Performance analysis of full-duplex decode-and-forward relay network with spatial modulation

 dB.
 Fig. 2 illustrate the impact of the data transmission rates on the OP of the SM-FD
relay network for three typical values of R, i.e. R = 1, 2, 3 [bit/s/Hz], and compared
 R D ˜
it with conventional SM-HD relay network. We used Nr = Nr = 4, Ω = −10 dB. In
this figure, the OPs of the SM-FD relay network are plotted by using (9) in Theorem 1.
As can be seen in the figure, the analytical curves match perfectly with the simulation
ones, which validates Theorem 1. Noted that the OPs of the SM-HD relay network are
also used (9) after setting RSI to zero. Moreover, due to the different operation of FD
and HD modes, the threshold level to determine the OP for SM-FD is always smaller
than that of SM-HD relay network (specifically, the threshold for SM-FD is x = 2R − 1
while for SM-HD is x = 22R −1). Therefore, at the low SNR region, meaning low RSI,
the OP of the SM-FD relay network is significantly smaller than SM-HD relay network.
However, at high SNR regime, OPs of the SM-FD relay network suffer an outage floor
due to the impact of RSI. On the other hand, it is obvious that the transmission rate
has a strong impact on the OP performance of the SM-FD relay network. As shown
in Fig. 2, the higher transmission rate, the lower OPs performance of the SM-FD relay
system and the sooner the outage floor is reached.
 Fig. 3 investigates the SEP performance of the SM-FD relay network versus the
average SNR, where the BPSK modulation is used (i.e. a = 1, b = 2), Ω˜ = −10 dB
 R D
with the different number of reception antennas Nr = Nr = 4. In this figure, we use
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Section on Information and Communication Technology (ICT) - No. 14 (10-2019)
 0 
 10 
 -1
 10
 NNrRD 2,3,4
 -2
 10
 -3
 10
 Symbol Error Probability (SEP) Probability Error Symbol 
 -4
 10 FD Simulation
 FD Analytical
 HD Simulation
 HD Analytical
 -2 0 2 4 6 8 10 12 14 16 18 20
 SNR [dB]
 Fig. 3. The SEPs of the SM-FD relay system for different number of reception antennas
 R D ˜
 Nr = Nr = 4, Ω = −10 dB.
eq. (19) of Theorem 2 to plot the SEP curves of the SM-FD relay network. The SEPs
of the SM-HD relay network are also obtained from eq. (19) by setting the RSI to zero.
As shown in Fig. 3, the SEP of SM-FD system is alway worse than that of the SM-HD
due to the impact of the RSI in the FD mode. Moreover, at high SNR regime, the SEP
 2 ˜
of SM-FD system suffer an error floor. It is because the RSI is expressed as σRSI = ΩP ,
thus, higher transmission power results in higher RSI. For example, for Nr = 2, the SEP
of the SM-FD relay goes to the error floor quickly at 2.10−3. Besides, when increases
the number of reception antennas, the SEP performance of both SM-FD and SM-HD
systems is significantly improved due to the diversity gain. With 4 reception antennas,
the SM-FD relay system suffer an error floor at 10−5 while the SM-HD relay system
reaches SEP = 10−5 at SNR = 11 dB and further decreases with increasing SNR.
 In Fig. 4, the impact of the RSI on the SEP performance of the SM-FD relay system
 ˜
is investigate for the BPSK modulation, Nr = 4 and different values of Ω and SNR. It
is obvious that the RSI has a strong impact on the SEP of the SM-FD relay system,
especially when the RSI is high. Particularly, when the RSI is very small, i.e. Ω˜ =
−20 dB, the SEPs of the SM-FD and SM-HD system are nearly the same. When RSI
is larger (by increasing SNR and/or Ω˜), the SEP performance gap between FD and
HD mode is higher. For example, when Ω˜ = −10 dB, the performance gap is about 2
times at SNR = 5 dB, and increases to 10 times at SNR = 10 dB. Thus, using larger
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 Journal of Science and Technique - Le Quy Don Technical University - No. 202 (10-2019)
 0
 10 
 FD Simulation
 FD Analytical
 -1 HD Simulation
 10
 HD Analytical
 -2
 10 SNR 5 ,8 ,10dB
 -3
 10
 Symbol Error Probability (SEP) Probability Error Symbol 
 -4
 10
 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0
  [dB] 
 Fig. 4. Impact of the RSI on the SEP performance of the SM-FD relay system.
transmission power at the FD relay node is not the effective solution to improve the
system performance.
