Visible Light Communication Nonlinear Equalizer Based on Model Solving and Deep Learning

doi:10.12382/bgxb.2022.0679

Abstract

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

CLC Number:

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

Figures/Tables 9

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

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

Fig.3 LTAMP network architecture

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

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

Fig.6 Equalization accuracy of LTAMP under different SNRs

Fig.7 Comparison of equalization accuracies among different schemes

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

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

References 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