C. Chenot and J. Bobin, Blind separation of sparse sources in the presence of outliers, Signal Processing, vol.138, pp.233-243, 2017.
DOI : 10.1016/j.sigpro.2017.03.024
URL : https://hal.archives-ouvertes.fr/hal-01540186

S. Rambhatla and J. Haupt, Semi-blind source separation via sparse representations and online dictionary learning, 2013 Asilomar Conference on Signals, Systems and Computers, pp.1687-1691, 2013.
DOI : 10.1109/ACSSC.2013.6810587

D. L. Donoho, Compressed sensing, IEEE Transactions on Information Theory, vol.52, issue.4, pp.1289-1306, 2006.
DOI : 10.1109/TIT.2006.871582
URL : https://hal.archives-ouvertes.fr/inria-00369486

N. B. Karahanoglu and H. Erdogan, Compressed sensing signal recovery via forward???backward pursuit, Digital Signal Processing, vol.23, issue.5, p.1539, 2013.
DOI : 10.1016/j.dsp.2013.05.007
URL : http://arxiv.org/pdf/1210.5626.pdf

T. Liu, T. Qiu, R. Dai, J. Li, L. Chang et al., Nonlinear regression A*OMP for compressive sensing signal reconstruction, Digital Signal Processing, vol.69, pp.11-21, 2017.
DOI : 10.1016/j.dsp.2017.06.004

E. J. Candès, J. K. Romberg, and T. Tao, Stable signal recovery from incomplete and inaccurate measurements, Communications on Pure and Applied Mathematics, vol.7, issue.8, pp.1207-1223, 2006.
DOI : 10.1017/CBO9780511804441

K. Liu, Z. Xu, X. Xi, and S. Wang, Sparse signal reconstruction via concave continuous piecewise linear programming, Digital Signal Processing, vol.54
DOI : 10.1016/j.dsp.2016.03.010

H. Cui and H. Duan, Sparse Bayesian learning using correlated hyperparameters for recovery of block sparse signals, Digital Signal Processing, vol.68, pp.24-30, 2017.
DOI : 10.1016/j.dsp.2017.05.003

A. Aïssa-el-bey, D. Pastor, S. A. Sbaï, and Y. Fadlallah, Sparsity-Based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems, IEEE Transactions on Information Theory, vol.61, issue.4, 2008.
DOI : 10.1109/TIT.2015.2399914

O. L. Mangasarian and B. Recht, Probability of unique integer solution to a system of linear equations, European Journal of Operational Research, vol.214, issue.1, 2011.
DOI : 10.1016/j.ejor.2011.04.010

D. L. Donoho and J. Tanner, Counting faces of randomly projected polytopes when the projection radically lowers dimension, Journal of the American Mathematical Society, vol.22, issue.1, pp.1-53, 2009.
DOI : 10.1090/S0894-0347-08-00600-0
URL : http://www.ams.org/jams/2009-22-01/S0894-0347-08-00600-0/S0894-0347-08-00600-0.pdf

Y. Fadlallah, A. Aïssa-el-bey, K. Amis, D. Pastor, and R. Pyndiah, New Iterative Detector of MIMO Transmission Using Sparse Decomposition, IEEE Transactions on Vehicular Technology, vol.64, issue.8, pp.3458-3464, 2015.
DOI : 10.1109/TVT.2014.2360687
URL : https://hal.archives-ouvertes.fr/hal-01197389

Y. Fadlallah, A. Aïssa-el-bey, K. Amis, D. Pastor, and R. Pyndiah, New decoding strategy for underdetermined MIMO transmission using sparse decomposition, Proceedings of the 21st European Signal Processing Conference (EUSIPCO), pp.1-5, 2013.
DOI : 10.1109/tvt.2014.2360687

B. Panzner, W. Zirwas, S. Dierks, M. Lauridsen, P. Mogensen et al., Deployment and implementation strategies for massive MIMO in 5G, 2014 IEEE Globecom Workshops (GC Wkshps), pp.346-351, 2014.
DOI : 10.1109/GLOCOMW.2014.7063455
URL : http://vbn.aau.dk/files/217296633/Globecom14.pdf

B. Hassibi and H. Vikalo, On the sphere-decoding algorithm I. Expected complexity, IEEE Transactions on Signal Processing, vol.53, issue.8, 2005.
DOI : 10.1109/TSP.2005.850352

L. B. White, MMSE precoder design for diversity systems with temporal correlation, Digital Signal Processing, vol.16, issue.5, pp.607-618, 2006.
DOI : 10.1016/j.dsp.2005.02.006

X. He, Q. Guo, J. Tong, J. Xi, and Y. Yu, Low-complexity approximate iterative LMMSE detection for large-scale MIMO systems, Digital Signal Processing, vol.60, pp.134-139, 2017.
DOI : 10.1016/j.dsp.2016.09.004

A. H. Mehana and A. Nosratinia, Performance of MIMO single-carrier frequency domain zero-forcing equalizer, 2012 IEEE International Symposium on Information Theory Proceedings, pp.3023-3027, 2012.
DOI : 10.1109/ISIT.2012.6284116