 Fig. 5 shows the superiority of the SM-FD relay over SM-HD relay system in terms
of the ergodic capacity when the RSI level is small. In this figure, the analytical ergodic
capacity curves of the SM-FD relay system are obtained by using (24) of Theorem 3,
while the ergodic capacity of SM-HD relay system is determined by one-half of the
capacity of the SM-FD system with the RSI level being set to zero. As shown in Fig. 4
and Fig. 5, when the RSI is large, i.e. Ω˜ = 0, −5 dB, the capacity of the SM-FD
relay is larger but not significant than the SM-HD relay system at low SNR region
while the SEP performance is much lower than the SM-HD relay system. When the
RSI is smaller with Ω˜ = −10, −20 dB, the SM-FD relay system is nearly double the
capacity compared with SM-HD relay system in the observed region with an acceptable
performance degradation. Thus, depending on the system requirements we can choose
the FD or HD mode for the relay node.
5. Conclusion
 SM-FD technique is a promising transmission solution for MIMO wireless communi-
cations in both context of point-to-point and relaying transmission systems. In this paper,
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Section on Information and Communication Technology (ICT) - No. 14 (10-2019)
 8 
 FD Simulation
 7 FD Analytical
 HD Simulation
 HD Analytical
 6
 5
 4
 3
 Ergodic Capacity (bit/s/Hz) Capacity Ergodic
 2
 1
 0,5,10,20dB
 0 
 -5 0 5 10 15 20
 SNR [dB] 
 R D
 Fig. 5. Ergodic capacity comparison of the SM-FD and SM-HD relay system, Nr = Nr = 4.
we introduce a mathematical framework to derive the exact closed-form expressions for
the OP, SEP and ergodic capacity of the SM-FD relay system in the presence of SI
channels, and compare with that of SM-HD relay system. Both numerical and simulation
results showed that the RSI, data transmission rate and number of received antennas
have a substantial impact on the system performance. This result can be used as a
reference to choose the FD/HD mode for the relay node depending on requirements of
specific system.
References
 [1] Z. Zhang, X. Chai, K. Long, A. V. Vasilakos, and L. Hanzo, “Full duplex techniques for 5G networks: self-
 interference cancellation, protocol design, and relay selection,” IEEE Commununications Magazine, vol. 53,
 no. 5, pp. 128–137, May 2015.
 [2] B. Jiao, M. Wen, M. Ma, and H. V. Poor, “Spatial modulated full duplex,” IEEE Wireless Communications
 Letters, vol. 3, no. 6, pp. 641–644, 2014.
 [3] B. C. Nguyen, T. M. Hoang, and P. T. Tran, “Performance analysis of full-duplex decode-and-forward relay
 system with energy harvesting over nakagami-m fading channels,” AEU-International Journal of Electronics
 and Communications, vol. 98, pp. 114–122, 2019.
 [4] Z. Wei, X. Zhu, S. Sun, Y. Jiang, A. Al-Tahmeesschi, and M. Yue, “Research issues, challenges, and
 opportunities of wireless power transfer-aided full-duplex relay systems,” IEEE Access, vol. 6, pp. 8870–8881,
 2018.
60
 Journal of Science and Technique - Le Quy Don Technical University - No. 202 (10-2019)
 [5] M. Le, V. Ngo, H. Mai, X. N. Tran, and M. D. Renzo, “Spatially modulated orthogonal space-time block codes
 with non-vanishing de-terminants,” IEEE Transactions on Communications, vol. 62, no. 1, p. 85–99, 2014.
 [6] T. P. Nguyen, M. T. Le, V. D. Ngo, X. N. Tran, and H. W. Choi, “Spatial modulation for high-rate transmission
 systems,” in 2014 IEEE 79th Vehicular Technology Conference (VTC Spring). IEEE, 2014, pp. 1–5.
 [7] A. Koc, I. Altunbas, and E. Basar, “Full-duplex spatial modulation systems under imperfect channel state
 information,” in 2017 24th International Conference on Telecommunications (ICT). IEEE, 2017, pp. 1–5.
