A General Framework for Estimating Channel of Orthogonal Frequency Division Multiplexing Systems by Utilizing Sparse Representation

Document Type : Original Article


1 Department of Digital Communication, ICT Research Center, Tehran, Iran

2 Communication Department, college of Electrical Engineering, Yadegar-e-Imam Khomeini, Shahr-e-Rey branch, Islamic Azad University, Tehran, Iran


Channel estimation is a crucial task for orthogonal frequency division multiplexing (OFDM) modulation-based systems since this estimation is used for compensating impacts of a wireless channel. Recently, sparse representation (SR) is proposed for this task as wireless channels are considered as a sparse signal. However, SR considers sparse as the main feature and omit other features of the channel while estimating the channel. In this paper, we propose a general framework for utilizing other features of the channel in sparse channel estimation for OFDM systems, while these features are omitted in conventional sparse methods. In this regard, by utilizing maximum a posterior (MAP) estimation and defining new parameters, these features are conveyed into sparse channel estimation process to improve channel estimation. The simulation results indicate that our proposed framework not only improves the estimated parameter, but also reduces the number of resources such as the number of estimation pilots or transmitted power.


1.     Proakis, J.G., "Digital communications, McGraw-Hill,  (2001).
2.     K, C.K. and J, J., "An efficient hierarchical modulation based orthogonal frequency division multiplexing transmission scheme for digital video broadcasting”, International Journal of Engineering, Transactions A: Basics,  Vol. 31, No. 4, (2018), 574-579. doi: 10.5829/ije.2018.31.04a.08
3.     Panayirci, E. and Çirpan, H.A., "Maximum a posteriori multipath fading channel estimation for ofdm systems", European Transactions on Telecommunications,  Vol. 13, No. 5, (2002), 487-494. doi.org/10.1002/ett.4460130509
4.     Ghazi-Maghrebi, S.J.T.J.o.E.E. and Sciences, C., "An efficient ofdm-based system with an insufficient cyclic prefix via a novel constellation algorithm", Turkish Journal of Electrical Engineering & Computer Sciences  Vol. 25, No. 3, (2017), 2278-2292. doi:10.3906/elk-1505-273
5.     Pakrooh, P., Amini, A. and Marvasti, F., "Ofdm pilot allocation for sparse channel estimation", EURASIP Journal on Advances in Signal Processing,  Vol. 2012, No. 1, (2012), 59. doi: 10.1186/1687-6180-2012-59.
6.     Fereydouni, A., Charmin, A., vahdaty, h. and nasiraghdam, h., "Channel estimation and cfo compensation in ofdm system using adaptive filters in wavelet transform domai”. International Journal of Engineering Transactions A: Basics",  Vol. 33, No. 7, (2020), doi: 10.5829/ije.2020.33.07a.09
7.     Komalla, A.R., Kosaraju, S. and Ette, H., "Empirical mode decomposition based adaptive filtering for orthogonal frequency division multiplexing channel estimation”, International Journal of Engineering Transactions A: Basics ",  Vol. 30, No. 10, (2017), 1517-1525. doi: 10.5829/ije.2017.30.10a.13
8.     Elad, M., From exact to approximate solutions, in Sparse and redundant representations. 2010, Springer.79-109.
9.     Candes, E.J., Romberg, J.K., Tao, T.J.C.o.P. and Sciences, A.M.A.J.I.b.t.C.I.o.M., "Stable signal recovery from incomplete and inaccurate measurements", Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences, Vol. 59, No. 8, (2006), 1207-1223. doi.org/10.1002/cpa.20124
10.   Chen, S.S., Donoho, D.L. and Saunders, M.A., "Atomic decomposition by basis pursuit", SIAM Review,  Vol. 43, No. 1, (2001), 129-159. doi: 10.1137/S003614450037906X
11.   Hassanpour, H. and Asadi, S., "Deblocking joint photographic experts group compressed images via self-learning sparse representation, International Journal of Engineering, Transaction C: Aspects",  Vol. 29, No. 12, (2016), 1684-1690. doi: 10.5829/idosi.ije.2016.29.12c.07
12.   Sabzalian, B. and Abolghasemi, V., "Iterative weighted non-smooth non-negative matrix factorization for face recognition”, International Journal of Engineering, Transaction A: Basics",  Vol. 31, No. 10, (2018), 1698-1707. doi: 10.5829/ije.2018.31.10a.12
13.   ETSI, T., "101 154 v2. 3.1 (2017)", Digital Video Broadcasting (DVB), 
14.   Mallat, S. and Zhang, Z., “Matching pursuit with time-frequency dictionaries”. 1993, Courant Institute of Mathematical Sciences New York United States. doi: 10.1109/78.258082.
15.   Tropp, J.A., "Greed is good: Algorithmic results for sparse approximation", IEEE Transactions on Information Theory,  Vol. 50, No. 10, (2004), 2231-2242. doi: 10.1109/TIT.2004.834793.

