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Performance study of non-orthogonal multiple access (NOMA) with triangular successive interference cancellation

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The non-orthogonal multiple access (NOMA) allows allocating one carrier to more than one user at the same time in one cell. It is a promising technology to provide high throughput due to carrier reuse within a cell. In this paper, a novel interference cancellation (IC) technique is proposed for asynchronous NOMA systems. The proposed IC technique exploits a triangular pattern to perform the IC from all interfering users for the desired user. The bit error rate performance analysis of an uplink NOMA system with the proposed IC technique is presented, along with the comparison to conventional IC technique. The numerical and simulation results show that the NOMA with the proposed asynchronous IC technique outperforms the conventional IC. It is also shown that employing iterative IC provides significant performance gain for NOMA and the number of required iterations depends on the modulation level and the detection method. With hard-decision, two iterations are sufficient, however with soft-decision, two iterations are enough only for low modulation level, and more iterations are desirable for high modulation level.

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  1. 1.

    3rd Generation Partnership Project (2011) TS 36.213 v10.1.0 Release 10: Physical layer procedures for Evolved Universal Terrestrial Radio Access (E-UTRA).

  2. 2.

    3rd Generation Partnership Project (2014) Release 13: RP-141831. http://www.3gpp.org/release-13. Accessed April 16, 2016.

  3. 3.

    Akhtar, F., Rehmani, M. H., & Reisslein, M. (2016). White space: Definitional perspectives and their role in exploiting spectrum opportunities. Telecommunications Policy, 40(4), 319–331.

  4. 4.

    Al-Imari, M., Xiao, P., Imran, M., & Tafazolli, R. (2014). Uplink non-orthogonal multiple access for 5G wireless networks. In 2014 11th international symposium on wireless communications systems (ISWCS) (pp. 781–785). doi:10.1109/ISWCS.2014.6933459.

  5. 5.

    Bukhari, S. H. R., Rehmani, M. H., & Siraj, S. (2016). A survey of channel bonding for wireless networks and guidelines of channel bonding for futuristic cognitive radio sensor networks. IEEE Communications Surveys and Tutorials, 18(2), 924–948. doi:10.1109/COMST.2015.2504408.

  6. 6.

    Chen, C. Y., & Lin, D. W. (2014). Channel estimation for LTE and LTE-A MU-MIMO uplink with a narrow transmission band. In 2014 IEEE international conference on acoustics, speech and signal processing (pp. 6484–6488). doi:10.1109/ICASSP.2014.6854853.

  7. 7.

    Cover, T. M., & Thomas, J. A. (1991). Elements of information theory. New York, NY: Wiley-Interscience.

  8. 8.

    Ding, Z., Peng, M., & Poor, H. V. (2014). Cooperative non-orthogonal multiple access in 5G systems. arXiv:14105846s.

  9. 9.

    Ding, Z., Yang, Z., Fan, P., & Poor, H. (2014). On the performance of non-orthogonal multiple access in 5G systems with randomly deployed users. IEEE Signal Processing Letters, 21(12), 1501–1505. doi:10.1109/LSP.2014.2343971.

  10. 10.

    Ding, Z., Adachi, F., & Poor, H. (2015). The application of MIMO to non-orthogonal multiple access. IEEE Transactions on Wireless Communications, 99, 1–1. doi:10.1109/TWC.2015.2475746.

  11. 11.

    Endo, Y., Kishiyama, Y., & Higuchi, K. (2012). Uplink non-orthogonal access with MMSE-SIC in the presence of inter-cell interference. In 2012 international symposium on wireless communication systems (ISWCS) (pp. 261–265). doi:10.1109/ISWCS.2012.6328370.

  12. 12.

    Goldsmith, A. (2005). Wireless communications. New York, NY: Cambridge University Press.

  13. 13.

    Gong, C., Tajer, A., & Wang, X. (2012). Group decoding for multi-relay assisted interference channels. IEEE Journal on Selected Areas in Communications, 30(8), 1489–1499. doi:10.1109/JSAC.2012.120917.

  14. 14.

