Combining power allocation and superposition coding for an underlay two-way decode-and-forward scheme

B) when Ψ2 = 10 (dB), 
 1 system performance of the proposed SIC-SC 
 Ψ3 = 1 (dB), Ψ4 = 1 (dB), Ψ5 = 0.5 (dB), 1 0 . 3, protocol outperforms that of the RRS protocol 
 234 0.7,0.4,0.6 , N = 8, Q = 10 (dB) and in terms of the outage probabilities. 
  6 10(dB),5(dB)  . 
 Appendix A: Proof of Lemma 1 
 Substituting (7) into the probability of as 
5. Conclusions 1
 in (9), the 1 is expressed as 
 In this paper, we analyzed the underlay 1
 Pr log 1  R
 12 SRn sth1 
two-way DF scheme in which the secondary 2
relays use the SIC technology to decode the 2R
 Pr21  th
data of two secondary sources sequentially, and SRn s1
  Qgg
then make a coded signal by the SC technology, 5 SS12 SRn SS PR
  Qgggg  
known as the SIC-SC protocol. The SIC-SC Pr 445 SS2112 SRn SS PRSS PR SS PR 
protocol was designed to operate in two time 2Rth
 21
slots under effects from the interference 
 2Rth
 ggSS SRSS SR 21  4
constraint of the primary receiver and residual 12nn 
 gg
interference of the imperfect SIC processes. SS12 PRSS PR 5
 
Transmit powers provided to carry the data Pr 1
 2Rth
were allocated dynamically according to 21 45  
channel powers of interference and 
 5Q
transmission. The secondary relay was selected (A.1) 
 2
from considering strongest channel gain subject 
to increase decoding capacity of the first data fxgggg Fxdx 12 ,
 SS2211 SRnn SS PRSS SR SS PR
and decrease collection time of the CSIs. The 0
 where fx are Fx are the 
identical underlay two-way DF operation with ggXY ggXY 
the random relay selection and the fixed power PDF and CDF of the RVs gg, 
allocations (called the RRS protocol) was also XY
investigated to compare the proposed SIC-SC XY,SS ,SS 12 ,SR ,PR n  , nN 1,2,...,  . 
protocol. The closed-form outage probability By referring from [29] (see equations 
expressions were derived from mathematical 
 (24–25)), the fxgg is obtained as 
manipulations and verified exactly by SS22 SRSSn PR
12 P.N. Son et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 37, No. 1 (2021) 1-15 
 Fxgg 411 pp , the Lemma 1 is proven 
 SS22 SRSSn PR
 fxgg 
 SS22 SRSSn PR x completely. 
 (A.2) 
 25
 2 . Appendix B: Proof of Lemma 2 
  25  x 
 From (8) and (A.1), the probability 2 as in 
 The Fxgg is expressed as 
 SSSRSSPR11n (9) is expressed as 
 g 5QggSS SRSS PR
 Fxx Pr SS1 SRn 12n
 ggSS SRSS PR  Qgggg   
 11n g 445 SS2112 SRSSn PRSS PR SS PR
 SS1 PR 
 Pr 2Rth
 2 21
 Pr gxgSS SRSS PR (A.3) 1
 11n  log1  R
 2 SRsthn 2 
 2
 fyFxydygg , ggSS SRSS SR1
 SS11 PRSS SR n 12nn  
 0 gg 2
 SS12 PRSS PR 
 Pr 
 where Fxg is the CDF of the RV 
 SSSR1 n PgSSSS SR 2R
  22n 21th
 2
 g and is expressed as (see the equation  I hNn 0 
 S S1 S R n
 gg
(7–14) in [24]) SS12 SRSSnn SR 1
  2
 N gg
 N p p SS12 PRSS PR
  xpx 11(A.4) 
 Fxeeg 11. 
