrained PBFDAF is not full rank. Consequently, the mean coefficient behavior of the algorithm depends on the initialization of adaptive coefficients and the Wiener solution is non-unique. To address the above problems, a new theoretical model for the deficient-length unconstrained PBFDAF is proposed by constructing a modified filter weight vector within a system identification framework. Specifically, we analyze the transient and steady-state convergence behavior. Our analysis reveals that modified weight vector is independent of its initialization in the steady state. The deficient-length unconstrained PBFDAF converges to a unique Wiener solution, which does not match the true impulse response of the unknown plant. However, the unconstrained PBFDAF can recover more coefficients of the parameter vector of the unknown system than the constrained PBFDAF in certain cases. Also, the modified filter coefficient yields better mean square deviation (MSD) performance than previously assumed. The presented alternative performance analysis provides new insight into convergence properties of the deficient-length unconstrained PBFDAF. Simulations validate the analysis based on the proposed theoretical model.