Computationally efficient variational Bayesian method for PAPR reduction in multiuser MIMO-OFDM systems

  • Singh, Davinder (Department of Electronics and Communication Engineering, Dr. B.R. Ambedkar National Institute of Technology) ;
  • Sarin, Rakesh Kumar (Department of Electronics and Communication Engineering, Dr. B.R. Ambedkar National Institute of Technology)
  • Received : 2018.04.12
  • Accepted : 2018.09.05
  • Published : 2019.06.03


This paper investigates the use of the inverse-free sparse Bayesian learning (SBL) approach for peak-to-average power ratio (PAPR) reduction in orthogonal frequency-division multiplexing (OFDM)-based multiuser massive multiple-input multiple-output (MIMO) systems. The Bayesian inference method employs a truncated Gaussian mixture prior for the sought-after low-PAPR signal. To learn the prior signal, associated hyperparameters and underlying statistical parameters, we use the variational expectation-maximization (EM) iterative algorithm. The matrix inversion involved in the expectation step (E-step) is averted by invoking a relaxed evidence lower bound (relaxed-ELBO). The resulting inverse-free SBL algorithm has a much lower complexity than the standard SBL algorithm. Numerical experiments confirm the substantial improvement over existing methods in terms of PAPR reduction for different MIMO configurations.


  1. T. L. Marzetta, Noncooperative cellular wireless with unlimited numbers of base station antennas, IEEE Trans. Wireless Commun. 9 (2010), no. 11, 3590-3600.
  2. B. M. Hochwald, T. L. Marzetta, and V. Tarokh, Multiple‐antenna channel hardening and its implications for rate feedback and scheduling, IEEE Trans. Info. Theory 50 (2004), no. 9, 1893-1909.
  3. L. Lu et al., Overview of massive MIMO: Benefits and challenges, IEEE J. Sel. Topics in Sig. Process. 8 (2014), no. 5, 742-758.
  4. G. Wunder et al., The PAPR problem in OFDM transmission: New directions for a long‐lasting problem, IEEE Sig. Process. Mag. 30 (2013), no. 6, 130-144.
  5. M. J. Hao and C. H. Lai, Precoding for PAPR reduction of OFDM signals with minimum error probability, IEEE Trans. Broadcast. 56 (2010), no. 1, 120-128.
  6. L. Wang and C. Tellambura, A simplified clipping and filtering technique for PAR reduction in OFDM systems, IEEE Sig. Process. Lett. 12 (2005), no. 6, 453-456.
  7. L. Yang et al., PAPR reduction of an OFDM signal by use of PTS with low computational complexity, IEEE Trans. Broadcast. 52 (2006), no. 1, 83-86.
  8. J. C. Chen, M. H. Chiu, and Y. S. Yang, A suboptimal tone reservation algorithm based on cross‐entropy method for PAPR reduction in OFDM systems, IEEE Trans. Broadcast. 57 (2011), no. 3, 752-756.
  9. J. Yang et al., A modified selected mapping technique to reduce the peak‐to‐ average power ratio of OFDM signal, IEEE Trans. Consumer Electr. 53 (2007), no. 3, 846-851.
  10. B. S. Krongold and D. L. Jones, PAR reduction in OFDM via active constellation extension, IEEE Trans. Broadcast. 49 (2003), no. 3, 258-268.
  11. M. Iwasaki and K. Higuchi, Clipping and filtering-based PAPR reduction method for precoded OFDM-MIMO signals, in Proc. IEEE 71st Veh. Tech. Conf., Taipei, Taiwan, 2010, pp. 1-5.
  12. E. Manasseh, S. Ohno, and M. Nakamoto, Combined channel estimation and PAPR reduction technique for MIMO-OFDM systems with null subcarriers, EURASIP J. Wirel. Commun. Netw. 2012 (2012), no. 1, 1-15.
  13. H. B. Jeon, J.-S. No, and D.-J. Shin, A low‐complexity SLM Scheme using additive mapping sequences for PAPR Reduction of OFDM signals, IEEE Trans. Broadcast. 57 (2011), no. 4, 866-875.
  14. S.-J. Ku, Low‐complexity PTS‐based schemes for PAPR reduction in SFBC MIMO‐OFDM systems, IEEE Trans. Broadcast. 60 (2014), no. 4, 650-658.
  15. C. Studer and E. G. Larsson, PAR‐aware large‐scale multi‐user MIMO OFDM downlink, IEEE J. Sel. Areas Commun. 31 (2013), no. 2, 303-313.
  16. D. L. Donoho, Compressed sensing, IEEE Trans. Inform. Theory 52 (2006), no. 4, 1289-1306.
  17. B. Ebrahim et al., Peak reduction and clipping mitigation in OFDM by augmented compressive sensing, IEEE Trans. Sig. Process. 60 (2012), no. 7, 3834-3839.
  18. B. Liu et al., A low‐complexity compressive sensing algorithm for PAPR reduction, Wireless Pers. Commun. 78 (2014), no. 1, 283-295.
  19. M. E. Tipping, Sparse Bayesian learning and the relevance vector machine, J. Mach. Learn. Res 1 (2001), no. 1, 211-244.
  20. T. T. Ballen, J. A. Tropp, and A. C. Gilbert, Signal recovery from random measurements via orthogonal matching pursuit, IEEE Trans. Inform. Theory 53 (2007), no. 2, 4655-4666.
  21. E. J. Candes and T. Tao, Decoding by linear programming, IEEE Trans. Inform. Theory 51 (2005), no. 12, 4203-4215.
  22. J. P. Vila and P. Schniter, Expectation‐maximization gaussian‐mixture approximate message passing, IEEE Trans. Sig. Process. 61 (2013), no. 19, 4658-4672.
  23. S. Som and P. Schniter, Compressive imaging using approximate message passing and a Markov‐tree prior, IEEE Trans. Sig. Process. 60 (2012), no. 7, 3439-3448.
  24. J. Fang, L. Zhang, and H. Li, Two‐dimensional pattern‐coupled sparse Bayesian learning via generalized approximate message passing, IEEE Trans. Image Process. 25 (2016), no. 6, 2920-2930.
  25. H. Bao et al., An efficient Bayesian PAPR reduction method for OFDM‐ based massive MIMO systems, IEEE Trans. Wireless Commun. 15 (2016), no. 6, 4183-4195.
  26. H. Duan et al., Fast inverse‐free sparse Bayesian learning via relaxed evidence lower bound maximization, IEEE Sig. Process. Lett. 24 (2017), no. 6, 774-778.
  27. M. Joham, W. Utschick, and J. Nossek, Linear transmit processing in MIMO communications systems, IEEE Trans. Sig. Process. 53 (2005), no. 8, 2700-2712.
  28. C. Studer et al., Democratic representations, ArXiv preprint (2015), arXiv: 1401.3420.
  29. D. G. Tzikas, A. C. Likas, and N. P. Galatsanos, The variational approximation for Bayesian inference, IEEE Sig. Process. Mag. 25 (2008), no. 6, 131-146.
  30. J. P. Vila and P. Schniter, An empirical‐bayes approach to recovering linearly constrained non‐negative sparse signals, IEEE Trans. Sig. Process. 62 (2014), no. 18, 4689-4703.
  31. IEEE 802.11 Working Group, Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications, amendment 5: Enhancements for higher throughput, IEEE, 2009.
  32. H. Ochiai and H. Imai, On the distribution of the peak‐to‐average power ratio in OFDM signals, IEEE Trans. Commun. 49 (2001), no. 2, 282-289.