An augmented complex-valued gradient-descent total least-squares algorithm for noncircular signals

In this paper, we propose a novel augmented complex-valued gradient-descent total least-squares (ACGDTLS) adaptive filter for processing noisy input and output noncircular complex-valued signals. First, a Rayleigh quotient cost function is formulated by incorporating augmented complex-valued statistics and the output-to-input-noise-ratio within the widely linear error-in-variable model, whereby the ACGDTLS is developed using the gradient-descent approach. Next, rigorous analysis is conducted to establish a conservative step-size bound guaranteeing mean convergence, a closed-form expression for the steady-state mean-squared deviation, and the algorithm’s computational complexity. Finally, through simulations conducted in system identification, wind/speech prediction, and stereophonic acoustic echo cancellation, the analytical findings are validated, and the proposed ACGDTLS filter demonstrates superior estimation accuracy compared to the augmented complex-valued least-mean-square algorithm and two state-of-the-art bias-compensated methods. Remarkably, this performance advantage persists across a wide range of step-sizes, input noise variances, and output noise variances.