    Haci, H. (2015). Non-orthogonal multiple access (NOMA) with asynchronous interference cancellation. Ph.D. thesis, School of Engineering and Digital Arts, University of Kent.

  15. 15.

    Haci, H., & Zhu, H. (2015). Performance of non-orthogonal multiple access with a novel interference cancellation method. In 2015 IEEE international conference on communications (ICC) (pp. 2912–2917). doi:10.1109/ICC.2015.7248769.

  16. 16.

    Haci, H., Zhu, H., & Wang, J. (2012). Novel scheduling for a mixture of real-time and non-real-time traffic. In 2012 IEEE global communications conference (GLOBECOM) (pp. 4647–4652). doi:10.1109/GLOCOM.2012.6503852.

  17. 17.

    Haci, H., Zhu, H., & Wang, J. (2012). Resource allocation in user-centric wireless networks. In 2012 IEEE 75th vehicular technology conference (VTC Spring) (pp. 1–5). doi:10.1109/VETECS.2012.6240307.

  18. 18.

    Haci, H., Zhu, H., & Wang, J. (2015). A novel interference cancellation technique for non-orthogonal multiple access (NOMA). In 2015 IEEE global communications conference (GLOBECOM) (pp. 1–6). doi:10.1109/GLOCOM.2015.7417128.

  19. 19.

    Jiang, M., Yue, G., Prasad, N., & Rangarajan, S. (2012). Enhanced DFT-based channel estimation for LTE uplink. In 2012 IEEE 75th vehicular technology conference (pp. 1–5). doi:10.1109/VETECS.2012.6240325.

  20. 20.

    Jungnickel, V., Manolakis, K., Zirwas, W., Panzner, B., Braun, V., Lossow, M., et al. (2014). The role of small cells, coordinated multipoint, and massive MIMO in 5G. IEEE Communications Magazine, 52(5), 44–51. doi:10.1109/MCOM.2014.6815892.

  21. 21.

    Kay, S. M. (1993). Fundamentals of statistical signal processing: Estimation theory. New York, NY: Prentice Hall.

  22. 22.

    Lopes, L. A., Sofia, R., Haci, H., & Zhu, H. (2015). A proposal for dynamic frequency sharing in wireless networks. IEEE/ACM Transactions on Networking, 99, 1–1. doi:10.1109/TNET.2015.2477560.

  23. 23.

    Miridakis, N., & Vergados, D. (2013). A survey on the successive interference cancellation performance for single-antenna and multiple-antenna OFDM systems. IEEE Communications Surveys and Tutorials, 15(1), 312–335. doi:10.1109/SURV.2012.030512.00103.

  24. 24.

    NTT DOCOMO. (2014). 5G Concept and Technologies. http://5gworkshop.hhi.fraunhofer.de/wp-content/uploads/2014/12/Globecom-2014-WS-on-5G-New-Air-Interface-NTT-DOCOMO.pdf. Accessed April 16, 2016.

  25. 25.

    Papoulis, A., & Pillai, S. U. (2002). Probability, random variables, and stochastic processes. New York, NY: Tata McGraw-Hill Education.

  26. 26.

    Park, M., Ko, K., Park, B., & Hong, D. (2010). Effects of asynchronous MAI on average SEP performance of OFDMA uplink systems over frequency-selective Rayleigh fading channels. IEEE Transactions on Communications, 58(2), 586–599. doi:10.1109/TCOMM.2010.02.050324.

  27. 27.

    Patel, P., & Holtzman, J. (1994). Analysis of a simple successive interference cancellation scheme in a DS/CDMA system. IEEE Journal on Selected Areas in Communications, 12(5), 796–807. doi:10.1109/49.298053.

  28. 28.

    Ping, L., Tong, J., Yuan, X., & Guo, Q. (2009). Superposition coded modulation and iterative linear MMSE detection. IEEE Journal on Selected Areas in Communications, 27(6), 995–1004. doi:10.1109/JSAC.2009.090817.

  29. 29.

    Reyni, A. (1970). Probability theory. Amsterdam: North-Holland.

  30. 30.

