Nonlinear iterative precoding algorithm for MIMO multiuser systems


A modification of the known linear precoding algorithm CLTD (closed-loop transmit diversity) intended for multiuser radio communication systems and using theMIMOtechnology has been proposed. The efficiency of the original precoding algorithm CLTD possessing a number of advantages as compared to earlier precoding methods based on complete information about the communication channel state is enhanced at the expense of introducing nonlinearity. The use of nonlinear procedure of ordered successive interference cancellation (OSIC) in forming the precoding matrix makes it possible to significantly increase the noise immunity of the entire system as a whole at the expense of a slight rise of algorithm computational complexity. In addition, the results of computer simulation are presented reflecting the efficiency of the proposed modification of the algorithm for forming a precoding matrix as compared to the original CLTD algorithm.

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  1. 1.

    W. Tong, P. Zhu, M. Jia, A. Chloma, M. Bakouline, and V. Kreindeline, International patent (PCT) No. WO 2005/046081, Method to determine precoding weights based on channel state information in MIMO communication systems, 04 November 2004.

    Google Scholar 

  2. 2.

    M. G. Bakulin, L. A. Varukina, and V. B. Kreyndelin, MIMO Technology: Principles and Algorithms [in Russian] (Goryachaya Liniya–Telekom, Moscow, 2014).

    Google Scholar 

  3. 3.

    A. Sibille, C. Oestges, A. Zanella, MIMO: From Theory to Implementation (Elsevier, UK, 2010).

    Google Scholar 

  4. 4.

    S. Zheng, H. Zhao, L. Zhao, J. Mei, W. Tang, “Multiuser beamforming with limited feedback for FDD massive MIMO systems,” Chinese J. Eng. 2016, ID 9821845, 9 p. (2016). DOI: 10.1155/2016/9821845.

  5. 5.

    H. Murata, R. Shinohara, “Performance improvement of ZF-precoded MU-MIMO transmission by collaborative interference cancellation,” IEICE Commun. Express 4, No. 5, 155 (2015). DOI: 10.1587/comex.4.155.

    Article  Google Scholar 

  6. 6.

    F. Wang, M. E. Bialkowski, “Performance of block diagonalization scheme for downlink multiuser MIMO system with estimated channel state information,” Int. J. Commun., Network and System Sciences 4, No. 2, 82 (2011). DOI: 10.4236/ijcns.2011.42010.

    Article  Google Scholar 

  7. 7.

    Varna L. Babu, Luxy Mathews, Sakuntala S. Pillai, “Performance analysis of linear and nonlinear precoding in MIMO systems,” Int. J. Advanced Res. Computer Commun. Eng. 4, No. 6, 373 (2015). DOI: 10.17148/IJARCCE.2015.4681.

    Google Scholar 

  8. 8.

    Q. H. Spencer, A. L. Swindlehurst, M. Haardt, “Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels,” IEEE Trans. Signal Processing 52, No. 2, 461 (2004). DOI: 10.1109/TSP.2003.821107.

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    G. Tsoulos, MIMO System Technology for Wireless Communications (CRC Press, Boca Raton, FL, 2006).

    Google Scholar 

  10. 10.

    K. Zu, “Novel efficient precoding techniques for multiuser MIMO systems,” Ph.D thesis. University of New York (May 2013).

    Google Scholar 

  11. 11.

    N. N. Moiseev, Yu. P. Ivanilov, and E. M. Stolyarova, Optimization Methods [in Russian] (Nauka, Moscow, 1978).

    Google Scholar 

  12. 12.

    F. P. Vasil’ev, Numerical Methods for Solving Extremum Problems [in Russian] (Nauka, Moscow, 1988).

    Google Scholar 

  13. 13.

    S. Sarkar, M. S. Rahman, “A unique equalizer to optimize BER in MIMO wireless multipath fading channel: modifiedMMSEvs. existing equalizers,” Int. J. Emerg. Sci. 3, No. 2, 200 (June 2013). URL:

    Google Scholar 

  14. 14.

    T. Foluwasu, “Receiver architectures for MIMO wireless communication systems based on VBLAST and sphere decoding algorithms,” A thesis submitted in partial fulfillment of the requirements of the University of Hertfordshire for the degree of Doctor of Philosophy (University of Hertfordshire, Hatfield, 2011).

    Google Scholar 

  15. 15.

    P. R. Kumari, C. K. Reddy, K. S. Ramesh, “Ordered successive interference cancellation for maximum throughput in multi stream MIMO using different modulation schemes,” Indian J. Sci. Technol. 9, No. 9, 1 (2016). DOI: 10.17485/ijst/2016/v9i9/85873.

    Article  Google Scholar 

  16. 16.

    P. W. Wolniansky, G. J. Foschini, G. D. Golden, R. A. Valenzuela, “V-BLAST: an architecture for realizing very high data rates over the rich scattering wireless channel,” Proc. of 1998 URSI Int. Symp. on Signals, Systems, and Electronics, 29 Sep.–2 Oct. 1998, Pisa, Italy (IEEE, 1998), pp. 295–300. DOI: 10.1109/ISSSE.1998.738086.

    Google Scholar 

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Correspondence to V. B. Kreyndelin.

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Original Russian Text © V.B. Kreyndelin and T.B.K. Ben Rejeb, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radioelektronika, 2017, Vol. 60, No. 10, pp. 581–591.

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Kreyndelin, V.B., Ben Rejeb, T.B.K. Nonlinear iterative precoding algorithm for MIMO multiuser systems. Radioelectron.Commun.Syst. 60, 449–457 (2017).

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