Exact secure outage probability performance of uplinkdownlink multiple access network under imperfect CSI
•
0 likes•27 views
In this paper, we study uplink-downlink non-orthogonal multiple access (NOMA) systems by considering the secure performance at the physical layer. In the considered system model, the base station acts a relay to allow two users at the left side communicate with two users at the right side. By considering imperfect channel state information (CSI), the secure performance need be studied since an eavesdropper wants to overhear signals processed at the downlink. To provide secure performance metric, we derive exact expressions of secrecy outage probability (SOP) and and evaluating the impacts of main parameters on SOP metric. The important finding is that we can achieve the higher secrecy performance at high signal to noise ratio (SNR). Moreover, the numerical results demonstrate that the SOP tends to a constant at high SNR. Finally, our results show that the power allocation factors, target rates are main factors affecting to the secrecy performance of considered uplink-downlink NOMA systems.
Report
Share
![Bulletin of Electrical Engineering and Informatics
Vol. 10, No. 6, December 2021, pp. 3274∼3281
ISSN: 2302-9285, DOI: 10.11591/eei.v10i6.2981 r 3274
Exact secure outage probability performance of uplink-
downlink multiple access network under imperfect CSI
Dinh-Thuan Do, Minh-Sang Van Nguyen
Department of Electronics and Communications, Faculty of Electronics Technology, Industrial University of Ho Chi Minh
City (IUH), Vietnam
Article Info
Article history:
Received Mar 18, 2021
Revised Aug 6, 2021
Accepted Oct 13, 2021
Keywords:
Channel state information
Non-orthogonal multiple
access
Secure performance
ABSTRACT
In this paper, we study uplink-downlink non-orthogonal multiple access (NOMA) sys-
tems by considering the secure performance at the physical layer. In the considered
system model, the base station acts a relay to allow two users at the left side commu-
nicate with two users at the right side. By considering imperfect channel state infor-
mation (CSI), the secure performance need be studied since an eavesdropper wants to
overhear signals processed at the downlink. To provide secure performance metric,
we derive exact expressions of secrecy outage probability (SOP) and and evaluating
the impacts of main parameters on SOP metric. The important finding is that we can
achieve the higher secrecy performance at high signal to noise ratio (SNR). Moreover,
the numerical results demonstrate that the SOP tends to a constant at high SNR. Fi-
nally, our results show that the power allocation factors, target rates are main factors
affecting to the secrecy performance of considered uplink-downlink NOMA systems.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Dinh-Thuan Do
Department of Electronics and Communications, Faculty of Electronics Technology
Industrial University of Ho Chi Minh City (IUH)
Ho Chi Minh City 700000, Vietnam
Email: dodinhthuan@iuh.edu.vn
1. INTRODUCTION
Due to high demands in terms of system capacity and spectrum efficiency, the traditional orthogonal
multiple access (OMA) has been unable to meet the user needs associated with the rapid growth of internet
of things (IoT) and mobile communications [1]–[7]. In order to meet the heavy demand for mobile services,
non-orthogonal multiple access (NOMA) is researched in recent years with promising applications [8], [9].
In some scenarios, NOMA benefits to device-to-device communications [10], [11] and cognitive radio (CR)-
aided NOMA [12]-[14] and these are considered as potential key technologies for the fifth generation mobile
communications (5G). The authors Do, et al. in [13] studied the secondary network of the considered CR-
NOMA by enabling the relaying scheme. In such network, the secondary transmitter is able to conduct energy
harvesting (EH) to perform signal forwarding to distant secondary users. Two main metrics including outage
behavior and throughput performance are studied in the context of EH-assisted CR-NOMA while imperfect
successive interference cancellation (SIC) is considered. Reference Do, et al. [14] presented relay-aided CR-
NOMA networks to improve the performance of far users by enabling partial relay selection architecture. They
explored system performance in terms of full-duplex (FD) and half duplex (HD) relays for both uplink and
downlink communications.
