Complex multi-kernel random Fourier adaptive algorithms under the complex kernel risk-sensitive p-power loss

Abstract

The complex least mean square (CLMS) adaptive algorithm based on the minimum mean square error (MSE) criterion has been widely used for linear applications with Gaussian noises in complex domain. However, the MSE criterion suffers from performance degeneration in the presence of non-Gaussian noise. To address this issue, a novel complex kernel risk-sensitive p-power loss (CKRSP-L) criterion is first constructed to combat non-Gaussian noises. Then, based on the constructed CKRSP-L criterion, a novel complex kernel risk-sensitive p-power (CKRSP) algorithm is proposed to provide robustness to non-Gaussian noises and performance improvement for linear systems, simultaneously. Further, to extend the CKRSP algorithm into nonlinear systems, a novel complex multi-kernel random Fourier mapping (CMRFM) is proposed to transform the original input data into a complex multi-kernel random Fourier features space (CMRFFS), and thus another novel complex multi-kernel random Fourier kernel risk-sensitive p-power (CMRFKRSP) algorithm is presented for nonlinear applications in complex domain. Finally, the steady-state excess mean square errors (SEMSEs) of CKRSP and CMRFKRSP are also calculated for theoretical analysis of performance. Monte Carlo simulations conducted in different noise environments validate the correctness of the obtained SEMSEs and performance advantages of CKRSP and CMRFKRSP.