基于小批量梯度下降法的FIR滤波器

doi:10.16088/j.issn.1001-6600.2020062602

摘要/Abstract

摘要： 针对梯度下降算法收敛速度慢,每次更新梯度都使用全部的样本点数且计算量大、复杂度高等问题,提出一种新型的用于相干光接收机的色散补偿FIR(finite-length impulse response)滤波器。在Matlab中搭建基带多速率相干光通信系统传输模型,利用小批量梯度下降法(mini-batch gradient descent),每次使用百分之一的样本数更新梯度和抽头权值h(n),计算均方误差,使计算复杂度降低为原来的1%,且当学习效率为0.05时,收敛值达到0.005 5,均方误差收敛值更小。均方误差收敛后得到滤波器抽头的权值,本方法得到的滤波器权值在全频带具有更好的滤波效果。通过基带脉冲成型限制基带信号有效带宽,滤波器的抽头数目为197,相对全频带抽头数减少37.5%,所以能在窄频带设计出抽头数目更少,滤波效果更佳的最优滤波器。

关键词: 相干光通信系统模型, 均方误差, FIR滤波器, 抽头权值, 小批量梯度下降, 最优滤波器

Abstract: In order to solve the problem that the gradient descent algorithm has a slow convergence speed, uses all the sample points each time to update the gradient, and has a large amount of calculation and high complexity, a novel dispersion compensated FIR (fine length impulse response) filter for coherent optical receiver is proposed. Through building coherent optical communication system baseband multi-rate transmission model in Matlab, using the Mini-Batch Gradient Descent method with 1% of the total samples to update the weights of filter tap h(n) every time calculating the mean square error and updating the filter gradient, the computational complexity can be reduced to 1% of the original. When the learning efficiency is 0.05, the convergence value reaches 0.005 5, which has a smaller mean square error convergence value. When the mean square error converges, the weight of the filter tap is obtained. The filter weights obtained by this method has a better filtering effect and lower bit error in the whole frequency band. After using baseband pulse shaping to limit the effective bandwidth of the baseband signal, the number of filter taps is 197, which is 37.5% less than the number of taps in the full frequency band. Therefore, an optimal filter with fewer taps and better filtering effects can be designed in a narrow frequency band.

Key words: coherent optical communication system model, mean square error, FIR filter, tap weights, mini-batch gradient descent, optimal filter

中图分类号:

TN713

武康康, 周鹏, 陆叶, 蒋丹, 闫江鸿, 钱正成, 龚闯. 基于小批量梯度下降法的FIR滤波器[J]. 广西师范大学学报（自然科学版）, 2021, 39(4): 9-20.

WU Kangkang, ZHOU Peng, LU Ye, JIANG Dan, YAN Jianghong, QIAN Zhengcheng, GONG Chuang. FIR Equalizer Based on Mini-batch Gradient Descent Method[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(4): 9-20.

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