 [8] C. Liu, L. Yang, and W. Wang, “Secure spatial modulation with a full-duplex receiver,” IEEE Wireless
 Communications Letters, vol. 6, no. 6, pp. 838–841, Dec 2017.
 [9] S. Peters, A. Panah, K. Truong, and R. Heath, “Relay architectures for 3gpp lte-advanced,” EURASIP Journal
 on Wireless Communications and Networking, vol. 2009, 01 2009.
[10] J. Zhang, Q. Li, K. J. Kim, Y. Wang, X. Ge, and J. Zhang, “On the performance of full-duplex two-way relay
 channels with spatial modulation,” IEEE Transactions on Communications, vol. 64, no. 12, p. 4966–4982, 2016.
[11] P. Raviteja, Y. Hong, and E. Viterbo, “Spatial modulation in full-duplex relaying,” IEEE Communications
 Letters, vol. 20, no. 10, pp. 2111–2114, 2016.
[12] S. Narayanan, H. Ahmadi, and M. F. Flanagan, “On the performance of spatial modulation MIMO for full-
 duplex relay networks,” IEEE Transactions on Wireless Communications, vol. 16, no. 6, pp. 3727–3746, 2017.
[13] A. Bhowal and R. S. Kshetrimayum, “Outage probability bound of decode and forward two-way full-duplex
 relay employing spatial modulation over cascaded α- µ channels,” International Journal of Communication
 Systems, vol. 32, no. 3, p. e3876, 2019.
[14] A. Koc, I. Altunbas, and E. Basar, “Two-way full-duplex spatial modulation systems with wireless powered AF
 relaying,” IEEE Wireless Communications Letters, vol. 7, no. 3, pp. 444–447, 2018.
[15] T. Riihonen, S. Werner, and R. Wichman, “Mitigation of loopback self-interference in full-duplex MIMO
 relays,” IEEE Transactions on Signal Processing, vol. 59, no. 12, pp. 5983–5993, 2011.
[16] E. Aryafar, M. A. Khojastepour, K. Sundaresan, S. Rangarajan, and M. Chiang, “MIDU: Enabling MIMO full
 duplex,” in Proceedings of the 18th annual international conference on Mobile computing and networking.
 ACM, 2012, pp. 257–268.
[17] E. Everett, A. Sahai, and A. Sabharwal, “Passive self-interference suppression for full-duplex infrastructure
 nodes,” IEEE Transactions on Wireless Communications, vol. 13, no. 2, pp. 680–694, 2014.
[18] B. C. Nguyen and X. N. Tran, “Performance analysis of full-duplex amplify-and-forward relay system with
 hardware impairments and imperfect self-interference cancellation,” Wireless Communications and Mobile
 Computing, vol. 2019, 2019.
[19] D. Bharadia, E. McMilin, and S. Katti, “Full duplex radios,” in ACM SIGCOMM Computer Communication
 Review, vol. 43. ACM, 2013, Conference Proceedings, pp. 375–386.
[20] B. C. Nguyen, X. N. Tran, T. M. Hoang et al., “Performance analysis of full-duplex vehicle-to-vehicle relay
 system over double-rayleigh fading channels,” Mobile Networks and Applications, pp. 1–10, 2019.
[21] R. Rajashekar, K. Hari, and L. Hanzo, “Antenna selection in spatial modulation systems,” IEEE Communications
 Letters, vol. 17, no. 3, pp. 521–524, 2013.
[22] A. Leon-Garcia and A. Leon-Garcia, Probability, statistics, and random processes for electrical engineering.
 Pearson/Prentice Hall 3rd ed. Upper Saddle River, NJ, 2008.
[23] A. Goldsmith, Wireless communications. Cambridge university press, 2005.
[24] H. Cui, M. Ma, L. Song, and B. Jiao, “Relay selection for two-way full duplex relay networks with amplify-
 and-forward protocol,” IEEE Transactions on Wireless Communications, vol. 13, no. 7, pp. 3768–3777, July
 2014.
[25] P. Yang, M. Di Renzo, Y. Xiao, S. Li, and L. Hanzo, “Design guidelines for spatial modulation,” IEEE
 Communications Surveys Tutorials, vol. 17, no. 1, pp. 6–26, Firstquarter 2015.