    Saito, Y., Kishiyama, Y., Benjebbour, A., Nakamura, T., Li, A., & Higuchi, K. (2013). Non-orthogonal multiple access (NOMA) for cellular future radio access. In 2013 IEEE 77th vehicular technology conference (VTC Spring) (pp. 1–5). doi:10.1109/VTCSpring.2013.6692652.

  31. 31.

    Schaepperle, J. (2010). Throughput of a wireless cell using superposition based multiple-access with optimized scheduling. In 2010 IEEE international symposium on personal indoor and mobile radio communications (pp. 212–217). doi:10.1109/PIMRC.2010.5671661.

  32. 32.

    Tong, J., & Ping, L. (2010). Performance analysis of superposition coded modulation. Physical Communication, 3(3), 147–155. doi:10.1016/j.phycom.2009.08.008.

  33. 33.

    University of Alabama in Huntsville, Virtual Laboratories. (2016). Special Distribution Simulator. http://www.math.uah.edu/stat/apps/SpecialSimulation.html. Accessed April 16, 2016.

  34. 34.

    Xinxin, F., Minn, H., Yan, L., & Jinhui, L. (2010). PIC-based iterative SDR detector for OFDM systems in doubly-selective fading channels. IEEE Transactions on Wireless Communications, 9(1), 86–91. doi:10.1109/TWC.2010.01.090462.

  35. 35.

    Zafar, A., Shaqfeh, M., Alouini, M. S., & Alnuweiri, H. (2013). On multiple users scheduling using superposition coding over Rayleigh fading channels. IEEE Communications Letters, 17(4), 733–736. doi:10.1109/LCOMM.2013.021213.122465.

  36. 36.

    Zhang, R., & Hanzo, L. (2011). A unified treatment of superposition coding aided communications: Theory and practice. IEEE Communications Surveys and Tutorials, 13(3), 503–520. doi:10.1109/SURV.2011.061610.00102.

  37. 37.

    Zhou, M., Jiang, B., Li, T., Zhong, W., & Gao, X. (2009). DCT-based channel estimation techniques for LTE uplink. In 2009 IEEE 20th international symposium on personal, indoor and mobile radio communications (pp. 1034–1038). doi:10.1109/PIMRC.2009.5450015.

  38. 38.

    Zhu, H. (2012). On frequency reuse in cooperative distributed antenna systems. IEEE Communications Magazine, 50(4), 85–89. doi:10.1109/MCOM.2012.6178838.

  39. 39.

    Zhu, H., & Wang, J. (2012). Chunk-based resource allocation in OFDMA systems part II: joint chunk, power and bit allocation. IEEE Transactions on Communications, 60(2), 499–509. doi:10.1109/TCOMM.2011.112811.110036.

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Correspondence to Huseyin Haci.

Appendix: The mean square error of detection at the lth iteration

Appendix: The mean square error of detection at the lth iteration

Given (10), \(\left( {\text {D}}_{k}^{(\mathfrak {L})}[\varsigma ] \,\big \vert \, {\text {z}}_{k}^{(\mathfrak {L})}[\varsigma ] \right) = E[(X_{k}[\varsigma ] - \hat{X}_{k}^{(\mathfrak {L})}[\varsigma ])^{2}]\) represents the MSE of the detection at the \(\mathfrak {L}\)th iteration for the \(\varsigma\)th symbol of the kth user. For \(\mathfrak {L}=0\), there was no a priori detection done for the symbol yet, so \({\text {D}}_{k}^{(0)}[\varsigma ] =1\). For \(\mathfrak {L} \ge 1\), a priori detection was done for the symbol. With probability \((1-{\text {Pe}}_{k}^{(\mathfrak {L})}[\varsigma ])\) the detection was correct so \(\left( {\text {D}}_{k}^{(\mathfrak {L})}[\varsigma ] \,\big \vert \,X_{k}[\varsigma ] = \hat{X}_{k}^{(\mathfrak {L})}[\varsigma ] \right) =0\); with probability \({\text {Pe}}_{k}^{(\mathfrak {L})}[\varsigma ]\) the detection was in error and \(\left( {\text {D}}_{k}^{(\mathfrak {L})}[\varsigma ] \,\big \vert \, X_{k}[\varsigma ] \ne \hat{X}_{k}^{(\mathfrak {L})}[\varsigma ] \right)\) is obtained as follows. Let \({\text {P}}(m_{i} \,\big \vert \, m_{j})\) denote the probability of detecting constellation point \(m_{i}\), given that constellation \(m_{j}\) is transmitted. For M-QAM constellation \(\left( {\text {D}}_{k}^{(\mathfrak {L})}[\varsigma ] \,\big \vert \, X_{k}[\varsigma ] \ne \hat{X}_{k}^{(\mathfrak {L})}[\varsigma ] \right)\) is given by

