Adaptive filtering for complex data has received more attentions recently. As a similarity measure for the complex random variables, complex correntropy has been shown robustness in the design of adaptive filter. However, existing works using complex correntropy are limited to a Gaussian kernel function, which is not always the optimal choice. In this paper, we propose a class of new adaptive filtering algorithm for complex data using complex correntropy, which employs the complex generalized Gaussian density function as kernel function. Stability analysis provides the bound for learning rate and the steady-state excess mean square error is derived for theoretical analysis. Simulation results show that the proposed algorithm has zero probability of divergence and verify its superiority.

With the emergence of complex correntropy, the maximum complex correntropy criterion (MCCC) has been applied to the complex-domain adaptive filtering. The MCCC uses the fixed point method to find the optimal solution, which provides good robustness in the non-Gaussian noise environment, especially for the impulse noise. However, the convergence analysis for the fixed point method is limited to the real-domain filtering. In this letter, we provide the convergence analysis of fixed point based MCCC algorithm in complex-domain filtering. First, by using the matrix inversion lemma, we rewrite the MCCC algorithm to a gradient-like version. In addition, we provide two computationally efficient versions of MCCC. Then, we provide the stability analysis and obtain the excess mean square error for MCCC. Finally, simulation results confirm the correctness of the convergence analysis in this letter.

Recently, affine projection algorithm has been extensively studied in the Gaussian noise environment. However, the performance of affine projection algorithm will deteriorate rapidly in the presence of impulsive noise and other non-Gaussian noise. To address this issue, this paper proposes a novel affine projection algorithm based on the complex Gaussian kernel function, called widely linear maximum complex correntropy criterion affine projection algorithm (WL-MCCC-APA). With the maximum complex correntropy criterion (MCCC), the robustness of affine projection algorithm is improved significantly in the non-Gaussian noise environment, especially in the presence of impulsive noise. Meanwhile, a variable step size WL-MCCC-APA (VSS-WL-MCCC-APA) method based on fixed-point theory is proposed to further balance the convergence rate and steady-state misalignment of the algorithm. Finally, the step size boundary analysis and steady-state analysis are presented for theoretical analysis. Simulation results verify the correctness of obtained theoretical results and the superiority of the proposed WL-MCCC-APA and VSS-WL -MCCC-APA.

Adaptive filtering for complex-valued data plays a key role in the field of signal processing. So far, there has been very little research for the adaptive filtering in complex-valued errors-in-variables (EIV) model. Compared with the complex correntropy, the total complex correntropy has shown superior performance in the EIV model. However, the current gradient based maximum total complex correntropy (MTCC) adaptive filtering algorithm has suffered from the tradeoff between fast convergence rate and low weight error power. In order to improve the performance of MTCC, we develop a fixed point maximum total complex correntropy (FP-MTCC) adaptive filtering algorithm in this study. The convergence analysis of the FP-MTCC is also provided in the paper. Furthermore, we develop two recursive FP-MTCC (RFP-MTCC) algorithms for the online adaptive filtering and provide the transient analysis of RFP-MTCC. Finally, the validity of the convergence and the superiority of the proposed algorithms are verified by simulations.

This paper considers a novel algorithmic framework for the joint spectral sharing design of a colocated MIMO pulse radar and a MIMO communication system under signal direction mismatch, wherein both radar transceiver and communication transmitter designs are investigated, and the mutual information (MI) is maximized under a number of constraints to suppress the mutual interference of the coexistence system. The designed multi-variate formulation is non-convex, an iterative procedure is derived to compute a sequence of simpler sub-problems which admit a low complexity closed-form solution for each primal variable. The convergence of all devised algorithms is guaranteed. Finally, a thorough performance assessment is conducted to demonstrate the merits of the proposed solutions.