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 Wentao Tong,Wei Ge,Yizhen Jia,et al.Gibbs Sampling-based Sparse Estimation Method over Underwater Acoustic Channels[J].Journal of Marine Science and Application,2024,(2):434-442.[doi:10.1007/s11804-024-00415-4]
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Gibbs Sampling-based Sparse Estimation Method over Underwater Acoustic Channels


Gibbs Sampling-based Sparse Estimation Method over Underwater Acoustic Channels
Wentao Tong123 Wei Ge45 Yizhen Jia123 Jiaheng Zhang123
Wentao Tong123 Wei Ge45 Yizhen Jia123 Jiaheng Zhang123
1 National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University, Harbin 150001, China;
2 Key Laboratory for Polar Acoustics and Application of Ministry of Education, Harbin Engineering University, Harbin 150001, China;
3 College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China
Sparse bayesian learning|Channel estimation|Variational inference|Gibbs sampling
The estimation of sparse underwater acoustic (UWA) channels can be regarded as an inference problem involving hidden variables within the Bayesian framework. While the classical sparse Bayesian learning (SBL), derived through the expectation maximization (EM) algorithm, has been widely employed for UWA channel estimation, it still differs from the real posterior expectation of channels. In this paper, we propose an approach that combines variational inference (VI) and Markov chain Monte Carlo (MCMC) methods to provide a more accurate posterior estimation. Specifically, the SBL is first re-derived with VI, allowing us to replace the posterior distribution of the hidden variables with a variational distribution. Then, we determine the full conditional probability distribution for each variable in the variational distribution and then iteratively perform random Gibbs sampling in MCMC to converge the Markov chain. The results of simulation and experiment indicate that our estimation method achieves lower mean square error and bit error rate compared to the classic SBL approach. Additionally, it demonstrates an acceptable convergence speed.


Casella G, George E I (1992) Explaining the Gibbs sampler. The American Statistician 46(3):167-174. https://doi.org/10.1080/00031305.1992.10475878
Cho YH (2022) Fast Sparse Bayesian learning-based channel estimation for underwater acoustic OFDM systems. Applied Sciences 12(19):10175. https://doi.org/10.3390/app121910175
Coleri S, Ergen M, Puri A, Bahai, A (2002) Channel estimation techniques based on pilot arrangement in OFDM systems. IEEE Transactions on broadcasting 48(3):223-229. https://doi.org/10.1109/tbc.2002.804034
Feng X, Wang J, Sun H, Qi J, Qasem Z A, Cui Y (2023) Channel estimation for underwater acoustic OFDM communications via temporal sparse Bayesian learning. Signal Processing 207:108951. https://doi.org/10.1016/j.sigpro.2023.108951
Gelfand AE, Lee TM (1993) Discussion on the meeting on the Gibbs sampler and other Markov Chain Monte Carlo methods. Journal of the Royal Statistical Society. Series B 55(1):72-73. https://doi.org/10.1111/j.2517-6161.1993.tb01469.x
Goudie RJB, Mukherjee S (2016) A Gibbs sampler for learning DAGs. Journal of Machine Learning Research 17(2):1-39
Jia S, Zou S, Zhang X, Tian D, Da L (2022) Multi-block Sparse Bayesian learning channel estimation for OFDM underwater acoustic communication based on fractional Fourier transform. Applied Acoustics 192:108721. https://doi.org/10.1016/j.apacoust.2022.108721
Kang SG, Ha YM, Joo EK (2003) A comparative investigation on channel estimation algorithms for OFDM in mobile communications. IEEE Transactions on Broadcasting 49(2):142-149. https://doi.org/10.1109/tbc.2003.810263
Li Y, Wang Y, Jiang T (2016) Norm-adaption penalized least mean square/fourth algorithm for sparse channel estimation. Signal processing 128:243-251. https://doi.org/10.1016/j.sigpro.2016.04.003
Martino L, Elvira V, Camps-Valls G (2018) The recycling Gibbs sampler for efficient learning. Digital Signal Processing 74:1-13. https://doi.org/10.1016/j.dsp.2017.11.012
Panayirci E, Altabbaa MT, Uysal M, Poor H V (2019) Sparse channel estimation for OFDM-based underwater acoustic systems in Rician fading with a new OMP-MAP algorithm. IEEE Transactions on Signal Processing 67(6):1550-1565. https://doi.org/10.1109/tsp.2019.2893841
Prasad R, Murthy CR, Rao BD (2014) Joint approximately sparse channel estimation and data detection in OFDM systems using sparse Bayesian learning. IEEE Transactions on Signal Processing 62(14):3591-3603. https://doi.org/10.1109/tsp.2014.2329272
Tipping, Michael E (2001) Sparse Bayesian learning and the relevance vector machine. Journal of machine learning research 1(Jun):211-244
Tsai Y, Zheng L, Wang X (2018) Millimeter-wave beamformed fulldimensional MIMO channel estimation based on atomic norm minimization. IEEE Transactions on Communications 66(12):6150-6163. https://doi.org/10.1109/tcomm.2018.2864737
Wang Y, Dong X (2006) Frequency-domain channel estimation for SC-FDE in UWB communications. IEEE transactions on communications, 54(12):2155-2163. https://doi.org/10.1109/glocom.2005.1578453
Wang Z, Li Y, Wang C, Ouyang D, Huang Y (2021) A-OMP:An adaptive OMP algorithm for underwater acoustic OFDM channel estimation. IEEE Wireless Communications Letters 10(8):1761-1765. https://doi.org/10.1109/lwc.2021.3079225
Wu FY, Zhou YH, Tong F, Kastner R (2013) Simplified p-norm-like constraint LMS algorithm for efficient estimation of underwater acoustic channels. Journal of marine science and application 12(2):228-234. https://doi.org/10.1007/s11804-013-1189-7
Zhang C, Bütepage J, Kjellström H, Mandt S (2018) Advances in variational inference. IEEE transactions on pattern analysis and machine intelligence 41(8):2008-2026. https://doi.org/10.1017/9781009218245.011
Zhang Z, Rao BD (2011) Sparse signal recovery with temporally correlated source vectors using sparse Bayesian learning. IEEE Journal of Selected Topics in Signal Processing 5(5):912-926.https://doi.org/10.1109/jstsp.2011.2159773
Zheng YR, Xiao C, Yang TC, Yang WB (2010) Frequency-domain channel estimation and equalization for shallow-water acoustic communications. Physical Communication 3(1):48-63. https://doi.org/10.1016/j.phycom.2009.08.010


Received date: 2023-06-15;Accepted date: 2023-07-31。
Foundation item: This study is funded by the Excellent Youth Science Fund of Heilongjiang Province (Grant No.YQ2022F001).
Corresponding author: Wei Ge,E-mail:gewei@hrbeu.edu.cn
Last Update: 2024-05-28