Recently, an alternative approach is enabled to conduct cryptography at physical layer security (PLS)
Journal homepage: http://beei.org](https://cdn.statically.io/img/image.slidesharecdn.com/372981-220128013423/85/Exact-secure-outage-probability-performance-of-uplinkdownlink-multiple-access-network-under-imperfect-CSI-1-320.jpg)
![Bulletin of Electr Eng & Inf ISSN: 2302-9285 r 3275
has considered. This method is more advanced due to complications of secure techniques applied at higher
layers in existing RFID systems. To aim to decrease chance of eavesdroppers getting information from the
legal transmitter, the wireless channel characteristics is utilized to PLS-based system act relevant approach to
against eavesdroppers’ overhearing operations. The authors in [15]-[20] studied PLS applied for a 5G NOMA
system. The authors in [15] explored the two-user case and then extend our results to a multi-user case. The
main results indicated that the given users’ data rate corresponds to positive secrecy rate. The PLS of millimeter
wave (mmWave) NOMA networks was studied for mmWave channels in [16] by examining imperfect CSI at
receivers and the limited scattering characteristics of concerned channels. the formula of the secrecy outage
probability (SOP) was derived since the system adopts random distributions of legitimate users and eavesdrop-
pers. While [15], [16] presented NOMA downlink scenario, the authors in [18] investigated uplink secure
NOMA system. The typical system including one base station, one eavesdropper and multiple users. However,
there is lack of work considering secure performance of uplink-downlink NOMA system under imperfect CSI
circumstance, which motive us to study secure outage probability in this article.
2. SYSTEM MODEL
In this system model, we consider uplink-downlink of two pairs of source-destination S1−D1, S2−D2
under existence of eavesdropper E, shown in Figure 1. The flat slow Rayleigh fading is assumed for all links
and the channel coefficients pertaining to the links S1 → R, S2 → R, R → D1, R → D2 and R → E
are denoted as g1r, g2r, gd1, gd2 and ge, respectively. Accordingly, the corresponding channel power gains
conform to |g1r|
2
∼ CN (0, λ1r), |g2r|
2
∼ CN (0, λ2r), |gd1|
2
∼ CN (0, λd1), |gd2|
2
∼ CN (0, λd2) and
|ge|
2
∼ CN (0, λe), respectively.
Figure 1. System model
Two sources sends their signals to the relay R in the same time. In particular, the received signal at R
can be expressed as [21].
yS−R = (g1r + h1r)
p
a1Ps1z1 + (g2r + h2r)
p
a2Ps2z2 + nr, (1)
where Psi represents the transmit power at Si; nr is denoted as the variance of the additive white Gaussian
noise (AWGN) at R with nr ∼ CN (0, N0); zi is the signal of Di; ai are the power allocation coefficients of
zi transmitted signals with a1 + a2 = 1 and assuming that a1 > a2; hir is the error term related to imperfect
CSI, which follow a complex Gaussian distributed random variable with CN 0, σ2
hi
. In this circumstance,
σ2
hi is assumed as constant [22].
With regard to higher priority, the relay always first decodes z1 by considering z2 as noise. Following
NOMA principle, the system can performs SIC to decode z2. To further compute system performance metric,
we first calculaye the received signal-to-interference-plus-noise ratio (SINR) for symbol z1. Then, we can
Exact secure outage probability performance of uplink-downlink multiple access network ... (Dinh-Thuan Do)](https://cdn.statically.io/img/www.slideshare.net/data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Recommended for you
More Related Content
What's hot
What's hot (20)
Similar to Exact secure outage probability performance of uplinkdownlink multiple access network under imperfect CSI
