A stochastic model for the deficient length Pseudo Affine Projection adaptive algorithm

This paper presents a statistical analysis of the deficient length Pseudo Affine Projection (PAP) adaptive algorithm. The PAP algorithm is obtained by introducing a step size control parameter in the weight update equation of the unity step size Affine Projection (AP) algorithm assuming autoregressive input signals. The deficient case occurs when the number of adaptive coefficients is smaller than the necessary to whiten the error signal. Deterministic recursive equations are derived for the mean weight and mean-square error behaviours. Monte Carlo simulations show excellent agreement with the theoretically predicted behaviour in steady-state conditions. It is shown that the PAP coefficients converge in the mean to the initial plant coefficients, producing an unbiased solution even for correlated inputs.