Dong Fei, Qian Guobing, Wang Shiyuan
College of Electronic and Information Engineering, Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, Southwest University, Chongqing 400715, China.
Entropy (Basel). 2020 Jan 6;22(1):70. doi: 10.3390/e22010070.
The complex correntropy has been successfully applied to complex domain adaptive filtering, and the corresponding maximum complex correntropy criterion (MCCC) algorithm has been proved to be robust to non-Gaussian noises. However, the kernel function of the complex correntropy is usually limited to a Gaussian function whose center is zero. In order to improve the performance of MCCC in a non-zero mean noise environment, we firstly define a complex correntropy with variable center and provide its probability explanation. Then, we propose a maximum complex correntropy criterion with variable center (MCCC-VC), and apply it to the complex domain adaptive filtering. Next, we use the gradient descent approach to search the minimum of the cost function. We also propose a feasible method to optimize the center and the kernel width of MCCC-VC. It is very important that we further provide the bound for the learning rate and derive the theoretical value of the steady-state excess mean square error (EMSE). Finally, we perform some simulations to show the validity of the theoretical steady-state EMSE and the better performance of MCCC-VC.
复相关熵已成功应用于复域自适应滤波，并且相应的最大复相关熵准则（MCCC）算法已被证明对非高斯噪声具有鲁棒性。然而，复相关熵的核函数通常限于中心为零的高斯函数。为了提高MCCC在非零均值噪声环境中的性能，我们首先定义了具有可变中心的复相关熵并给出其概率解释。然后提出了具有可变中心的最大复相关熵准则（MCCC-VC），并将其应用于复域自适应滤波。接下来，我们使用梯度下降法来搜索代价函数的最小值。我们还提出了一种可行的方法来优化MCCC-VC的中心和核宽度。非常重要的是，我们进一步给出了学习率的界并推导了稳态超额均方误差（EMSE）的理论值。最后，我们进行了一些仿真以展示理论稳态EMSE的有效性以及MCCC-VC的更好性能。
