Exploiting NOMA in D2D assisted full-duplex cooperative relaying

Physical Communication 38 (2020) 100914

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Exploiting NOMA in D2D assisted full-duplex cooperative relaying Mohammed Belal Uddin a , Md. Fazlul Kader b , Soo Young Shin a , a b

∗

Department of IT Convergence Engineering, Kumoh National Institute of Technology, Gumi 39177, South Korea Department of Electrical and Electronic Engineering, University of Chittagong, Chittagong 4331, Bangladesh

article

info

Article history: Received 29 April 2019 Received in revised form 23 October 2019 Accepted 28 October 2019 Available online 31 October 2019 Keywords: Device-to-device communication Ergodic sum capacity Full-duplex relaying Non-orthogonal multiple access Outage probability

a b s t r a c t This paper proposes a device-to-device (D2D) enabling cellular full-duplex (FD) cooperative (DFC) protocol using non-orthogonal multiple access (NOMA) called DFC-NOMA, where an FD relay acting D2D transmitter assists in relaying a NOMA far user’s signal and transmits a D2D receiver’s signal simultaneously. The ergodic capacity, outage probability, and diversity order of DFC-NOMA are theoretically investigated under the assumption of both perfect and imperfect interference cancellation. The theoretical analysis is then validated by simulations. Both analysis and simulation results demonstrate the performance gain of DFC-NOMA over conventional FD cooperative NOMA and existing D2D aided FD NOMA. © 2019 Elsevier B.V. All rights reserved.

1. Introduction Non-orthogonal multiple access (NOMA) enables a transmitter to transmit multiple signals concurrently to multiple receivers with distinguished channel quality. Unlike the orthogonal multiple access technique, NOMA enables multiple users’ signals to share the same time, frequency, and code resources by utilizing power domain multiplexing at the transmitter and successive interference cancellation (SIC) at the receiver [1,2]. Owing to the feature of non-orthogonality, NOMA is capable of improving the spectral efficiency, user fairness by allocating optimal resources, e.g., bandwidth and transmit power [3–5], and it is therefore considered as one of the most promising techniques for future communication technology [6,7]. NOMA can also be combined with other technical features such as half-duplex relaying [8–11], visible light communication [12], bidirectional relaying [13], full-duplex relaying [14], device-to-device (D2D) communications [15–22] etc. However, the main focus of this paper is to study the performance of NOMA in D2D assisted cooperative relaying strategy. Cooperation among wireless nodes can effectively boost the signal reliability, enlarge the coverage area, alleviate fading, and enhance system capacity by exploiting transmit diversity. Cooperative communication using NOMA can further improve the system performance [8–10]. Cooperation in NOMA can be done by either a dedicated relay [8,10,11] or a user [9]. Based on the relaying strategy, cooperative communication can be categorized ∗ Corresponding author. E-mail addresses: [email protected] (M.B. Uddin), [email protected] (Md. Fazlul Kader), [email protected] (S.Y. Shin). https://doi.org/10.1016/j.phycom.2019.100914 1874-4907/© 2019 Elsevier B.V. All rights reserved.

into half-duplex (HD) [8–11] and full-duplex (FD) [14]. Although HD relay based cooperative NOMA [9,10] benefits the transmission reliability, it decreases the spectral efficiency because of the extra time slot needed for the relay transmission, which in turn offsets the performance gain facilitated by NOMA systems. An FD relay assisted cooperative NOMA system has been proposed [14] wherein the performance gain of FD relaying NOMA over HD relaying NOMA is justified in terms of ergodic capacity (EC), and outage probability (OP). However, owing to the imperfect SIC, the amount of performance gain in an FD relay system depends upon the residual self-interference (SI) experienced at the relay because of simultaneous signal reception and transmission. The previous studies [8–14] have investigated cooperative NOMA networks, but the feasibility of NOMA in D2D communication has not been evaluated. D2D communication facilitates point-to-point communication among users, whereas traditional communication systems require the help of a base station (BS). In heterogeneous networks, by utilizing the D2D communication technique, users can share resources (e.g., time, bandwidth, etc.) with the BS to assist transmission/relaying of signals to others, which in turn improves the overall performance [15,16]. NOMA integrated D2D communication systems can further improve the spectral efficiency [17,18]. To improve the outage performance of a NOMA user having bad channel experience, i.e., far user (FU), a simple FD D2Daided cooperative NOMA (D2D-NOMA) protocol was proposed in [18], where a NOMA user having good channel experience, i.e., near user (NU), relays the FU’s signal, and the FU decodes its signal after performing maximal-ratio-combining (MRC) of two signals those are received over the direct and relay-aided links. Another OP study of a NOMA adopted D2D network was

