DOI QR코드

DOI QR Code

SER Analysis of Multi-Way Relay Networks with M-QAM Modulation in the Presence of Imperfect Channel Estimation

  • Islam, Shama N. (The authors are with the Research School of Engineering, College of Engineering and Computer Science, The Australian National University) ;
  • Durrani, Salman (The authors are with the Research School of Engineering, College of Engineering and Computer Science, The Australian National University) ;
  • Sadeghi, Parastoo (The authors are with the Research School of Engineering, College of Engineering and Computer Science, The Australian National University)
  • 투고 : 2015.05.28
  • 심사 : 2016.01.23
  • 발행 : 2016.10.31

초록

Multi-way relay networks (MWRNs) allow multiple users to exchange information with each other through a single relay terminal. MWRNs are often incorporated with capacity achieving lattice codes to enable the benefits of high-rate signal constellations to be extracted. In this paper, we analytically characterize the symbol error rate (SER) performance of a functional decode and forward (FDF) MWRN in the presence of channel estimation errors. Considering M-ary quadrature amplitude modulation (QAM) with square constellations as an important special case of lattice codes, we obtain asymptotic expressions for the average SER for a user in FDF MWRN. The accuracy of the analysis at high signal-to-noise ratio is validated by comparison with the simulation results. The analysis shows that when a user decodes other users with better channel conditions than itself, the decoding user experiences better error performance. The analytical results allow system designers to accurately assess the non-trivial impact of channel estimation errors and the users' channel conditions on the SER performance of a FDF MWRN with M-QAM modulation.