 SS1 SRn  g
 p 0 N Pr. SS2 SRn 2R
    21th Q 
 g 454 
 SS2 PR
 p 
 In (A.4), denotes the binomial 5 (B.1) 
 N    212Rth g
 454 n
 p N! To solve the in (B.1) by closed-form 
coefficient . 2
 N pNp!! expressions, we consider two cases of perfect 
 Then, the Fxgg is solved as SICs  0 and imperfect SICs  1 as 
 SS11 SRSSn PR 
 y N
 e 4 p p follows. 
 Fxedy 1 py 1
 ggSS SRSS PR  
 11n  N - Perfect SICs ( 0 ): By referring from 
 0 4 p 0 (A.5) 
 (A.2) and using (A.5), the 2 is obtained as 
 N p 1 p
 5
 1  .
 N 212 fxFxdxgggg 1  
 p 0 14  px SS2211 SRnn SS PRSS SR SS PR 
 0
 Substituting (A.2) and (A.5) into (A.1), the 
 Fgg 5 
 is manipulated equivalently as SS22 SRn SS PR (B.2) 
 1 5
 p
 N fxgggg Fxdx 12 
 25 p 1 SS2211 SRnn SS PRSS SR SS PR
 11  dx 0
 2  N   px
 0 25  x p 0 14 12 N
 (A.6) 55 p p
    1 2 5  1 
 N p N
 p 1 dx 25 5   p 0 
 1  2  5 . 
  N 2 5 dx
 p 0 0 14 24ppxx  125   .
 2
 0  ppxx    
 By performing variable transformations as 14 24 12 55 2
 Also performing as (A.6), 2 is solved as in 
 1  p  p y
 yx   and 5 3 2 4 
 25 xp 4 Lemma 2 with the case  0 . 
 25
 - Imperfect SICs ( 1): The 2 in this 
, where 3 pp  1  4 2  1  4 and 
 case ( 1) is presented as 
 P.N. Son et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 37, No. 1 (2020) 1-15 13 
 5 1 Qx [4] T.M.C. Chu, H. Zepernick, Performance 
 212 fxFyggg 1  Optimization for Hybrid Two-Way Cognitive 
 nSS SRSS PR 11n 
 00 Cooperative Radio Networks With Imperfect 
 fydydxgg Spectrum Sensing, IEEE Access 6 (2018) 70582-
 SS22 SRSSn PR
 70596. https://doi.org/10.1109/ICC.2007.121. 
 x 6
 e  55 1 Qx 
 [5] K. Ho-Van, T. Do-Dac, Security Analysis for 
    1 Qx
 0 6255 Underlay Cognitive Network with Energy-
 p
 1 N p 1 Scavenging Capable Relay over Nakagami-m 
  Fading Channels, Wireless Communications and 
  p 0  N  pp 
 45324 Mobile Computing 2019 1-16. https://doi.org/ 
  1 Qxp 2  10.1155/2019/5080952. 
 55254 
  2555324    1 Qxpp [6] X. Zhang, Z. Zhang, J. Xing, R. Yu, P. Zhang, W. 
 dx. Wang, Exact Outage Analysis in Cognitive Two-
  2553   1 Qxp 
 ln Way Relay Networks With Opportunistic Relay 
  pQxp 1 
 2354  (B.3) Selection Under Primary User’s Interference, IEEE 
 Transactions on Vehicular Technology 64(6) (2015) 
 ln 
 By extending , changing varibables 2502-2511. https://doi.org/10.1109/ 
and then solving the integrals in (B.3), the TVT.2014.2346615. 
 [7] T.T. Duy, H.Y. Kong, Exact outage probability of 
probability 2 is answered as in Lemma 2 with 
 cognitive two-way relaying scheme with 
the remaining case  1. Hence, the Lemma 2 opportunistic relay selection under interference 
is verified commpletely. constraint, IET Communications 6(16) (2012), 2750-
 2759. https://doi.org/ 10.1049/iet-com. 2012.0235. 
