融合模型求解与深度学习的可见光通信非线性均衡器

doi:10.12382/bgxb.2022.0679

摘要/Abstract

摘要：

沃尔特拉非线性后均衡器(Volterra Series Nonlinear Post-Equalizer,VS-NPE)可以补偿可见光通信(Visible Light Communication, VLC)的非线性失真和多径效应,但其结构复杂且均衡精度有限。在VS-NPE内核求解基础上,提出一种基于阈值自学习近似消息传递(Learned Threshold Approximate Message Passing,LTAMP)网络的非线性均衡器。修正样本观测矩阵以克服其列高度相关的缺陷;在改进近似消息传递(Approximate Message Passing, AMP)算法迭代的基础上,将算法每一次迭代的计算过程映射为一层特殊的神经网络,经逐层展开后构建出完整的LTAMP均衡器。所提方法融合了模型求解和深度学习的优势,可从样本中学习最佳的AMP参数,以克服其对噪声敏感且输出不稳定的缺陷,进而提升内核求解稳定性与计算精度。仿真结果表明,与稳固阈值AMP算法相比,所提方法在误码率为1×10^-3时能取得2dB的信噪比增益,且对样本噪声具有较强的自适应性,展现出优异的非线性失真补偿能力。

关键词: 沃尔特拉非线性后均衡器, 可见光通信, 近似消息传递算法, 深度学习

Abstract:

The Volterra series nonlinear post-equalizer (VS-NPE) can compensate for the nonlinear distortion and multipath effects of visible light communication (VLC), but its structure is complex and the equalization accuracy is limited. A nonlinear equalizer for learning threshold approximate message passing (LTAMP) networks is proposed based on the VS-NPE kernel calculation. The sample observation matrix is modified to overcome the defect that its columns are highly correlated. Then the calculation process of each iteration of the improved approximate message passing(AMP) algorithm is mapped to a special neural network, which is expanded layer by layer to construct a complete LTAMP equalizer. The proposed method combines the advantages of model solving and deep learning, and can learn the best AMP parameters from samples to overcome the defects of its sensitivity to noise and unstable output, thereby improving the stability of kernel solving and the calculation accuracy. Simulations show that, compared with the stability threshold AMP algorithm, the proposed method can achieve a signal-to-noise ratio gain of 2dB when the bit error rate (BER) is 1×10^-3, and has a strong sampling adaptive ability, showing an excellent nonlinear distortion compensation ability.

Key words: Volterra nonlinear post-equalizer, visible light communication, approximate message passing algorithm, deep learning

中图分类号:

田大明, 苗圃. 融合模型求解与深度学习的可见光通信非线性均衡器[J]. 兵工学报, 2024, 45(2): 466-473.

TIAN Daming, MIAO Pu. Visible Light Communication Nonlinear Equalizer Based on Model Solving and Deep Learning[J]. Acta Armamentarii, 2024, 45(2): 466-473.

图/表 9

图1 基于VS的非线性失真后均衡器

Fig.1 Volterra series-based nonlinear distortion post-equalizer

图2 基于LTAMP的非线性失真后均衡器

Fig.2 Nonlinear distortion post-equalizer based on learned threshold approximate message oassing

图3 LTAMP网络结构图

Fig.3 LTAMP network architecture

图4 无噪情况下LTAMP网络部署不同层对应的NMSE性能

Fig.4 NMSE performance of LTAMP network deployment at different layers under noise-free conditions

图5 含噪情况下LTAMP网络部署不同层对应的NMSE性能

Fig.5 NMSE performance of LTAMP network deployment at different layers under noisy conditions

