HPA Predistortion Algorithm Based on Adaptive Extended Kalman Filter and Neural Network
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摘要: 针对强记忆功放的非线性问题,提出一种基于自适应扩展卡尔曼滤波与神经网络的高功放(High power amplifier, HPA)预失真算法.采用实数固定延时神经网络(Real-valued focused time-delay neural network, RVFTDNN)对间接学习结构预失真系统中的预失真器和逆估计器进行建模,扩展卡尔曼滤波(Extended Kalman filter, EKF)算法训练神经网络,从理论上指出Levenberg-Marquardt(LM)算法是EKF算法的特殊情况,并用李亚普诺夫稳定性理论分析EKF算法的稳定收敛条件,推导出测量误差矩阵的自适应迭代公式.结果表明:自适应EKF算法的训练误差和泛化误差均比LM算法更低,预失真后的邻道功率比(Adjacent channel power ratio, ACPR)比LM算法改善了2dB.
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关键词:
- 高功率放大器 /
- 预失真 /
- 神经网络 /
- 非线性 /
- 自适应扩展卡尔曼滤波
Abstract: For the nonlinearity of high power amplifier(HPA) with strong memory effects, a novel HPA predistortion algorithm based on adaptive extended Kalman filter and neural network is proposed. In the predistortion system with indirect learning architecture, the predistorter and HPA inverse estimator are modeled with the same real-valued focused time-delay neural network(RVFTDNN), and the extended Kalman filter(EKF) is used to iteratively train and update the coefficients of the neural network. It is concluded that Levenberg-Marquardt(LM) algorithm is a special case of EKF algorithm in theory. The stably convergence condition of EKF training algorithm is analysed with the Lyapunov stability theory and adaptive covariance matrix of measurement noise is derived for iterative computation. Simulation results show that compared with LM algorithm the training error and generalization error of adaptive EKF predistortion algorithm are both less. The adjacent channel power ratio(ACPR) of HPA output signal with adaptive EKF predistortion is better than that of LM predistortion by 2dB. -
图 1 三层实数固定延时神经网络结构
Fig. 1 Real-valued focused time-delay neural network architecture with three layers
图 2 间接学习结构的神经网络预失真系统
Fig. 2 Indirect learning architecture of neural network predistortion system
图 3 LM算法和自适应EKF算法的训练误差比较
Fig. 3 Comparison of training errors using LM algorithm and adaptive EKF algorithm
图 6 LM和EKF预失真后的信号功率谱密度图比较
Fig. 6 Comparison of signal power spectrum density with LM and EKF predistortion
表 1 LM算法和自适应EKF算法的训练误差和泛化误差比较
Table 1 Comparison of training errors and generalization errors using LM algorithm and adaptive EKF algorithm
训练误差(样本数3000) 泛化误差(样本数3000) 训练误差(样本数1000) 泛化误差(样本数1000) LM算法 $7.5877×10^{-7}$ $1.7229×10^{-6}$ $4.9250×10^{-6}$ $9.4585×10^{-6}$ 自适应EKF算法 $5.4270×10^{-8}$ $7.4936×10^{-7}$ $2.4373×10^{-6}$ $6.8848×10^{-6}$ 
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