$$\begin{aligned} \left( {\text {D}}_{k}^{(\mathfrak {L})}[\varsigma ] \,\big \vert \, X_{k}[\varsigma ] \ne \hat{X}_{k}^{(\mathfrak {L})}[\varsigma ] \right) = \sum _{\begin{array}{c} i=1\\ i \ne j \end{array}}^{M} \left( m_{j} - m_{i} \right) ^{2} \cdot {\text {P}}(m_{i} \,\big \vert \, m_{j}). \end{aligned}$$

With hard-decision, the event with \({\text {P}}(m_{i} \,\big \vert \,m_{j})\) occurs when the power of residual interference plus noise exceeds half of the distance between nearest constellation points and the resultant ICed signal is closest to constellation point \(m_{i}\). Since the power of residual interference plus noise is Gaussian distributed (as explained in Sect. 5) and Gaussian distribution has tail distribution with exponential falloff, the error probability for a constellation point for another point that is not one of its nearest neighbour is much less than that for a nearest neighbour. Thus nearest neighbour approximation to the detection error is used in this paper [12, Chap. 5.1]. Then, for Gray coded QAM constellation with average unit power,

$$\begin{aligned} \left( {\text {D}}_{k}^{(\mathfrak {L})}[\varsigma ] \,\big \vert \, X_{k}[\varsigma ] \ne \hat{X}_{k}^{(\mathfrak {L})}[\varsigma ] \right) = (m_{i} - m_{j})^{2} = (2 \cdot {\text {d}}_{{\text {unit}}})^{2} = (^{6}/_{(M-1)}), \end{aligned}$$

where \({\text {d}}_{{\text {unit}}} = \sqrt{^{3}/_{2(M-1)}}\) is half of the distance between two nearest neighbour constellation points at a constellation with average unit power. Then, the unified expression for all above cases is given by

$$\begin{aligned} &\big ({\text {D}}_{k}^{(\mathfrak {L})}[\varsigma ] \,\big \vert \, {\text {z}}_{k}^{(\mathfrak {L})}[\varsigma ] \big ) \\&\quad= {\left\{ \begin{array}{ll} 1, & {\text {for }}\, \mathfrak {L}=0, {\text {i.e. no priori detection was done for the symbol}} \\ ^{6}/_{(M-1)}, & {\text {for }}\, \mathfrak {L} \ge 1 {\text { and }} {\text {z}}_{k}^{(\mathfrak {L})}[\varsigma ] = {\text {e}}_{k}^{(\mathfrak {L})}[\varsigma ], {\text {i.e. priori detection was in error}} \\ 0, & {\text {for }}\, \mathfrak {L} \ge 1 {\text { and }} {\text {z}}_{k}^{(\mathfrak {L})}[\varsigma ] = {\text {c}}_{k}^{(\mathfrak {L})}[\varsigma ], {\text {i.e. priori detection was correct}}. \end{array}\right. } \end{aligned}$$

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Haci, H. Performance study of non-orthogonal multiple access (NOMA) with triangular successive interference cancellation. Wireless Netw 24, 2145–2163 (2018). https://doi.org/10.1007/s11276-017-1464-7

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  • Wireless communications
  • Non-orthogonal multiple access
  • Asynchronous interference cancellation
  • Bit-error-rate analysis