图6 不同训练SNR下的LTAMP均衡精度

Fig.6 Equalization accuracy of LTAMP under different SNRs

图7 不同方案的均衡精度对比

Fig.7 Comparison of equalization accuracies among different schemes

图8 基于LTAMP的NPE输出信号功率谱密度

Fig.8 Power spectral density of NPE output signal based on LTAMP

图9 基于ST-AMP算法和LTAMP网络的 NPE误码率曲线

Fig.9 Bit error rate curves of NPE based on ST-AMP algorithm and LTAMP network

参考文献 20

[1]	JIA L Q, SHU F, HUANG N, et al. Capacity and optimum signal constellations for VLC systems[J]. Lightwave Technology, 2020, 38(8): 2180-2189. doi: 10.1109/JLT.50 URL
[2]	JIA L Q, SHU F, HUANG N, et al. Joint constellation-labeling optimization for VLC-CSK systems[J]. IEEE Wireless Communications Letters, 2019, 8(4): 1280-1284. doi: 10.1109/LWC.2019.2916336
[3]	MITRA R, BHATIA V, JAIN S et al. Performance analysis of random fourier features-based unsupervised multistage-clustering for VLC[J]. IEEE Communications Letters, 2021, 25(8): 2659-2663. doi: 10.1109/LCOMM.2021.3089933 URL
[4]	LI X Y, CHEN H J, LI S B, et al. Volterra-based nonlinear equalization for nonlinearity mitigation in organic VLC[C]//Proceedings of the 2017 13th International Wireless Communications and Mobile Computing Conference. Valencia, Spain:IEEE, 2017: 616-621.
[5]	MIAO P, CHEN G J, WANG X B, et al. Adaptive nonlinear equalization combining sparse bayesian learning and kalman filtering for visible light communications[J]. Journal of Lightwave Technolog, 2020, 38(24): 6732-6745.
[6]	KEKATOS V, GIANAKIS G B. Sparse volterra and polynomial regression models: recoverability and estimation[J]. IEEE Transactions on Signal Processing, 2011, 59(12): 5907-5920. doi: 10.1109/TSP.2011.2165952 URL
[7]	MIAO P, CHEN G J, CUMANAN K, et al. Deep hybrid neural network-based channel equalization in visible light communication[J]. IEEE Communications Letters, 2022, 26(7): 1593-1597. doi: 10.1109/LCOMM.2022.3172219 URL
[8]	LU X Y, LU C, YU W X, et al. Memory-controlled deep LSTM neural network post-equalizer used in high-speed PAM VLC system[J]. Optics Express, 2019, 27(5):7822-7833. doi: 10.1364/OE.27.007822 pmid: 30876338
[9]	ZHOU Y J, WEI Y R, HU F C, et al. Comparison of nonlinear equalizers for high-speed visible light communication utilizing silicon substrate phosphorescent white LED[J]. Optics Express, 2020, 28(2):2302-2316. doi: 10.1364/OE.383775 pmid: 32121923
[10]	MIAO P, ZHU B C, QI C H, et al. A model-driven deep learning method for LED nonlinearity mitigation in OFDM-based optical communications[J]. IEEE Access, 2019, 7: 71436-71446. doi: 10.1109/Access.6287639 URL
[11]	BORGERDING M, SCHNIRTER P. Onsager-corrected deep learning for sparse linear inverse problems[C] //Proceedings of 2016 IEEE Global Conference on Signal and Information Processing. Washington, DC, US: IEEE, 2016: 227-231.
[12]	BORGERDING M, SCHNITER P, RANGAN S. AMP-inspired deep networks for sparse linear inverse problems[J]. IEEE Transactions on Signal Processing, 2017, 65(16): 4293-4308. doi: 10.1109/TSP.2017.2708040 URL
[13]	刘希, 苗圃, 田大明. 基于压缩感知的VLC非线性均衡器研究[J]. 青岛大学学报(工程技术版), 2022, 37(2):7-13 LIU X, MIAO P, TIAN D M.
	Research on VLC nonlinear equalizer based on compressed sensing[J]. Journal of Qingdao University, 2022, 37(2): 7-13. (in Chinese)
[14]	唐芳, 徐智勇, 汪井源, 等. 弱湍流下逆向调制光通信直流偏置光正交频分复用系统性能分析[J]. 兵工学报, 2020, 41(7): 1368-1374. doi: 10.3969/j.issn.1000-1093.2020.07.014
	TANG F, XU Z Y, WANG J Y, et al. Performance analysis of DCO-OFDM in modulated retro-reflector optical communication over weak turbulence[J]. Acta Armamentarii, 2020, 41(7): 1368-1374. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.07.014
[15]	LIU X, MIAO P. Performance investigation of volterra-based digital predistortion using orthogonal matching pursuit[C] //Proceedings of 2020 International Conference on Communications, Information System and Computer Engineering. Kuala Lumpur, Malaysia: IEEE, 2020: 63-67.
[16]	MA J J, LIU L, YUAN X J, et al. On orthogonal AMP in coded linear vector systems[J]. IEEE Transactions on Wireless Communications, 2019, 18(12): 5658-5672. doi: 10.1109/TWC.7693 URL
[17]	BORGERDING M, SCHNITER P. Onsager-corrected deep learning for sparse linear inverse problems[C]//Proceedings of 2016 IEEE Global Conference on Signal and Information Processing. Washington, DC, US: IEEE, 2016: 227-231.
[18]	MIAO P, YIN W, PENG H, et al. Deep learning based nonlinear equalization for DCO-OFDM systems[C]//Proceedings of 2021 IEEE International Conference on Electrical Engineering and Mechatronics Technology. Qingdao, China: IEEE, 2021: 699-703.
[19]	WEI X H, HU C, DAI L L. Deep learning for beamspace channel estimation in millimeter-wave massive MIMO systems[J]. IEEE Transactions on Communications, 2021, 69(1): 182-193. doi: 10.1109/TCOMM.26 URL
[20]	BORGERDING M, SCHNITER P, RANGAN S. AMP-inspired deep networks for sparse linear inverse problems[J]. IEEE Transactions on Signal Processing, 2017, 65(16): 4293-4308. doi: 10.1109/TSP.2017.2708040 URL