키워드

참고문헌

  1. D. Gunduz, A. Yener, A. Goldsmith, and H. V. Poor, "The multi-way relay channel," IEEE Trans. Inf. Theory, vol. 59, no. 1, pp. 51-63, Jan. 2013. https://doi.org/10.1109/TIT.2012.2219156
  2. L. Ong, S. J. Johnson, and C. M. Kellett, "An optimal coding strategy for the binary multi-way relay channel," IEEE Commun. Lett., vol. 14, no. 4, pp. 330-332, Apr. 2010. https://doi.org/10.1109/LCOMM.2010.04.092427
  3. S. Zhang, S. C. Liew, and P. P. Lam, "Hot topic: Physical-layer network coding," in Proc. ACM MOBICOM, 2006, pp. 358-365.
  4. S. Katti, S. Gollakota, and D. Katabi, "Embracing wireless interference: Analog network coding," in Proc. ACM SIGCOMM, 2007, pp. 397-408.
  5. B. Rankov and A. Wittneben, "Spectral efficient signaling for half-duplex relay channels," in Proc. Asilomar Conference on Signals, Systems and Computers, Nov. 2005, pp. 1066-1071.
  6. X. Liang, S. Jin, X. Gao, and K.-K. Wong, "Outage performance for decode-and-forward two-way relay network with multiple interferers and noisy relay," IEEE Trans. Commun., vol. 61, no. 2, pp. 521-531, Feb. 2013. https://doi.org/10.1109/TCOMM.2012.122112.110778
  7. M. Chen and A. Yener, "Multiuser two-way relaying: Detection and interference management strategies," IEEE Trans. Wireless Commun., vol. 8, no. 8, pp. 4296-4305, Aug. 2009. https://doi.org/10.1109/TWC.2009.081165
  8. W. Xu, X. Dong, and W.-S. Lu, "Joint precoding optimization for multiuser multi-antenna relaying downlinks using quadratic programming," IEEE Trans. Commun., vol. 59, no. 5, pp. 1228-1235, May 2011. https://doi.org/10.1109/TCOMM.2011.041111.090713
  9. G. Amarasuriya, C. Tellambura, and M. Ardakani, "Performance analysis of pairwise amplify-and-forward multi-way relay networks," IEEE Wire- less Commun. Lett., vol. 1, no. 5, pp. 524-527, Oct. 2012. https://doi.org/10.1109/WCL.2012.072012.120473
  10. G. Amarasuriya, "Multi-way MIMO amplify-and-forward relay networks with zero-forcing transmission," IEEE Trans. Commun., vol. 61, no. 12, pp. 4847-4863, Dec. 2013. https://doi.org/10.1109/TCOMM.2013.110413.120762
  11. S. N. Islam, "Achievable rate and error performance of an af multi-way relay network in the presence of imperfect channel estimation," IET Com-mun., vol. 10, no. 3, pp. 272-282, Jan. 2016. https://doi.org/10.1049/iet-com.2015.0484
  12. L. Ong, C. Kellett, and S. Johnson, "On the equal-rate capacity of the AWGN multiway relay channel," IEEE Trans. Inf. Theory, vol. 58, no. 9, pp. 5761-5769, Sept. 2012. https://doi.org/10.1109/TIT.2012.2204510
  13. G. Wang, W. Xiang, and J. Yuan, "Outage performance for compute-andforward in generalized multi-way relay channels," IEEE Commun. Lett., vol. 16, no. 12, pp. 2099-2102, Dec. 2012. https://doi.org/10.1109/LCOMM.2012.112012.122273
  14. B. Nazer and M. Gastpar, "Compute-and-forward: Harnessing interference through structured codes," IEEE Trans. Inf. Theory, vol. 57, no. 10, pp. 6463-6486, Oct. 2011. https://doi.org/10.1109/TIT.2011.2165816
  15. M. Noori and M. Ardakani, "Optimal user pairing for asymmetric multiway relay channels with pairwise relaying," IEEE Commun. Lett., vol. 16, no. 11, pp. 1852-1855, Nov. 2012. https://doi.org/10.1109/LCOMM.2012.100812.121258
  16. T. Huang, J. Yuan, and Q. Sun, "Opportunistic pair-wise compute-andforward in multi-way relay channels," in Proc. IEEE ICC, June 2013, pp. 4614-4619.
  17. R. R. Borujeny, M. Noori, and M. Ardakani, "On the achievable rates of pairwise multiway relay channels," in Proc. IEEE ISIT, June 2014.
  18. S. Islam, "Optimal user pairing to improve the sum rate of a pairwise AF multi-way relay network," IEEE Wireless Commun. Lett., vol. 4, no. 3, pp. 261-264, June 2015. https://doi.org/10.1109/LWC.2015.2405061
  19. S. N. Islam, P. Sadeghi, and S. Durrani, "A novel pairing scheme to reduce error propagation in an amplify and forward multi-way relay network," in Proc. IEEE SSP, June 2014, pp. 544-547.
  20. C. Feng, D. Silva, and F. Kschischang, "An algebraic approach to physical-layer network coding," IEEE Trans. Inf. Theory, vol. 59, no. 11, pp. 7576-7596, Nov. 2013. https://doi.org/10.1109/TIT.2013.2274264
  21. C. Wang, T.-K. Liu, and X. Dong, "Impact of channel estimation error on the performance of amplify-and-forward two-way relaying," IEEE Trans. Veh. Technol., vol. 61, no. 3, pp. 1197-1207, Mar. 2012. https://doi.org/10.1109/TVT.2012.2185964
  22. Z. Ding and K. Leung, "Impact of imperfect channel state information on bi-directional communications with relay selection," IEEE Trans. Signal Process., vol. 59, no. 11, pp. 5657-5662, Nov. 2011. https://doi.org/10.1109/TSP.2011.2163403
