Expectation maximization channel estimation for nonlinear OFDM systems



  • Nguyen Thanh (Corresponding Author) Le Quy Don Technical University
  • Mai Thanh Hai Le Quy Don Technical University
  • Nguyen Huu Tho Le Quy Don Technical University
  • Nguyen Thi Thao Academy of Military Science and Technology
  • Nguyen Tat Nam Department for Standard, Metrology & Quality




Nonlinear distortion; Channel estimation; Expectation maximization; OFDM.


This paper introduces the expectation maximization (EM)-based channel estimation for the high power amplifier (HPA)-incurred nonlinear orthogonal frequency division multiplexing (OFDM) systems based on the linearization using extended Bussgang decomposition. Analyses and numerical simulations show that the proposed algorithm only requires reasonable computation complexity with relatively small number of iterations while vastly improves the estimation performance compared to the other conventional estimation methods such as least square error (LSE) or minimum mean square error (MMSE) applied to such system. Moreover, the EM-LSE estimator could give almost the same performance as the EM-MMSE counterpart while does not require channel statistics, forming a robust estimator for both fading and nonlinear channels with reduced computation complexity. This makes the estimator more applicable.


[1]. Dardari D., Tralli V., & Vaccari A., “A theoretical characterization of nonlinear distortion effects in OFDM systems”, IEEE Trans. Commun., Vol. 48, No. 10, pp. 1755-1764, (2004). DOI: https://doi.org/10.1109/26.871400

[2]. Y.S. Cho et al., “MIMO-OFDM Wireless Communications with MATLAB”, John Wiley & Sons (Asia) Pte Ltd, Singapore, pp. 190-192, (2010). DOI: https://doi.org/10.1002/9780470825631

[3]. J. Guerreiro, R. Dinis, and P. Montezuma, “On the optimum multicarrier performance with memoryless nonlinearities,” IEEE Trans. on Commun., Vol. 63, No. 2, pp. 498-509, (2015). DOI: https://doi.org/10.1109/TCOMM.2015.2388484

[4]. T. K. Moon, “The expectation-maximization algorithm”, IEEE Signal Processing Magazine, Vol. 13, No. 6. pp. 47-60, (1997). DOI: https://doi.org/10.1109/79.543975

[5]. Ma X., Kobayashi H., & Schwartz S.C., “An EM-based estimation of OFDM signals”, Wireless Communication and Networking Conf, Vol. 1, pp. 228-232, (2002).

[6]. Ma X., Kobayashi H., & Schwartz S.C., “EM-based channel estimation for OFDM”, IEEE Pacific Rim Conf. on Communications, Computer and Signal Processing, Vol. 2, pp. 449-4524, (2001).

[7]. L. Mazet et al., “An EM based semi-blind channel estimation algorithm designed for OFDM systems”, IEEE Conf. on Signal, System and Computers, Vol.2, pp. 1642-1646, (2002).

[8]. Bin Li et al., “A Bayesian approach for nonlinear equalization and signal detection in millimeter-wave communications”, IEEE Trans. Wireless Commun., Vol. 14, No. 7, pp. 3794-3809, (2015). DOI: https://doi.org/10.1109/TWC.2015.2412119

[9]. Ladaycia A., et al., “Semi-blind MIMO-OFDM channel estimation using expectation maximisation like techniques”, IET Communications, Vol. 13, No. 20, pp. 3452 – 3462, (2019). DOI: https://doi.org/10.1049/iet-com.2019.0583

[10]. K. Fazel, and S. Kaiser, “Multi-Carrier and Spread Spectrum Systems”, Wiley, pp. 24-30, (2003). DOI: https://doi.org/10.1002/0470871385

[11]. Rohit Negi, and John Cioffi, “Pilot tone selection for channel estimation in a mobile OFDM system”, IEEE Trans. on Consumer Electronics, Vol. 44, No. 3, pp. 1122-1128, (1998). DOI: https://doi.org/10.1109/30.713244

[12]. D.O. Tugfe, B. Emil, “The Bussgang decomposition of nonlinear systems: Basic theory and MIMO extensions [Lecture Notes]”, IEEE Signal Processing Magazine, Vol. 38, No. 1, pp. 131-136, (2021). DOI: https://doi.org/10.1109/MSP.2020.3025538

[13]. Vittorio Camarchia et al., “A review of technologies and design techniques of millimeter-wave power amplifiers”, IEEE Trans. on Microwave Theory and Techniques Vol. 68, No. 7, pp. 2957-2983, (2020). DOI: https://doi.org/10.1109/TMTT.2020.2989792

[14]. A. Aghasi, A. Ghorbani, and H. Amindavar, “Polynomial based predistortion for solid state power amplifier nonlinearity compensation”, in Proc. 2006 IEEE North-East Workshop on Circuits and Systems, QC, Canada, pp. 181-184, (2006). DOI: https://doi.org/10.1109/NEWCAS.2006.250913

[15]. Maryam Imani, and Hamidreza Bakhshi, “The Tight Bound for the Number of Pilots in Channel Estimation for OFDM Systems”, Communications and Network, No. 4, pp. 146-150, (2012), doi: http://dx.doi.org/10.4236/cn.2012.42019. DOI: https://doi.org/10.4236/cn.2012.42019

[16]. Gunther Auer, and Eleftherios Karipidis, “Pilot Aided Channel Estimation for OFDM: A Separated Approach for Smoothing and Interpolation”, in Proceedings of the 40th IEEE International Conference on Commununications (ICC 2005), pp. 2173-2178, (2005).




How to Cite

Nguyễn, T., Mai Thanh Hai, Nguyen Huu Tho, Nguyen Thi Thao, and Nguyen Tat Nam. “Expectation Maximization Channel Estimation for Nonlinear OFDM Systems”. Journal of Military Science and Technology, no. 81, Aug. 2022, pp. 31-43, doi:10.54939/1859-1043.j.mst.81.2022.31-43.



Research Articles