Similar to Exact secure outage probability performance of uplinkdownlink multiple access network under imperfect CSI (20)
More from journalBEEI
More from journalBEEI (20)
Recently uploaded
Recently uploaded (20)
Exact secure outage probability performance of uplinkdownlink multiple access network under imperfect CSI
- 1. Bulletin of Electrical Engineering and Informatics Vol. 10, No. 6, December 2021, pp. 3274∼3281 ISSN: 2302-9285, DOI: 10.11591/eei.v10i6.2981 r 3274 Exact secure outage probability performance of uplink- downlink multiple access network under imperfect CSI Dinh-Thuan Do, Minh-Sang Van Nguyen Department of Electronics and Communications, Faculty of Electronics Technology, Industrial University of Ho Chi Minh City (IUH), Vietnam Article Info Article history: Received Mar 18, 2021 Revised Aug 6, 2021 Accepted Oct 13, 2021 Keywords: Channel state information Non-orthogonal multiple access Secure performance ABSTRACT In this paper, we study uplink-downlink non-orthogonal multiple access (NOMA) sys- tems by considering the secure performance at the physical layer. In the considered system model, the base station acts a relay to allow two users at the left side commu- nicate with two users at the right side. By considering imperfect channel state infor- mation (CSI), the secure performance need be studied since an eavesdropper wants to overhear signals processed at the downlink. To provide secure performance metric, we derive exact expressions of secrecy outage probability (SOP) and and evaluating the impacts of main parameters on SOP metric. The important finding is that we can achieve the higher secrecy performance at high signal to noise ratio (SNR). Moreover, the numerical results demonstrate that the SOP tends to a constant at high SNR. Fi- nally, our results show that the power allocation factors, target rates are main factors affecting to the secrecy performance of considered uplink-downlink NOMA systems. This is an open access article under the CC BY-SA license. Corresponding Author: Dinh-Thuan Do Department of Electronics and Communications, Faculty of Electronics Technology Industrial University of Ho Chi Minh City (IUH) Ho Chi Minh City 700000, Vietnam Email: dodinhthuan@iuh.edu.vn 1. INTRODUCTION Due to high demands in terms of system capacity and spectrum efficiency, the traditional orthogonal multiple access (OMA) has been unable to meet the user needs associated with the rapid growth of internet of things (IoT) and mobile communications [1]–[7]. In order to meet the heavy demand for mobile services, non-orthogonal multiple access (NOMA) is researched in recent years with promising applications [8], [9]. In some scenarios, NOMA benefits to device-to-device communications [10], [11] and cognitive radio (CR)- aided NOMA [12]-[14] and these are considered as potential key technologies for the fifth generation mobile communications (5G). The authors Do, et al. in [13] studied the secondary network of the considered CR- NOMA by enabling the relaying scheme. In such network, the secondary transmitter is able to conduct energy harvesting (EH) to perform signal forwarding to distant secondary users. Two main metrics including outage behavior and throughput performance are studied in the context of EH-assisted CR-NOMA while imperfect successive interference cancellation (SIC) is considered. Reference Do, et al. [14] presented relay-aided CR- NOMA networks to improve the performance of far users by enabling partial relay selection architecture. They explored system performance in terms of full-duplex (FD) and half duplex (HD) relays for both uplink and downlink communications. Recently, an alternative approach is enabled to conduct cryptography at physical layer security (PLS) Journal homepage: http://beei.org