Acknowledgments [8] H.V. Toan, V.N.Q. Bao, Opportunistic relaying for 
 cognitive two-way network with multiple primary 
 This research is funded by Vietnam receivers over Nakagami-m fading, presented at 
National Foundation for Science and 2016 International Conference on Advanced 
Technology Development (NAFOSTED) under Technologies for Communications (ATC), Hanoi 
 city, 2016, 141-146. 
grant number 102.04-2019.13. Khuong Ho-Van https://doi.org/10.1109/ATC.2016.7764762. 
acknowledges the support of time and facilities [9] H.V. Toan, V.N.Q. Bao, H. Nguyen-Le, Cognitive 
from Ho Chi Minh City University of two-way relay systems with multiple primary 
Technology (HCMUT), VNU-HCM, for receivers: exact and asymptotic outage formulation, 
this study. IET Communications 11(16) (2017), 2490-2497. 
 https://doi.org/10.1049/iet-com.2017. 0400. 
 [10] H.V.Toan, V.N.Q. Bao, K.N. Le, Performance 
References analysis of cognitive underlay two-way relay 
 networks with interference and imperfect channel 
 [1] P. Popovski, H. Yomo, Physical Network Coding in state information, EURASIP Journal on Wireless 
 Two-Way Wireless Relay Channels, presented at Communications and Networking 2018 53 (2018). 
 2007 IEEE International Conference on https://doi.org/10.1186/s13638-018-1063-z. 
 Communications (ICC), Glasgow, 2007, 707-712. [11] S. Solanki, P.K. Sharma, P.K. Upadhyay, Adaptive 
 https://doi.org/10.1109/ICC.2007.121. Link Utilization in Two-Way Spectrum Sharing 
 [2] Z. Cao, X. Ji, J. Wang, S. Zhang, Y. Ji, J. Wang, Relay Systems Under Average Interference 
 Security-Reliability Tradeoff Analysis for Underlay Constraints, IEEE Systems Journal 12(4) (2018), 
 Cognitive Two-Way Relay Networks, IEEE 3461-3472. https://doi.org/10.1109/ 
 Transactions on Wireless Communications 18(12) JSYST.2017.2713887. 
 (2019) 6030-6042. https://doi.org/10.1109/ [12] X. Yue, Y. Liu, S. Kang, A. Nallanathan, Y. Chen, 
 TWC.2019.2941944. Modeling and Analysis of Two-Way Relay Non-
 [3] J. Mitola, G.Q. Maguire, Cognitive radio: making Orthogonal Multiple Access Systems, IEEE 
 software radios more personal, IEEE Personal Transactions on Communications 66(9) (2018), 
 Communications 6(4) (1999) 13-18. https://doi. org 3784-3796. https://doi.org/10.1109/TCOMM. 
 /10.1109/98.788210. 2018.2816063. 
14 P.N. Son et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 37, No. 1 (2021) 1-15 
[13] X. Zou, B. He, H. Jafarkhani, An Analysis of E98-B(4) (2015), 661-672. 
 TwoUser Uplink Asynchronous Non-orthogonal https://doi.org/10.1587/transcom.E98.B.661. 
 Multiple Access Systems, IEEE Transactions on [23] K. Tourki, K.A. Qaraqe, M. Alouini, Outage 
 Wireless Communications 18(2) (2019), 1404-1418. Analysis for Underlay Cognitive Networks Using 
 https://doi.org/10.1109/TWC.2019.2892486 Incremental Regenerative Relaying, IEEE 
[14] Z. Yang, Z. Ding, P. Fan, N. Al-Dhahir, The Impact Transactions on Vehicular Technology 62(2) (2013) 
 of Power Allocation on Cooperative Nonorthogonal 721-734. https://doi.org/10.1109/TVT. 
 Multiple Access Networks With SWIPT, IEEE 2012.2222947. 
