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.

基于最小均方误差（MSE）准则的复数最小均方（CLMS）自适应算法已广泛用于复杂域中具有高斯噪声的线性应用。但是，MSE准则在存在非高斯噪声的情况下会导致性能下降。为了解决这个问题，首先构造了一种新的复杂的内核风险敏感的p功率损耗（CKRSP-L）准则来对抗非高斯噪声。然后，基于构造的CKRSP-L准则，提出了一种新的复杂核风险敏感p提出了高功率（CKRSP）算法，以同时提供非高斯噪声的鲁棒性和线性系统的性能改进。此外，为了将CKRSP算法扩展到非线性系统，提出了一种新颖的复杂多核随机傅里叶映射（CMRFM），将原始输入数据转换为复杂的多核随机傅里叶特征空间（CMRFFS），从而实现了另一种新颖的复杂多核随机傅里叶核风险敏感p针对复杂领域中的非线性应用，提出了高功率（CMRFKRSP）算法。最后，还对CKRSP和CMRFKRSP的稳态超均方误差（SEMSE）进行了计算，以对性能进行理论分析。在不同噪声环境中进行的蒙特卡洛模拟验证了所获得的SEMSE的正确性以及CKRSP和CMRFKRSP的性能优势。