- 2. Bulletin of Electr Eng & Inf ISSN: 2302-9285 r 3275 has considered. This method is more advanced due to complications of secure techniques applied at higher layers in existing RFID systems. To aim to decrease chance of eavesdroppers getting information from the legal transmitter, the wireless channel characteristics is utilized to PLS-based system act relevant approach to against eavesdroppers’ overhearing operations. The authors in [15]-[20] studied PLS applied for a 5G NOMA system. The authors in [15] explored the two-user case and then extend our results to a multi-user case. The main results indicated that the given users’ data rate corresponds to positive secrecy rate. The PLS of millimeter wave (mmWave) NOMA networks was studied for mmWave channels in [16] by examining imperfect CSI at receivers and the limited scattering characteristics of concerned channels. the formula of the secrecy outage probability (SOP) was derived since the system adopts random distributions of legitimate users and eavesdrop- pers. While [15], [16] presented NOMA downlink scenario, the authors in [18] investigated uplink secure NOMA system. The typical system including one base station, one eavesdropper and multiple users. However, there is lack of work considering secure performance of uplink-downlink NOMA system under imperfect CSI circumstance, which motive us to study secure outage probability in this article. 2. SYSTEM MODEL In this system model, we consider uplink-downlink of two pairs of source-destination S1−D1, S2−D2 under existence of eavesdropper E, shown in Figure 1. The flat slow Rayleigh fading is assumed for all links and the channel coefficients pertaining to the links S1 → R, S2 → R, R → D1, R → D2 and R → E are denoted as g1r, g2r, gd1, gd2 and ge, respectively. Accordingly, the corresponding channel power gains conform to |g1r| 2 ∼ CN (0, λ1r), |g2r| 2 ∼ CN (0, λ2r), |gd1| 2 ∼ CN (0, λd1), |gd2| 2 ∼ CN (0, λd2) and |ge| 2 ∼ CN (0, λe), respectively. Figure 1. System model Two sources sends their signals to the relay R in the same time. In particular, the received signal at R can be expressed as [21]. yS−R = (g1r + h1r) p a1Ps1z1 + (g2r + h2r) p a2Ps2z2 + nr, (1) where Psi represents the transmit power at Si; nr is denoted as the variance of the additive white Gaussian noise (AWGN) at R with nr ∼ CN (0, N0); zi is the signal of Di; ai are the power allocation coefficients of zi transmitted signals with a1 + a2 = 1 and assuming that a1 > a2; hir is the error term related to imperfect CSI, which follow a complex Gaussian distributed random variable with CN 0, σ2 hi . In this circumstance, σ2 hi is assumed as constant [22]. With regard to higher priority, the relay always first decodes z1 by considering z2 as noise. Following NOMA principle, the system can performs SIC to decode z2. To further compute system performance metric, we first calculaye the received signal-to-interference-plus-noise ratio (SINR) for symbol z1. Then, we can Exact secure outage probability performance of uplink-downlink multiple access network ... (Dinh-Thuan Do)
- 3. 3276 r ISSN: 2302-9285 determine the signal-to-noise (SNR) for symbol z2. In particular, these values are given as, γu z1 = a1ρs1|g1r| 2 a2ρs2|g2r| 2 + a1ρs1σ2 h1 + a2ρs2σ2 h2 + 1 , γu z2 = a2ρs2|g2r| 2 a1ρs1σ2 h1 + a2ρs2σ2 h2 + 1 , (2) where ρs1 = Ps1 N0 , ρs2 = Ps2 N0 whoch represent SNR at sources. Next, the signals received at the destinations can be determined. The relay in the second phase wants to send superimposed signal generated from zi to destinations Di. Therefore, we can achieve the received signal at Di as. yR−Di = (gdi + hdi) p a1Prz1 + p a2Prz2 + ndi (3) where hdi is the