  23. F. Tabataba, P. Sadeghi, C. Hucher, and M. Pakravan, "Impact of channel estimation errors and power allocation on analog network coding and routing in two-way relaying," IEEE Trans. Veh. Technol., vol. 61, no. 7, pp. 3223-3239, Sept. 2012. https://doi.org/10.1109/TVT.2012.2201969
  24. B. Jiang, F. Gao, X. Gao, and A. Nallanathan, "Channel estimation and training design for two-way relay networks with power allocation," IEEE Trans. Wireless Commun., vol. 9, no. 6, pp. 2022-2032, June 2010. https://doi.org/10.1109/TWC.2010.06.090870
  25. S. Abdallah and I. N. Psaromiligkos, "Blind channel estimation for amplify-and-forward two-way relay networks employing m-psk modulation," IEEE Trans. Signal Process., vol. 60, no. 7, pp. 3604-3615, 2012. https://doi.org/10.1109/TSP.2012.2193577
  26. S. N. Islam, P. Sadeghi, and S. Durrani, "Error performance analysis of decode-and-forward and amplify-and-forward multi-way relay networks with binary phase shift keying modulation," IET Commun., vol. 7, no. 15, pp. 1605-1616, Oct. 2013. https://doi.org/10.1049/iet-com.2013.0284
  27. S. Islam and P. Sadeghi, "Joint decoding: Extracting the correlation among user pairs in a multi-way relay channel," in Proc. IEEE PIMRC, Sept. 2012, pp. 54-59.
  28. G. Kramer, M. Gastpar, and P. Gupta, "Cooperative strategies and capacity theorems for relay networks," IEEE Trans. Inf. Theory, vol. 51, no. 9, pp. 3037-3063, Sept. 2005. https://doi.org/10.1109/TIT.2005.853304
  29. M. Ju and I.-M. Kim, "Error performance analysis of BPSK modulation in physical layer network coded bidirectional relay networks," IEEE Trans. Commun., vol. 58, no. 10, pp. 2770-2775, Oct. 2010. https://doi.org/10.1109/TCOMM.2010.082010.090256
  30. J. N. Laneman, D. N. C. Tse, and G.W.Wornell, "Cooperative diversity in wireless networks: Efficient protocols and outage behavior," IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 3062-3080, Dec. 2004. https://doi.org/10.1109/TIT.2004.838089
  31. A. Nosratinia, T. Hunter, and A. Hedayat, "Cooperative communication in wireless networks," IEEE Commun. Mag., vol. 42, no. 10, pp. 74-80, Oct. 2004. https://doi.org/10.1109/MCOM.2004.1341264
  32. C. Patel and G. Stuber, "Channel estimation for amplify and forward relay based cooperation diversity systems," IEEE Trans. Wireless Commun., vol. 6, no. 6, pp. 2348-2356, June 2007. https://doi.org/10.1109/TWC.2007.05875
  33. B. Hassibi and B. Hochwald, "How much training is needed in multipleantenna wireless links?" IEEE Trans. Inf. Theory, vol. 49, no. 4, pp. 951-963, 2003. https://doi.org/10.1109/TIT.2003.809594
  34. F. Tabataba, P. Sadeghi, and M. Pakravan, "Outage probability and power allocation of amplify and forward relaying with channel estimation errors," IEEE Trans. Wireless Commun., vol. 10, no. 1, pp. 124-134, Jan. 2011. https://doi.org/10.1109/TWC.2010.102810.091729
  35. Y. Ma, T. Huang, J. Li, J. Yuan, Z. Lin, and B. Vucetic, "Novel nested convolutional lattice codes for multi-way relaying systems over fading channels," in Proc. IEEE WCNC, Apr. 2013, pp. 2671-2676.
  36. S. N. Islam, S. Durrani, and P. Sadeghi, "A novel user pairing scheme for functional decode-and-forward multi-way relay network," Physical Com-mun., vol. 17, pp. 128-148, Dec. 2015. https://doi.org/10.1016/j.phycom.2015.08.009
  37. U. Erez and R. Zamir, "Achieving 1/2 log (1+SNR) on the awgn channel with lattice encoding and decoding," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2293-2314, Oct. 2004. https://doi.org/10.1109/TIT.2004.834787
  38. W. Nam, S.-Y. Chung, and Y. H. Lee, "Nested lattice codes for gaussian relay networks with interference," IEEE Trans. Inf. Theory, vol. 57, no. 12, pp. 7733-7745, Dec. 2011. https://doi.org/10.1109/TIT.2011.2170102
  39. K. Pappi, G. Karagiannidis, and R. Schober, "How sensitive is computeand-forward to channel estimation errors?" in Proc. IEEE ISIT, July 2013, pp. 3110-3114.
  40. R. Chang, S.-J. Lin, andW.-H. Chung, "Symbol and bit mapping optimization for physical-layer network coding with pulse amplitude modulation," IEEE Trans. Wireless Commun., vol. 12, no. 8, pp. 3956-3967, Aug. 2013. https://doi.org/10.1109/TWC.2013.071613.121520
  41. M. K. Simon and M.-S. Alouini, Digital Communication over Fading Channels, 2000.
  42. R. H. Y. Louie, Y. Li, and B. Vucetic, "Practical physical layer network coding for two-way relay channels: Performance analysis and comparison," IEEE Trans. Wireless Commun., vol. 9, no. 2, pp. 764-777, Feb. 2010. https://doi.org/10.1109/TWC.2010.02.090314