Abstract: This article introduces the principle of LS-SVM and describes the implementation of LS-SVM based on Conjugate Gradient algorithm, starting from the learning theory of support vector machine. For the common equalization problem in communication, the LS-SVM is applied to nonlinear equalization task in case of nonlinear channel with color noise. Comparing the performances with the Bayesian optimal equalizer, the LS-SVM equalizer is testified to solve the nonlinear equalization effectively. In real digital communication, in case of unknown channel states, the receiver can learn from the training series to determine the parameters of equalizer and predict the incoming transmitted signal.

Key words: Least square support vector machine, nonlinear equalization, Gaussian color noise

摘要： 本文从支持向量机（Support Vector Machine, SVM）学习理论出发，介绍了最小二乘支持向量机(Least squares support vector machine, LS-SVM)的原理[1]，并详细描述了使用共轭梯度(Conjugate Gradient, CG)算法来实现LS-SVM。结合通信中常见的非线性均衡问题，讨论了在信道呈现非线性，色噪声干扰情况下，使用LS-SVM实现均衡任务，通过同最优贝叶斯均衡器性能的比较，证明了LS-SVM处理非线性均衡问题的有效性。在实际数字通信中，接收端可以在不知道信道状态的前提下，通过接收训练序列并对其进行学习，确定均衡器模型参数，从而对未知的发送信号进行预测。

关键词: 最小二乘支持向量机 非线性均衡 高斯色噪声