A low-complexity AMP detection algorithm with deep neural network for massive mimo systems

Abstract

Signal detection plays an essential role in massive Multiple-Input Multiple-Output (MIMO) systems. However, existing detection methods have not yet made a good tradeoff between Bit Error Rate (BER) and computational complexity, resulting in slow convergence or high complexity. To address this issue, a low-complexity Approximate Message Passing (AMP) detection algorithm with Deep Neural Network (DNN) (denoted as AMP-DNN) is investigated in this paper. Firstly, an efficient AMP detection algorithm is derived by scalarizing the simplification of Belief Propagation (BP) algorithm. Secondly, by unfolding the obtained AMP detection algorithm, a DNN is specifically designed for the optimal performance gain. For the proposed AMP-DNN, the number of trainable parameters is only related to that of layers, regardless of modulation scheme, antenna number and matrix calculation, thus facilitating fast and stable training of the network. In addition, the AMP-DNN can detect different channels under the same distribution with only one training. The superior performance of the AMP-DNN is also verified by theoretical analysis and experiments. It is found that the proposed algorithm enables the reduction of BER without signal prior information, especially in the spatially correlated channel, and has a lower computational complexity compared with existing state-of-the-art methods.

Keywords

Massive MIMO system / Approximate message passing (AMP) detection algorithm / Deep neural network (DNN) / Bit error rate (BER) / Low-complexity

References

[1] X. Wang, L.T. Yang, L. Ren, Y. Wang, M.J. Deen, A tensor-based computing and optimization model for intelligent edge services, IEEE Network 36 (1) (2022) 40-44.

[2] T.L. Marzetta, Noncooperative cellular wireless with unlimited numbers of base station antennas, IEEE Trans. Wireless Commun. 9 (11) (2010) 3590-3600.

[3] E. Bj€ornson, J. Hoydis, L. Sanguinetti, Massive MIMO networks: spectral, energy and hardware efficiency, Foundation Trend. Signal Process. 11 (3-4) (2017) 154-655.

[4] S. Yang, L. Hanzo, Fifty years of MIMO detection: the road to large-scale MIMOs, IEEE Commun. Surv. Tutor. 17 (4) (2015) 1941-1988.

[5] P.H. Tan, L.K. Rasmussen, Asymptotically optimal nonlinear MMSE multiuser detection based on multivariate Gaussian approximation, IEEE Trans. Wireless Commun. 54 (8) (2006) 1427-1428.

[6] S. Suh, J.R. Barry, Reduced-complexity MIMO detection via a slicing breadth-first tree search, IEEE Trans. Wireless Commun. 16 (3) (2017) 1782-1790.

[7] P. Li, D. Paul, R. Narasimhan, et al., On the distribution of SINR for the MMSE MIMO receiver and performance analysis, IEEE Trans. Inf. Theor. 52 (1) (2005) 271-286.

[8] F. Rusek, D. Persson, B.K. Lau, et al., Scaling up MIMO: opportunities and challenges with very large arrays, IEEE Signal Process. Mag. 30 (1) (2012) 40-60.

[9] H. Wang, A. Kosasih, C.K. Wen, et al., Expectation propagation detector for extra-large scale massive MIMO, IEEE Trans. Wireless Commun. 19 (3) (2020) 2036-2051.

[10] B. Yin, M. Wu, J.R. Cavallaro, et al., Conjugate gradient-based soft-output detection and precoding in massive MIMO systems, in: 2014 IEEE Global Communications Conference, 2014, pp. 3696-3701.

[11] F. Jin, Q. Liu, H. Liu, et al., A low complexity signal detection scheme based on improved Newton iteration for massive MIMO systems, IEEE Commun. Lett. 23 (4)(2019) 748-751.

[12] H. Liu, C. Yuen, Y.L. Guan, et al., Convergence analysis and assurance for Gaussian message passing iterative detector in massive MU-MIMO systems, IEEE Trans. Wireless Commun. 15 (9) (2016) 6487-6501.

[13] T.L. Narasimhan, A. Chockalingam, Channel hardening-exploiting message passing (CHEMP) receiver in large MIMO systems, in: 2014 IEEE Wireless Communications and Networking Conference, WCNC), 2014, pp. 815-820.

[14] S.K. Mohammed, A. Chockalingam, B.S. Rajan, A low-complexity near-ML performance achieving algorithm for large MIMO detection, in: 2008 IEEE International Symposium on Information Theory, 2008, pp. 2012-2016.

[15] M. Mandloi, V. Bhatia, Low-complexity near-optimal iterative sequential detection for uplink massive MIMO systems, IEEE Commun. Lett. 21 (3) (2016) 568-571.

[16] A. Datta, M. Mandloi, V. Bhatia, Reliability feedback-aided low-complexity detection in uplink massive MIMO systems, Int. J. Commun. Syst. 32 (15) (2019) e4085.

[17] J. Yang, W. Song, S. Zhang, et al., Low-complexity belief propagation detection for correlated large-scale MIMO systems, J. Signal Process. Syst. Signal Image Video 90 (4) (2018) 585-599.

[18] J. Zeng, J. Lin, Z. Wang, Low complexity message passing detection algorithm for large-scale MIMO systems, IEEE Wireless Commun. Lett. 7 (5) (2018) 708-711.

[19] S. Wu, L. Kuang, Z. Ni, et al., Low-complexity iterative detection for large-scale multiuser MIMO-OFDM systems using approximate message passing, IEEE J. Sel. Topics Signal Process. 8 (5) (2014) 902-915.