error term which is considered as a complex Gaussian distributed random variable with CN 0, σ2 di ; ndi stand for the variance of the additive white Gaussian noise (AWGN) at Di with ndi ∼ CN (0, N0). By processing signals transferred from R, D1 decodes its intended symbol z1 when it treats z2 as noise. Then, we compute corresponding SINR of z1 at D1 as. γd z1 = a1ρr|gd1| 2 a2ρr|gd1| 2 + ρrσ2 d1 + 1 (4) where ρr = Pr N0 . At the other side, user D2 first decodes z1 and then employing SIC to achieve signal z2 . At user D2, SINR of z1 and the SNR of z2 at are expressed respectively by. γd 1→2 = a1ρr|gd2| 2 a2ρr|gd2| 2 + ρrσ2 d2 + 1 , γd z2 = a2ρr|gd2| 2 ρrσ2 d2 + 1 (5) The received signal at E from R can be expressed as. yE = ge p a1Prz1 + p a2Prz2 + ne. (6) After employing the parallel interference cancellation (PIC) scheme, the received SINR at the eaves- dropper to detect Di’s message can be formulated by [23]. γe zi = aiρe|ge| 2 , (7) where ρe = Pr ne . In the next step, the achievable secrecy rates of two pairs of users can be examined. Following (2), (4), and (7), we compute the achievable secrecy rates of S1 − D1 as. χ1 = 1 2 log2 min 1 + γu z1 1 + γe z1 , 1 + γd z1 1 + γe z1 !#+ , (8) where [x] + = max {0, x}. From (2), (5) and (7), the achievable secrecy rates of S2 − D2 is written as. χ2 = 1 2 log2 min 1 + γu z2 1 + γe z2 , 1 + γd 1→2 1 + γe z2 , 1 + γd z2 1 + γe z2 !#+ . (9) In the next section, we intends to examine secure performance metric which relies on secrecy rates obtained in these steps. Bulletin of Electr Eng Inf, Vol. 10, No. 6, December 2021 : 3274 – 3281
- 4. Bulletin of Electr Eng Inf ISSN: 2302-9285 r 3277 3. SECRECY OUTAGE PROBABILITY (SOP) 3.1. SOP for user pair S1 − D1 To evaluate SOP performance, the secrecy outage event S1 − D1 need be known when z1 cannot be securely decoded by R or by D1, the SOP for S1 − D1 can be expressed as [23], [24]. SOPS1 D1 = Pr (χ1 R1) = 1 − Pr min 1+γu z1 1+γe z1 , 1+γd z1 1+γe z1 ≥ γd1 = 1 − Pr 1 + γu z1 1 + γe z1 ≥ γd1 | {z } Ψ1 Pr 1 + γd z1 1 + γe z1 ≥ γd1 ! | {z } Ψ2 . (10) 3.1.1. Proposition 1 The SOP of user pair S1 − D1 is approximated computed as. SOPS1 D1 = 1 + ρs1λ1rη1 γd1 ρeλeλea2ρs2λ2r exp β1β2 − φ1κ1 a1ρs1λ1r Ei (−β1β2) , (11) where φi = γdi −1, γdi = 22Ri , (i = 1, 2), Ri is the target data rate for user Di, κ1 = a1ρs1σ2 h1+a2ρs2σ2 h2+1, κ2 = ρrσ2 d1 + 1, η1 = R ∞ 0 exp − κ2γd1 a1ρex+φ1κ2 (a1−a2φ1−a1a2γd1 ρex)ρrλd1 − x λe dx, β1 = γd1 ρeλeκ1+ρs1λ1r γd1 ρeλea2ρs2 , β2 = φ1a2ρs2 a1ρs1λ1r + 1 λ2r . 3.1.2. Proof From (10), Ψ1 can written by. Ψ1 = Pr 1+γu z1 1+γe z1 ≥ γd1 = Pr γu z1 ≥ φ1 + γd1 γe z1 = Pr |g1r| 2 ≥ φ1a2ρs2|g2r|2 +φ1κ1+γd1 a1ρe|ge|2 (a2ρs2|g2r|2 +κ1) a1ρs1 = R ∞ 0 R ∞ 0 1 − F|g1r|2 γd1 a1ρex(a2ρs2y+κ1)+φ1a2ρs2y+φ1κ1 a1ρs1 f|ge|2 (x)f|g2r|2 (y) dxdy, (12) where φ1 = γd1 −1 and κ1 = a1ρs1σ2 h1+a2ρs2σ2 h2+1. By conveying the Rayleigh distribution with probability density function (PDF) and cumulative density function (CDF) f|X|2 (x) = 1 ϕX exp − x ϕX , F|X|2 (x) = 1 − exp − x ϕX , Ψ1 can be formulated by Ψ1 = R ∞ 0 R ∞ 0 exp − γd1 a1ρex(a2ρs2y+κ1)+φ1a2ρs2y+φ1κ1 a1ρs1λ1r 1 λe exp − x λe 1 λ2r exp − y λ2r dxdy = 1 λe 1 λ2r exp − φ1κ1 a1ρs1λ1r R ∞ 0 R ∞ 0 exp − γd1 ρe(a2ρs2y+κ1) ρs1λ1r + 1 λe x exp − φ1a2ρs2 a1ρs1λ1r + 1 λ2r y ×dxdy = 1 λ2r exp − φ1κ1 a1ρs1λ1r R ∞ 0 ρs1λ1r γd1 ρeλea2ρs2y+γd1 ρeλeκ1+ρs1λ1r exp − φ1a2ρs2 a1ρs1λ1r + 1 λ2r y dxdy. (13) By applying some polynomial expansion manipulations and based on [25] (3.352.4) a5, we obtain Ψ1 as. Ψ1 = − ρs1λ1r γd1 ρeλea2ρs2λ2r exp β1β2 − φ1κ1 a1ρs1λ1r Ei (−β1β2) , (14) where β1 = γd1 ρeλeκ1+ρs1λ1r γd1 ρeλea2ρs2 , β2 = φ1a2ρs2 a1ρs1λ1r + 1 λ2r . Exact secure outage probability performance of uplink-downlink multiple access network ... (Dinh-Thuan Do)
