Bias-compensated augmented complex-valued NSAF algorithm and its low-complexity implementation

Abstract

The performance of traditional adaptive filtering algorithms will be degraded when the input signal contains noise. To handle colored noisy input and output measurements in the complex domain, this paper proposes an augmented complex-valued estimation-input NSAF (ACEI-NSAF) algorithm, derived by using estimated noiseless input, which is obtained by the minimization of an instantaneous perturbation with both input and output data, to update the weight vectors. Benefiting from this, the proposed algorithm can achieve unbiased estimation of the unknown system in the presence of noisy inputs, thereby surpassing the augmented complex-valued NSAF (ACNSAF) algorithm. The mean stability, excess mean-square error, and computational complexity are investigated, and the unbiasedness condition of the proposed algorithm is presented. Subsequently, a low-complexity ACEI-NSAF (SACEI-NSAF) algorithm is introduced by using the subband selection approach. Experimental results in system identification demonstrate the effectiveness of the proposed algorithms and analysis.