[20] S. Lyu, C. Ling, Hybrid vector perturbation precoding: the blessing of approximate message passing, IEEE Trans. Signal Process. 67 (1) (2018) 178-193.

[21] C. Guo, M.E. Davies, Near optimal compressed sensing without priors: parametric SURE approximate message passing, IEEE Trans. Signal Process. 63 (8) (2015) 2130-2141.

[22] M. Khumalo, W.T. Shi, C.K. Wen, Fixed-point implementation of approximate message passing (AMP) algorithm in massive MIMO systems, Digital Commun. Network 2 (4) (2016) 218-224.

[23] J. Ma, L. Ping, Orthogonal amp, IEEE Access 5 (2017) 2020-2033.

[24] J.C. Chen, A low complexity data detection algorithm for uplink multiuser massive MIMO systems, IEEE J. Sel. Area. Commun. 35 (8) (2017) 1701-1714.

[25] F. Xing, Y. Xie, H. Su, et al., Deep learning in microscopy image analysis: a survey, IEEE Transact. Neural Networks Learn. Syst. 29 (10) (2017) 4550-4568.

[26] S. Nie, S. Liang, W. Liu, et al., Deep learning based speech separation via NMF-style reconstructions, IEEE/ACM Trans. Audio Speech Lang. 26 (11) (2018) 2043-2055.

[27] X. Wang, L. Ren, R. Yuan, L.T. Yang, M.J. Deen, QTT-DLSTM: a cloud-edge-aided distributed LSTM for cyber-physical-social big data, IEEE Transact. Neural Networks Learn. Syst. (2022), https://doi.org/10.1109/TNNLS.2022.3140238.

[28] C. Gan, L. Wang, Z. Zhang, et al., Sparse attention based separable dilated convolutional neural network for targeted sentiment analysis, Knowl.-Based syst. 188 (2020) 104827.

[29] T. Oshea, J. Hoydis, An introduction to deep learning for the physical layer, IEEE Trans. Cogn. Comm. & Netw. 3 (4) (2017) 563-575.

[30] H. He, S. Jin, C.K. Wen, et al., Model-driven deep learning for physical layer communications, IEEE Wireless Commun. 26 (5) (2019) 77-83.

[31] Z. Zhang, C. Wang, C. Gan, et al., Automatic modulation classification using convolutional neural network with features fusion of SPWVD and BJD, IEEE Trans. Signal Inf. Proc. Netw. 5 (3) (2019) 469-478.

[32] J.M. Kang, C.J. Chun, I.M. Kim, Deep-learning-based channel estimation for wireless energy transfer, IEEE Commun. Lett. 22 (11) (2018) 2310-2313.

[33] H. Ye, G.Y. Li, B.H. Juang, Power of deep learning for channel estimation and signal detection in OFDM systems, IEEE Wireless Commun. Lett. 7 (1) (2017) 114-117.

[34] Q. Mao, F. Hu, Q. Hao, Deep learning for intelligent wireless networks: a comprehensive survey, IEEE Commun. Surv. Tutor. 20 (4) (2018) 2595-2621.

[35] C. Zhang, P. Patras, H. Haddadi, Deep learning in mobile and wireless networking: a survey, IEEE Commun. Surv. Tutor. 21 (3) (2019) 2224-2287.

[36] H. He, C.K. Wen, S. Jin, et al., A model-driven deep learning network for MIMO detection, in: 2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP), IEEE, 2018, pp. 584-588.

[37] H. He, C.K. Wen, S. Jin, et al., Model-driven deep learning for MIMO detection, IEEE Trans. Signal Process. 68 (2020) 1702-1715.

[38] M. Khani, M. Alizadeh, J. Hoydis, et al., Adaptive neural signal detection for massive MIMO, IEEE Trans. Wireless Commun. 19 (8) (2020) 5635-5648.

[39] K. Gregor, Y. LeCun,Learning fast approximations of sparse coding, in:Proceedings of the 27th International Conference on International Conference on Machine Learning, 2010, pp. 399-406.

[40] J. R. Hershey, J. L. Roux,F. Weninger, Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures, arXiv preprint arXiv:1409.2574.

[41] N. Samuel, T. Diskin, A. Wiesel, Deep MIMO detection, in: 2017 IEEE 18th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), IEEE, 2017, pp. 1-5.

[42] N. Samuel, T. Diskin, A. Wiesel, Learning to detect, IEEE Trans. Signal Process. 67 (10) (2019) 2554-2564.

[43] X. Tan, W. Xu, Y. Be’ery, et al, Improving Massive MIMO Belief Propagation Detector with Deep Neural Network, arXiv preprint arXiv:1804.01002.

[44] X. Tan, Z. Zhong, Z. Zhang, et al., Low-complexity message passing MIMO detection algorithm with deep neural network, in: 2018 IEEE Global Conference on Signal and Information Processing, GlobalSIP), 2018, pp. 559-563.

[45] Z. Jia, W. Cheng, H. Zhang, A partial learning-based detection scheme for massive MIMO, IEEE Wireless Commun. Lett. 8 (4) (2019) 1137-1140.

[46] A. Montanari, Y.C. Eldar, G. Kutyniok, Graphical Models Concepts in Compressed Sensing, 2012.

[47] K. Yu, M. Bengtsson, B. Ottersten, et al., Modeling of wide-band MIMO radio channels based on NLoS indoor measurements, IEEE Trans. Veh. Technol. 53 (3)(2004) 655-665.

[48] M. Chiani, M.Z. Win, A. Zanella, On the capacity of spatially correlated MIMO Rayleigh-fading channels, IEEE Trans. Inf. Theor. 49 (10) (2003) 2363-2371.