- 5. 3278 r ISSN: 2302-9285 From (10), Ψ2 can written by Ψ2 = Pr 1+γd z1 1+γe z1 ≥ γd1 = Pr γd z1 ≥ φ1 + γd1 γe z1 = Pr |gd1| 2 ≥ κ2γd1 a1ρe|ge|2 +φ1κ2 (a1−a2(φ1+γd1 a1ρe|ge|2 ))ρr = R ∞ 0 1 − F|gd1|2 κ2γd1 a1ρex+φ1κ2 (a1−a2(φ1+γd1 a1ρex))ρr f|ge|2 (x) dx = R ∞ 0 exp − κ2γd1 a1ρex+φ1κ2 (a1−a2φ1−a1a2γd1 ρex)ρrλd1 1 λe exp − x λe dx = 1 λe R ∞ 0 exp − κ2γd1 a1ρex+φ1κ2 (a1−a2φ1−a1a2γd1 ρex)ρrλd1 − x λe dx, (15) where κ2 = ρrσ2 d1 + 1. It completes the proof. 3.2. SOP for S2 − D2 Similar the user pair S1 − D1, we need examine the secrecy outage event for user pair S2 − D2. Several cases are examined such as R cannot detect z2, D2 cannot detect its own message z2 when D1 can detect z1 successfully. As a result, we compute the SOP for user pair S2 − D2 as. SOPS2 D2 = Pr (χ2 R2) = 1 − Pr min 1+γu z2 1+γe z2 , 1+γd 1→2 1+γe z2 , 1+γd z2 1+γe z2 ≥ γd2 = 1 − Pr 1 + γu z2 1 + γe z2 ≥ γd2 | {z } Φ1 Pr 1 + γd 1→2 1 + γe z2 ≥ γd2 | {z } Φ2 Pr 1 + γd z2 1 + γe z2 ≥ γd2 ! | {z } Φ3 . (16) 3.2.1. Proposition 2 The exact SOP for user pair S2 − D2 is calculated by. SOPS2 D2 = 1 − a2ρs2λ2r κ1γd2 a2ρeλe + a2ρs2λ2r a2ρrλd2η2 (κ3γd2 a2ρeλe + a2ρrλd2) λe exp − κ1φ2 a2ρs2λ2r − κ3φ2 a2ρrλd2 , (17) where κ3 = ρrσ2 d2 + 1, η2 = R ∞ 0 exp − κ3(φ2+γd2 a2ρex) (a1−a2φ2−γd2 a2a2ρex)ρrλd2 − x λe dx. 3.2.2. Proof From (16), Φ1 can be calculated as. Φ1 = Pr 1+γu z2 1+γe z2 ≥ γd2 = Pr γu z2 ≥ φ2 + γd2 γe z2 = Pr |g2r| 2 ≥ κ1φ2+κ1γd2 a2ρe|ge|2 a2ρs2 = R ∞ 0 1 − F|g2r|2 κ1φ2+κ1γd2 a2ρex a2ρs2 f|ge|2 (x) dx = 1 λe exp − κ1φ2 a2ρs2λ2r R ∞ 0 exp − κ1γd2 a2ρe a2ρs2λ2r + 1 λe x dx = a2ρs2λ2r κ1γd2 a2ρeλe+a2ρs2λ2r exp − κ1φ2 a2ρs2λ2r , (18) where φ2 = γd2 − 1. Bulletin of Electr Eng Inf, Vol. 10, No. 6, December 2021 : 3274 – 3281
- 6. Bulletin of Electr Eng Inf ISSN: 2302-9285 r 3279 Next, Φ2 can be computed as. Φ2 = Pr 1+γd 1→2 1+γe z2 ≥ γd2 = Pr γd 1→2 ≥ φ2 + γd2 γe z2 = Pr |gd2| 2 ≥ κ3(φ2+γd2 a2ρe|ge|2 ) (a1−a2φ2−γd2 a2a2ρe|ge|2 )ρr = R ∞ 0 1 − F|gd2|2 κ3(φ2+γd2 a2ρex) (a1−a2φ2−γd2 a2a2ρex)ρr f|ge|2 (x) dx = 1 λe R ∞ 0 exp − κ3(φ2+γd2 a2ρex) (a1−a2φ2−γd2 a2a2ρex)ρrλd2 − x λe dx, (19) where κ3 = ρrσ2 d2 + 1. Using result from (16), Φ3 is expressed by. Φ3 = Pr 1+γd z2 1+γe z2 ≥ γd2 = Pr γd z2 ≥ φ2 + γd2 γe z2 = Pr |gd2| 2 ≥ κ3φ2+κ3γd2 a2ρe|ge|2 a2ρr = R ∞ 0 1 − F|gd2|2 κ3φ2+κ3γd2 a2ρex a2ρr f|ge|2 (x) dx = 1 λe exp − κ3φ2 a2ρrλd2 R ∞ 0 exp − κ3γd2 a2ρe a2ρrλd2 + 1 λe x dx = a2ρrλd2 κ3γd2 a2ρeλe+a2ρrλd2 exp − κ3φ2 a2ρrλd2 (20) This is end of the proof. 4. SIMULATION RESULTS To conduct these simulations, we set ρ = ρs1 = ρs2 = ρr, σ = σ2 h1 = σ2 h2 = σ2 d1 = σ2 d2. In Figure 2, we show the SOP versus transmit SNR at the source. It can be seen clearly that higher transmit power at the source will enhance SOP performance, especially in high SNR region. By assigning different power allocation factors, the second user pair S2 − D2 outperforms that that of S1 − D1 when SNR is greater than 20 dB. The higher power factor a1 = 0.9 leads to improvement of SOP for S1 − D1. Similarly, we evaluate the impact of rates R1 R2 on SOP performance, shown in Figure 3. The lower requirement of target rates indicate the best SOP among three cases of R1 R2 examined. In Figure 4, we can see similar SOP performance for two user pairs when we change σ. It can be concluded that the quality of channels make influence on SOP metric.. 0 5 10 15 20 25 30 35 40 ρ (dB) 10-2 10-1 100 SOP S1 − D1 ana. S2 − D2 ana. a1= 0.8 sim. a1= 0.85 sim. a1= 0.9 sim. Figure 2. SOP for S1 − D1 and S2 − D2 versus ρ as changing a1 with R1 = R2 = 1 (bps/Hz), σ = 0.001, λ1r = λ2r = 1, λd2 = 2, λe = 1, ρe = −20 (dB) 0 5 10 15 20 25 30 35 40 ρ (dB) 10-2 10-1 100 SOP S1 − D1 ana. S2 − D2 ana. R1 = R2= 0.7 (bps/Hz) sim. R1 = R2= 0.8 (bps/Hz) sim. R1 = R2= 1 (bps/Hz) sim. Figure 3. SOP for S1 − D1 and S2 − D2 versus ρ as changing R1 = R2 with a1 = 0.9, σ = 0.001, λ1r = λ2r = 1, λd2 = 2, λe = 1, ρe = −20 (dB) Exact secure outage probability performance of uplink-downlink multiple access network ... (Dinh-Thuan Do)