2

M.B. Uddin, Md. Fazlul Kader and S.Y. Shin / Physical Communication 38 (2020) 100914

performed in [19], where a D2D transmitter communicates with the receiver via a direct link and a relay (BS acts as a relay) assisted link. In [20], the OP of a D2D network was analyzed when the communication could be possible in a direct way, relay-aided way, and the relay was either energy constrained or not. It was claimed that the OP was better in direct communication than the relay-aided one, and also better in linear energy harvesting strategy than the non-linear one. In [21], a downlink non-cooperative two-user NOMA protocol was devised with an underlay pair of D2D users in a cell, and the impact of interference from a D2D transmitter on a cellular user’s performance was investigated. It was concluded that the sum-rate of NOMA cellular users could be superior to that of conventional orthogonal multiple access users in a D2D integrated system. Another latency aware and similar to [21] but uplink cellular network was considered in [22], where the performance in terms of sum rate and latency trade-off was investigated by assuming the interference from cellular to D2D and D2D to cellular communications. It was concluded that the fixed power allocation strategy has an advantage over adaptive one in achieving throughput and low latency, whereas adaptive one has an advantage over fixed one in achieving individual rate, fairness, and power efficiency. Since the focus was only on either relaying the NOMA FU signal in HD/FD mode [18–20] or analyzing the D2D incorporation in a non-cooperative NOMA system [21,22], there is still a need to explore an integrated FD D2D cooperative NOMA system. In [23], a dedicated FD relay was used to transmit the signal to a FU. The outage probability (OP) and ergodic sum capacity (ESC) were improved compared to the existing corresponding HD cooperative relaying system. By focusing on achieving better spectral efficiency than [23], and unlike [18,21], a NOMA exploiting D2D and cellular communication integrated protocol is proposed in this paper, where an FD relay acting D2D transmitter assists in simultaneous data transmission to cellular and D2D users. The contributions of this work are summarized as follows:

• A D2D assisted FD relaying cooperative (DFC) protocol exploiting NOMA (termed as DFC-NOMA) is proposed, where BS communicates with a NOMA NU by a direct link and with a NOMA FU via the assistance of a D2D transmitter. • Based on two cases, i.e., (a) case #1: no interference from BS, and (b) case #2: interference from BS, the performance of D2D receiver is evaluated. • A closed-form and/or an asymptotic expressions of each user’s EC, OP, and system’s ESC are analyzed over a Rayleigh fading channel. The diversity order (DO) of each user is also investigated. • Finally, the performance gain of the proposed DFC-NOMA over conventional full-duplex cooperative NOMA (FCNOMA) [23] and D2D-NOMA [18] is shown by theoretical analysis and justified by a simulation. The rest of this paper is structured as follows. The system model along with the protocol description is comprehensively explained in Section 2, which is followed by the performance analysis of DFC-NOMA in Section 3. Numerical results are extensively discussed in Section 4. The concluding remarks along with the future research direction are presented in Section 5. 2. System model and protocol description As shown in Fig. 1, a downlink DFC-NOMA is considered that consists of a BS, two cellular users U1 (NU) and U3 (FU), an FD decode-and-forward (DF) relay acting D2D transmitter (U2 ), and a D2D user (D1 ). U3 resides at the cell edge area. Therefore, due to the hindrance in signal propagation, the BS-to-U3 link is considered unavailable [23]. BS transmits a superimposed NOMA

Fig. 1. Proposed network model.

signal containing symbols of U1 and U3 . Based on the wireless environment, two probable cases are considered in signal reception of D1 . In case #1, D1 experiences no interference from the BS. In case #2, D1 suffers interference (link is not drawn in Fig. 1 for avoiding the overlap of lines) from the BS. The remaining links of the system are available. Since there is no available BS-to-U3 link, U2 conveys the information from BS to U3 . In [23], the relay forwards the decoded symbol only to the FU. In contrast, in DFC-NOMA, the relay transmits a superimposed NOMA signal containing symbols of U3 and D1 . Applying the optimal downlink NOMA power allocation strategy at BS and U1 , the FU U3 ’s throughput and thus the fairness can be improved compared with that of conventional orthogonal multiple access scheme [4]. The channel experiences Rayleigh fading, and so the channel coefficient between two nodes i and j will be the complex Gaussian random variable with zero mean and variance λij = dij−ϑ that can be denoted by hij ∼ CN(0, d−ϑ ij ); i, j ∈ {BS, U1 , U2 , U3 , D1 }, and i ̸ = j. The path loss exponent and the distance between nodes i and j are denoted by ϑ , and dij , respectively. The channel gain gij = |hij |2 will be the exponentially distributed random variable with the scale parameter of λi,j [14]. Subscripts b, 1, 2, 3, and d are used for BS, U1 , U2 , U3 , and D1 , respectively. Each node, excluding U2 , is equipped with a single antenna. As U2 operates in full-duplex mode, it is equipped with one transmit and one receive antennas. Therefore, due to the simultaneous transmission and reception of signals, the relay suffers from a self-interference (SI) that can be subsided by applying the multistage SI cancellation technique [24]. In practice, SI may not be removed perfectly. Therefore, imperfect SI cancellation is considered that causes residual SI at the relay, which is symbolized by h˜ 22 ∼ CN(0, ς22 λ22 ) with zero mean and ς22 λ22 variance. Hence, 2

