Complex-Valued adaptive networks based on entropy estimation

In distributed estimation, the mean-square error (MSE) criterion has been extensively studied. When complex-valued signals are involved, the additive noise can present different degrees of non-circular properties. The MSE criterion can be optimal only when the error signal is circular, and may not perform well for non-circular error signal. To improve the performance, we present a new diffusion adaptive strategy using the Gaussian entropy criterion as the cost function. Complex-valued Gaussian entropy was early introduced for linear and widely linear filtering. Unfortunately, the closed-form solution based on Gaussian entropy was not obtained due to the nonlinearity of the entropy equation. In this paper, we derive a closed-form solution based on Gaussian entropy for linear and widely linear filters, and provide mean value steady and mean-square performance analysis for the network in detail. Our theoretical analysis demonstrates that the steady-state error approaches zero when the additive noise is maximally non-circular. The simulations demonstrate that the proposed method outperforms the MSE criterion for non-circular noise.