 Transactions on Wireless Communications 16(7) [24] A. Papoulis, S.U. Pillai, Probability, random 
 (2017), 4332-4343. variables and stochastic processes, 4th ed., 
 https://doi.org/10.1109/TWC.2017.2697380. McGrawHill, New York, 2002. 
[15] P.N. Son, T.T. Duy, K. Ho-Van, SIC-Coding [25] L. Pei, T. Zhifeng, L. Zinan, E. Erkip, S. Panwar, 
 Schemes for Underlay Two-Way Relaying Cooperative wireless communications: a cross-layer 
 Cognitive Networks, Wireless Communications and approach, IEEE Wireless Communications 13(4) 
 Mobile Computing 2020 1-24. https://doi.org/ (2006) 84-92. https://doi.org/10.1109/ 
 10.1155/2020/8860551. MWC.2006.1678169. 
[16] M.F. Kader, M.B. Shahab, S.Y. Shin, Exploiting [26] A. Ghasemi, E.S. Sousa, Fundamental limits of 
 Non-Orthogonal Multiple Access in Cooperative spectrum-sharing in fading environments, IEEE 
 Relay Sharing, IEEE Communications Letters 21(5) Transactions on Wireless Communications 6(2) 
 (2017) 1159-1162. https://doi.org/ (2007) 649-658. https://doi.org/10.1109/TWC. 
 10.1109/LCOMM.2017.2653777. 2007.05447. 
[17] X. Yue, Y. Liu, S. Kang, A. Nallanathan, Z. Ding, [27] J. M. Peha, Approaches to spectrum sharing, IEEE 
 Spatially Random Relay Selection for Full/Half- Communications Magazine 43(2) (2005) 10-12. 
 Duplex Cooperative NOMA Networks, IEEE https://doi.org/10.1109/MCOM.2005. 1391490. 
 Transactions on Communications 66(8) (2018) [28] H. Kim, S. Lim, H. Wang, D. Hong, Optimal Power 
 3294-3308. https://doi.org/10.1109/TCOMM. Allocation and Outage Analysis for Cognitive Full 
 2018.2809740. Duplex Relay Systems, IEEE Transactions on 
[18] Y. Liu, Z. Ding, M. Elkashlan, J. Yuan, Wireless Communications 11(10) (2012) 3754-3765. 
 Nonorthogonal Multiple Access in Large-Scale https://doi.org/10.1109/TWC. 2012.083112.120127. 
 Underlay Cognitive Radio Networks, IEEE [29] P.N. Son, T.T. Duy, Performance analysis of 
 Transactions on Vehicular Technology 65(12) underlay cooperative cognitive full-duplex networks 
 (2016) 10152-10157. https://doi.org/10.1109/ with energy-harvesting relay, Computer 
 TVT.2016.2524694. Communications 122 (2018) 9-19. https://doi.org/ 
[19] Y. Song, W. Yang, Z. Xiang, N. Sha, H. Wang, Y. 10.1016/j.comcom.2018.03.003. 
 Yang, An Analysis on Secure Millimeter Wave [30] T.V. Nguyen, T. Do, V.N.Q. Bao, D.B.d. Costa, B. 
 NOMA Communications in Cognitive Radio An, On the Performance of Multihop Cognitive 
 Networks, IEEE Access 8 (2020), 78965-78978. Wireless Powered D2D Communications in WSNs, 
 https://doi.org/10.1109/ACCESS.2020.2989860. IEEE Transactions on Vehicular Technology 69(3) 
[20] X. Ding, T. Song, Y. Zou, X. Chen, L. Hanzo, (2020) 2684-2699. 
 Security-Reliability Tradeoff Analysis of Artificial https://doi.org/10.1109/TVT.2020.2963841. 