B. Hassibi, An efficient square-root algorithm for BLAST, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100), pp.737-740, 2000.
DOI : 10.1109/ICASSP.2000.859065
URL : https://authors.library.caltech.edu/54815/1/An%20efficient%20square-root%20algorithm%20for%20BLAST.pdf

D. Wubben, R. Bohnke, V. Kuhn, and K. D. Kammeyer, MMSE-based lattice-reduction for near-ML detection of MIMO systems, ITG Workshop on Smart Antennas (IEEE Cat. No.04EX802), pp.106-113, 2004.
DOI : 10.1109/WSA.2004.1407656
URL : http://www.ant.uni-bremen.de/whomes/wuebben/publications/itg_wsa_2004.pdf

J. G. , A Problem in Geometric Probability., MATHEMATICA SCANDINAVICA, vol.11, 1962.
DOI : 10.7146/math.scand.a-10655

S. S. Chen, D. L. Donoho, and M. A. Saunders, Atomic Decomposition by Basis Pursuit, SIAM Journal on Scientific Computing, vol.20, issue.1, pp.33-61, 1998.
DOI : 10.1137/S1064827596304010

Z. Hajji, K. A. Cavalec, A. Aïssa-el-bey, and F. Abdelkefi, Lowcomplexity half-sparse decomposition-based detection for massive MIMO transmission, 5th International Conference on Communications and Networking (ComNet), pp.1-6, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01308364

X. Fan, J. Song, D. P. Palomar, and O. C. Au, Universal Binary Semidefinite Relaxation for ML Signal Detection, IEEE Transactions on Communications, vol.61, issue.11, pp.4565-4576, 2013.
DOI : 10.1109/TCOMM.2013.092013.120988

T. Cui and C. Tellambura, An efficient generalized sphere decoder for rankdeficient MIMO systems, IEEE Communications Letters, vol.9, issue.5, 2005.

H. Karloff, The Simplex Algorithm, pp.23-47, 1991.
DOI : 10.1007/978-0-8176-4844-2_2

Y. Nesterov and A. Nemirovskii, Interior-Point Polynomial Algorithms in Convex Programming, Path-Following Interior-Point Methods, Society for Industrial and Applied Mathematics, issue.3, pp.57-99, 1994.
DOI : 10.1137/1.9781611970791

D. L. Donoho and J. Tanner, Counting the Faces of Randomly-Projected Hypercubes and Orthants, with Applications, Discrete & Computational Geometry, vol.42, issue.2, pp.522-541, 2010.
DOI : 10.1007/978-1-4613-8431-1

M. Grant and S. Boyd, CVX: Matlab software for disciplined convex programming , version 2, 2014.
DOI : 10.1007/0-387-30528-9_7
URL : http://www.stanford.edu/~boyd/papers/pdf/disc_cvx_prog.pdf

M. Grant and S. Boyd, Graph Implementations for Nonsmooth Convex Programs, Recent Advances in Learning and Control, Lecture Notes in Control and Information Sciences, pp.95-110, 2008.
DOI : 10.1007/978-1-84800-155-8_7
URL : http://www.stanford.edu/~boyd/papers/pdf/graph_dcp.pdf

E. D. Andersen, C. Roos, and T. Terlaky, On implementing a primal-dual interior-point method for conic quadratic optimization, Mathematical Programming, vol.95, issue.2, pp.249-277, 2003.
DOI : 10.1007/s10107-002-0349-3

P. B. Stark and R. L. Parker, Bounded-variable least-squares: an algorithm and applications, Computational Statistics, vol.10, issue.2, pp.129-141, 1995.

K. V. Mardia, J. T. Kent, and J. M. Bibby, Multivariate analysis, Academic press, 1980.

K. Cho and D. Yoon, On the general ber expression of one-and twodimensional amplitude modulations, IEEE Transactions on Communications, vol.50, issue.7, 2002.

Y. H. Gan and W. H. Mow, Complex lattice reduction algorithms for low-complexity MIMO detection, IEEE Global Telecommunications Conference (GLOBECOM), pp.2953-2957, 2005.

, URL

A. Zaib, M. Masood, A. Ali, W. Xu, and T. , Distributed Channel Estimation and Pilot Contamination Analysis for Massive MIMO-OFDM Systems, IEEE Transactions on Communications, vol.64, issue.11, pp.4607-4621, 2016.
DOI : 10.1109/TCOMM.2016.2593924

, Thanks The authors would like to thank the Brittany Region and PRACOM for their financial support

H. Authors-'biographies-zahran and . Was-born-in-djerba, He received the Dr from Higher School of Communication of Tunis (SupCom) Since His main research interests include wireless communications, massive MIMO technologies , iterative decoding and detection and compressed sensing, he has been pursuing the Ph.D. degree at the the Signal and Communication department of Telecom Bretagne, 1992.

, Abdeldjalil Aïssa-El-Bey received the State Engineering degree from

, Ecole Nationale Polytechnique (ENP) the M.S, 2003.