[26] A. Jeffrey and D. Zwillinger, Table of integrals, series, and products. Academic press, 2007.
[27] Z. Zhang, Z. Ma, Z. Ding, M. Xiao, and G. K. Karagiannidis, “Full-duplex two-way and one-way relaying:
 Average rate, outage probability, and tradeoffs,” IEEE Transactions on Wireless Communications, vol. 15, no. 6,
 pp. 3920–3933, June 2016.
[28] T. M. C. Chu and H. Zepernick, “On capacity of full-duplex cognitive cooperative radio networks with optimal
 power allocation,” in 2017 IEEE Wireless Communications and Networking Conference (WCNC), March 2017,
 pp. 1–6.
 Manuscript received 30-7-2019; Accepted 18-12-2019.
 
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Section on Information and Communication Technology (ICT) - No. 14 (10-2019)
 Nguyen Le Van was born in Vinh Phuc, Vietnam, in 1985. She received the B.E. degree in
 Electronic and Telecommunication Engineering in 2008, and the M.E. degree in Electronics
 Engineering in 2010, both from Le Quy Don Technical University, Hanoi, Vietnam. Since
 October 2015, she has been working toward her Ph.D degree at Le Quy Don Technical
 University. Her current research interests include MIMO, spatial modulation, in-band full-
 duplex, and signal processing for wireless communication systems.
 Nguyen Ba Cao was born in Nghe An, Vietnam. He received the B.S. in 2006 in Telecom-
 munication University and M.S. in 2011 in Posts and Telecommunications, Institute of Tech-
 nology, (VNPT), Vietnam. He is currently pursuing the Ph.D degree at Le Quy Don Technical
 University, Hanoi, Vietnam. His research interests include energy harvesting, full-duplex, and
 cooperative communication.
 Tran Xuan Nam is currently an Associate Professor at Department of Communications
 Engineering, Le Quy Don Technical University, Vietnam. He received his master of engineering
 (ME) in telecommunications engineering from University of Technology Sydney, Australia in
 1998, and doctor of engineering in electronic engineering from The University of Electro -
 Communications, Japan in 2003. From November 2003 to March 2006 he was a research
 associate at the Information and Communication Systems Group, Department of Information
 and Communication Engineering, The University of Electro - Communications, Tokyo, Japan.
 His research interests are in the areas of adaptive antennas, space-time processing, space-time
 coding and MIMO systems. He is a recipient of the 2003 IEEE AP-S Japan Chapter Young
 Engineer Award. He is a member of IEEE, IEICE, and the Radio-Electronics Association of
 Vietnam. 
62
 Journal of Science and Technique - Le Quy Don Technical University - No. 202 (10-2019)
 PHÂN TÍCH PHẨM CHẤT MẠNG GIẢI MÃ
 VÀ CHUYỂN TIẾP SONG CÔNG TRÊN CÙNG BĂNG
TẦN SỬ DỤNG KỸ THUẬT ĐIỀU CHẾ KHÔNG GIAN
 Tóm tắt
 Bài báo này đánh giá phẩm chất và dung lượng mạng chuyển tiếp song công trên cùng
 băng tần (IBFD: In-Band Full-Duplex) sử dụng kỹ thuật điều chế không gian (SM: Spatial
 Modulation) trong trường hợp triệt nhiễu tự giao thoa (SIC: Self-Interference Cancellation)
 không hoàn hảo. Bằng phương pháp giải tích, chúng tôi tìm ra biểu thức chính xác về xác
 suất dừng (OP: Outage Probability), xác suất lỗi ký hiệu (SEP: Symbol Error Probability) và
 dung lượng trung bình (Ergodic capacity) của mạng chuyển tiếp SM-FD qua kênh pha-đinh
 Rayleigh. Từ đó đánh giá được ảnh hưởng của nhiễu dư (RSI: Residual Self-Interference),
 số lượng ăng-ten thu và tốc độ truyền dẫn đến phẩm chất và dung lượng hệ thống khi so
 sánh với mạng chuyển tiếp SM bán song công (HD: Half-Duplex). Cuối cùng, mô phỏng
 Monte-Carlo được sử dụng để kiểm chứng kết quả phân tích.
 63