16.   Mohimani, H., Babaie-Zadeh, M. and Jutten, C., "A fast approach for overcomplete sparse decomposition based on smoothed ℓ0 Norm", IEEE Transactions on Signal Processing, Vol. 57, No. 1, (2009), 289-301. Doi:10.1109/TSP.2008.2007606.

17.   Stanković, V., Stanković, L. and Cheng, S., "Sparse signal recovery with side information", in 2009 17th European Signal Processing Conference, IEEE., (2009), 100-104.
18.   Zhang, X., Cui, W. and Liu, Y., "Compressed sensing with prior information via maximizing correlation", in 2017 IEEE International Symposium on Information Theory (ISIT), IEEE., (2017), 221-225. doi: 10.1109/ISIT.2017.8006522.
19.   Mota, J.F., Deligiannis, N. and Rodrigues, M.R.J.I.T.o.I.T., "Compressed sensing with prior information: Strategies, geometry, and bounds", IEEE Transactions on Information Theory, Vol. 63, No. 7, (2017), 4472-4496.
20.   Jorgensen, B., "Statistical properties of the generalized inverse gaussian distribution, Springer Science & Business Media,  Vol. 9,  (2012).
21.   Coleri, S., Ergen, M., Puri, A. and Bahai, A., "Channel estimation techniques based on pilot arrangement in ofdm systems", IEEE Transactions on Broadcasting,  Vol. 48, No. 3, (2002), 223-229. doi: 10.1109/TBC.2002.804034.
22.   Berger, J.O., "Statistical decision theory and bayesian analysis, Springer Science & Business Media,  (2013).
23.   Li, Y., Cichocki, A. and Amari, S.-i., "Analysis of sparse representation and blind source separation", Neural Computation,  Vol. 16, No. 6, (2004), 1193-1234. doi: 10.1162/089976604773717586.
24.   Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R., "Least angle regression", The Annals of Statistics,  Vol. 32, No. 2, (2004), 407-499.
25.   Koh, K., Kim, S.-J. and Boyd, S., "An interior-point method for large-scale l1-regularized logistic regression", Journal of Machine Learning Research,  Vol. 8, No. Jul, (2007), 1519-1555.
26.   Tibshirani, R., "Regression shrinkage and selection via the lasso", Journal of the Royal Statistical Society. Series B (Methodological),  Vol. 58, No. 1, (1996), 267-288. doi: 10.1111/j.2517-6161.1996.tb02080.x
27.   Davis, G., Mallat, S. and Avellaneda, M., "Adaptive greedy approximations", Constructive Approximation,  Vol. 13, No. 1, (1997), 57-98.
28.   Donoho, D.L. and Elad, M., "Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization", Proceedings of the National Academy of Sciences,  Vol. 100, No. 5, (2003), 2197-2202.
29.   Papoulis, A., "Probability & statistics, Prentice Hall,  (1990). doi: 10.1073/pnas.0437847100.