- 7. 3280 r ISSN: 2302-9285 0 5 10 15 20 25 30 35 40 ρ (dB) 10-2 10-1 100 SOP S1 − D1 ana. S2 − D2 ana. σ= 0.001 sim. σ= 0.005 sim. σ= 0.01 sim. Figure 4. SOP for S1 − D1 and S2 − D2 versus ρ as changing σ with a1 = 0.9, R1 = R2 = 1 (bps/Hz), λ1r = λ2r = 1, λd2 = 2, λe = 1, ρe = −20 (dB) 5. CONCLUSION This paper investigates the joint uplink and downlink approach to evaluate SOP performance of two user pairs. By assigning fixed power allocation, we can derive exact formulas of SOP for two user pairs. Specifically, we can conclude that SOP will be enhanced at high transmit power at the sources. We further examine the impacts of target rate on SOP performance. Under the existence of eavesdropper, we guarabtee operation of uplink-downlink if we control the quality of channels. Furthermore, we have found that the imperfect CSI has slight impact on SOP performance. REFERENCES [1] H. Huang, W. Xia, J. Xiong, J. Yang, G. Zheng and X. Zhu, “Unsupervised learning-based fast beamforming design for downlink MIMO,” in IEEE Access, vvol. 7, pp. 7599-7605, 2019, doi: 10.1109/ACCESS.2018.2887308. [2] G. Gui, H. Sari and E. Biglieri, “A new definition of fairness for non-orthogonal multiple access,” in IEEE Commu- nications Letters, vol. 23, no. 7, pp. 1267-1271, July 2019, doi: 10.1109/LCOMM.2019.2916398. [3] B. Wang, F. Gao, S. Jin, H. Lin and G. Y. Li, “Spatial-and frequencywideband effects in millimeter-wave massive MIMO systems,” in IEEE Transactions on Signal Processing, vol. 66, no. 13, pp. 3393-3406, 1 July, 2018, doi: 10.1109/TSP.2018.2831628. [4] H. Xie, F. Gao, S. Zhang and S. Jin, “A unified transmission strategy for TDD/FDD massive MIMO systems with spatial basis expansion model,” in IEEE Transactions on Vehicular Technology, vol. 66, no. 4, pp. 3170-3184, April 2017, doi: 10.1109/TVT.2016.2594706. [5] Z. M. Fadlullah, et al., “State-of-the-art deep learning: Evolving machine intelligence toward tomorrow’s intelli- gent network traffic control systems,” in IEEE Communications Surveys Tutorials, vol. 19, no. 4, pp. 2432-2455, Fourthquarter 2017, doi: 10.1109/COMST.2017.2707140. [6] N. Kato, et al., “The deep learning vision for heterogeneous network traffic control: Proposal, challenges, and future perspective,” in IEEE Wireless Communications, vol. 24, no. 3, pp. 146-153, June 2017, doi: 10.1109/MWC.2016.1600317WC. [7] F. Tang, B. Mao, Z. M. Fadlullah and N. Kato, “On a novel deep-learningbased intelligent partially overlapping channel assignment in SDN-IoT,” in IEEE Communications Magazine, vol. 56, no. 9, pp. 80-86, Sept. 2018, doi: 10.1109/MCOM.2018.1701227. [8] Dinh-Thuan Do and Anh-Tu Le, “NOMA based cognitive relaying: Transceiver hardware impairments, relay selec- tion policies and outage performance comparison,” Computer Communications, vol. 146, pp. 144-154, October 2019, doi: 10.1016/j.comcom.2019.07.023. [9] X. Li, Q. Wang, Y. Liu, T. A. Tsiftsis, Z. Ding and A. Nallanathan, “UAV-Aided Multi-Way NOMA Networks with Residual Hardware Impairments,” in IEEE Wireless Communications Letters, vol. 9, no. 9, pp. 1538-1542, September 2020, doi: 10.1109/LWC.2020.2996782. [10] X. Li, et al., “Cooperative Wireless-Powered NOMA Relaying for B5G IoT Networks with Hardware Impairments and Channel Estimation Errors,” in IEEE Internet of Things Journal, vol. 8, no. 7, pp. 5453-5467, April 2021, doi: 10.1109/JIOT.2020.3029754. Bulletin of Electr Eng Inf, Vol. 10, No. 6, December 2021 : 3274 – 3281
