α 稳定分布噪声下基于核方法的非线性信道均衡算法

为了提高α稳定分布噪声下非线性信道均衡器的性能，本文利用核方法处理非线性问题，结合最小平均p范数算法的核心思想，构造了α稳定分布噪声下基于核方法的非线性均衡器，提出并推导了α稳定分布噪声下核最小平均p范数均衡算法。首先，通过核函数将接收信号映射到高维特征空间；然后，在高维特征空间中利用LMP算法对信号进行均衡；最后，将均衡器的输出信号表示为内积形式并利用核函数将其转化到输入空间进行计算。理论分析和仿真实验结果表明，与核最小均方算法和最小平均p范数算法相比，新算法在保证收敛速度的前提下降低了稳态误差，能够更好地对α稳定分布噪声下的非线性信道失真进行补偿。 

Nonlinear channel equalization algorithm based on kernel method for -stable noise

In order to improve the performance of nonlinear channel equalizer for α-stable noise, combining with the core thought of the least mean p-norm (LMP) algorithm, the paper took advantage of the kernel method to deal with nonlinear problems and constructed the nonlinear equalizer which is based on kernel method for α-stable noise. At the same time, the kernel least mean p-norm (KLMP) algorithm was produced and inferred in this paper. First of all, received signal was mapped into the high dimensional feature spaces by kernel function; Then, the LMP algorithm was employed to equalize signal in the high dimensional feature spaces; In the end, output signal of the equalizer in the high dimensional feature spaces was expressed in inner product and turned into input spaces by kernel function to compute. Theoretical analysis and simulation results show that the new algorithm decreases the steady state error on the condition that the convergence rate is guaranteed and can better compensate nonlinear channel distortion when compared with the kernel least mean square (KLMS) algorithm and the LMP algorithm.