 Noise Aided Two-Way Opportunistic Relay [31] Y. Ruan, Y. Li, C. Wang, R. Zhang, H. Zhang, 
 Selection, IEEE Transactions on Vehicular Energy Efficient Power Allocation for Delay 
 Technology 66(5) (2017) 3930-3941. Constrained Cognitive Satellite Terrestrial Networks 
 https://doi.org/10.1109/TVT.2016.2601112. Under Interference Constraints, IEEE Transactions 
[21] B. Zheng, M. Wen, F. Chen, J. Tang, F. Ji, Secure on Wireless Communications 18(10) (2019) 4957-
 NOMA Based Full-Duplex Two-Way Relay 4969. https://doi.org/10.1109/TWC. 2019.2931321. 
 Networks with Artificial Noise against [32] H. Gao, S. Zhang, Y. Su, M. Diao, M. Jo, Joint 
 Eavesdropping, presented at 2018 IEEE International Multiple Relay Selection and Time Slot Allocation 
 Conference on Communications (ICC), Kansas City, Algorithm for the EH-Abled Cognitive Multi-User 
 2018, 1-6. https://doi.org/ Relay Networks, IEEE Access 7 (2019) 111993- 
 10.1109/ICC.2018.8422946. 112007. https://doi.org/10.1109/ 
[22] P.N. Son, H.Y. Kong, Exact Outage Analysis of ACCESS.2019.2932955. 
 Energy Harvesting Underlay Cooperative Cognitive 
 Networks, IEICE Transactions on Communications 
 P.N. Son et al. / VNU Journal of Science: Comp. Science & Com. Eng., Vol. 37, No. 1 (2020) 1-15 15 
[33] H. Arezumand, H. Zamiri-Jafarian, E. Soleimani- Networks, Wireless Communications and Mobile 
 Nasab, Exact and Asymptotic Analysis of Partial Computing 2019 1-7. 
 Relay Selection for Cognitive RF-FSO Systems https://doi.org/10.1155/2019/1839256. 
 With Non-Zero Boresight Pointing Errors, IEEE [37] A.A. Nasir, Z. Xiangyun, S. Durrani, R.A. Kennedy, 
 Access 7 (2019) 58611-58625. https://doi.org/ Relaying Protocols for Wireless Energy Harvesting 
 10.1109/ACCESS.2019.2914480. and Information Processing, IEEE Transactions on 
[34] P.N. Son, H.Y. Kong, Energy-Harvesting Relay Wireless Communications 12(7) (2013) 3622-3636. 
 Selection Schemes for Decode-and-Forward Dual- https://doi.org/10.1109/TWC. 2013.062413.122042. 
 Hop Networks, IEICE TRANSACTIONS on [38] R.I. Gradshteyn, I.M. Ryzhik, A.Jeffrey, D. 
 Communications E98-B(12) (2015) 2485-2495. Zwillinger, Table of integral, series and products, 7th 
 https://doi.org/10.1587/transcom.E98.B.2485. ed., Elsevier, Amsterdam, 2007. 
[35] T.N. Nguyen, T.H. Quang Minh, P.T. Tran, M. [39] H. Haiyan, L. Zan, S. Jiangbo, G. Lei, Underlay 
 Voznak, T.T. Duy, T.-L. Nguyen, P.T. Tin, cognitive relay networks with imperfect channel 
 Performance enhancement for energy harvesting state information and multiple primary receivers, 
 based two-way relay protocols in wireless ad-hoc IET Communications 9(4) (2015) 460-467. 
 networks with partial and full relay selection https://doi.org/10.1049/iet-com.2014.0429. 
 methods, Ad Hoc Networks 84 (2019) 178-187. [40] B. Zhong, Z. Zhang, Opportunistic Two-Way Full-
 https://doi.org/10.1016/j.adhoc.2018.10.005. Duplex Relay Selection in Underlay Cognitive 
[36] L. Pan, Z. Li, Z. Wang, F. Zhang, Joint Relay Networks, IEEE Systems Journal 12(1) (2018) 725-
 Selection and Power Allocation for the Physical 734. https://doi.org/10.1109/JSYST. 2016.2514601. 
 Layer Security of Two-Way Cooperative Relaying 
I