- 8. Bulletin of Electr Eng Inf ISSN: 2302-9285 r 3281 [11] Anh-Tu Le and Dinh-Thuan Do, ”Implement of multiple access technique by wireless power transfer and relay- ing network,” Bulletin of Electrical Engineering and Informatics, vol. 10, no. 2, pp. 793-800, April 2021, doi: 10.11591/eei.v10i2.1903. [12] Thi-Anh Hoang, Chi-Bao Le and Dinh-Thuan Do, ”Security performance analysis for power domain NOMA em- ploying in cognitive radio networks,” Bulletin of Electrical Engineering and Informatics, vol. 9, no. 3, pp. 1046-1054, June 2020, doi: 10.11591/eei.v9i3.1639. [13] Dinh-Thuan Do, A. Le and B. M. Lee, ”NOMA in Cooperative Underlay Cognitive Radio Networks Under Imperfect SIC,” in IEEE Access, vol. 8, pp. 86180-86195, 2020, doi: 10.1109/ACCESS.2020.2992660. [14] Dinh-Thuan Do, M. V. Nguyen, F. Jameel, R. Jäntti and I. S. Ansari, ”Performance Evaluation of Relay-Aided CR-NOMA for Beyond 5G Communications,” in IEEE Access, vol. 8, pp. 134838-134855, 2020, doi: 10.1109/AC- CESS.2020.3010842. [15] C. Zhang, F. Jia, Z. Zhang, J. Ge and F. Gong, ”Physical Layer Security Designs for 5G NOMA Systems With a Stronger Near-End Internal Eavesdropper,” in IEEE Transactions on Vehicular Technology, vol. 69, no. 11, pp. 13005-13017, November 2020, doi: 10.1109/TVT.2020.3018234. [16] S. Huang, M. Xiao and H. V. Poor, ”On the Physical Layer Security of Millimeter Wave NOMA Net- works,” in IEEE Transactions on Vehicular Technology, vol. 69, no. 10, pp. 11697-11711, October 2020, doi: 10.1109/TVT.2020.3017086. [17] R. M. Christopher and D. K. Borah, ”Physical Layer Security for Weak User in MISO NOMA Using Direc- tional Modulation (NOMAD),” in IEEE Communications Letters, vol. 24, no. 5, pp. 956-960, May 2020, doi: 10.1109/LCOMM.2020.2975193. [18] K. Cao, B. Wang, H. Ding, L. Lv, J. Tian and F. Gong, ”On the Security Enhancement of Uplink NOMA Systems With Jammer Selection,” in IEEE Transactions on Communications, vol. 68, no. 9, pp. 5747-5763, September 2020, doi: 10.1109/TCOMM.2020.3003665. [19] H. -M. Wang and X. Zhang, ”UAV Secure Downlink NOMA Transmissions: A Secure Users Oriented Per- spective,” in IEEE Transactions on Communications, vol. 68, no. 9, pp. 5732-5746, September 2020, doi: 10.1109/TCOMM.2020.3002268. [20] B. Li, X. Qi, K. Huang, Z. Fei, F. Zhou and R. Q. Hu, ”Security-Reliability Tradeoff Analysis for Cooperative NOMA in Cognitive Radio Networks,” in IEEE Transactions on Communications, vol. 67, no. 1, pp. 83-96, January 2019, doi: 10.1109/TCOMM.2018.2873690. [21] S. Arzykulov, T. A. Tsiftsis, G. Nauryzbayev and M. Abdallah, ”Outage Performance of Cooperative Underlay CR- NOMA With Imperfect CSI,” in IEEE Communications Letters, vol. 23, no. 1, pp. 176-179, January 2019, doi: 10.1109/LCOMM.2018.2878730. [22] Z. Yang, Z. Ding, P. Fan and G. K. Karagiannidis, ”On the Performance of Non-orthogonal Multiple Access Systems With Partial Channel Information,” in IEEE Transactions on Communications, vol. 64, no. 2, pp. 654-667, February 2016, doi: 10.1109/TCOMM.2015.2511078. [23] J. Chen, L. Yang and M. Alouini, ”Physical Layer Security for Cooperative NOMA Systems,” in IEEE Transactions on Vehicular Technology, vol. 67, no. 5, pp. 4645-4649, May 2018, doi: 10.1109/TVT.2017.2789223. [24] Y. Feng, S. Yan, C. Liu, Z. Yang and N. Yang, ”Two-Stage Relay Selection for Enhancing Physical Layer Security in Non-Orthogonal Multiple Access,” in IEEE Transactions on Information Forensics and Security, vol. 14, no. 6, pp. 1670-1683, June 2019, doi: 10.1109/TIFS.2018.2883273. [25] I. S. Gradshteyn and I. M. Ryzhik, ”Table of Integrals, Series and Products, 6th ed,” Academic Press, New York, NY, USA, 2000. Exact secure outage probability performance of uplink-downlink multiple access network ... (Dinh-Thuan Do)