the channel gain of residual SI at U2 is g˜22 = |h˜ 22 | . The variable ς22 limiting as 0 ≤ ς22 ≤ 1 specifies the effect of the remaining SI. Channel gains are considered as gb2 ≪ gb1 and g23 ≪ g2d . At any instant of time (t-th slot), the BS transmits a superposed downlink NOMA signal that can be written as sc [ t ] =

√

θ1 pb s1 [t ] +

√ θ3 pb s3 [t ],

(1)

where s1 and s3 are the symbols of U1 and U3 , respectively. Parameters pb , θ1 , and θ3 refer to the total transmit power of BS, the associated power allocation factor with s1 , and s3 , respectively, where θ1 + θ3 = 1 and θ1 < θ3 is maintained based on the channel gain. The relay U2 decodes s3 at the direct phase and retransmits this decoded symbol along with its own signal s2 with a processing delay ν ≥ 1 at the cooperative phase. This signal can be written as sr [t − ν] =

√ √ θ2 pu s2 [t − ν] + θ3′ pu s3 [t − ν],

(2)

where θ2 + θ3′ = 1, θ2 < θ3′ , pu is the total transmit power of U2 , θ2 and θ3′ are the assigned power allocation coefficients with

M.B. Uddin, Md. Fazlul Kader and S.Y. Shin / Physical Communication 38 (2020) 100914

s2 and s3 informations, respectively. The received signal at U2 is written as y2 [t ] = hb2 sc [t ] + h22 sr [t − ν] + n2 [t ],

(3)

where n2 is the additive white Gaussian noise (AWGN) at U2 with zero mean and σ22 variance. After decoding s3 by treating s1 as noise and performing SI cancellation, the related signalto-interference-plus-noise ratio (SINR) at U2 takes the following form as in [14, eq. (1)]: s3 b2

γ

θ3 ρb gb2 , = θ1 ρb gb2 + ρu g˜22 + 1

where ρb =

pb

σ22

and ρu =

pu

σ22

(4) are SNRs. Let the variances of AWGN

at all receivers be equal. When U1 receives the signal from the BS, it also receives the signal from U2 as interference. Therefore, the received signal at U1 can be modeled as y1 [t ] = hb1 sc [t ] + h21 sr [t − ν] + n1 [t ],

(5)

where n1 is the AWGN at U1 . During the self-information decoding, U1 decodes U3 ’s information s3 first and then performs successive interference cancellation (SIC) to obtain its own information s1 . Therefore, the information s3 in the interference signal from U2 is known to U1 as a priori and can be removed by applying the known interference cancellation technique [23,25]. However, U1 cannot remove s2 from the interference signal as this is unknown to U1 . To be more clear, by using SIC and known interference cancellation techniques, a receiver can cancel out the NOMA inter-symbol interference and known interference [23,25]. When U1 receives the composite NOMA signal from BS, it needs to decode s3 first, then cancel it out by using SIC process and thus decode s1 . Therefore, s3 is known as a priori to U1 , and so if it arrives later as an interference, U1 can cancel it out by applying known interference cancellation technique. However, the near cellular user U1 does not have any information about the D2D user’s symbol s2 . Therefore, this symbol cannot be canceled out and will be treated as a noise. Considering imperfect cancellation of known interference s3 and no cancellation of unknown interference s2 , the channel coefficient of the interference link from U2 to U1 can be designed as h˜ 21 ∼ CN(0, (ς2 θ2 + ς3′ θ3′ )λ21 ), where the parameters ς2 (=1) and ς3′ (0 ≤ ς3′ ≤ 1) refer to the level of residual interference. Accordingly, the received SINRs related to information s3 and s1 at U1 are obtained as in [14, eq. (1)] and [14, eq. (5)] respectively s

θ3 ρb gb1 , θ1 ρb gb1 + ρu g˜21 + 1 θ1 ρb gb1 = , ρu g˜21 + 1

γb13 = s1 b1

γ

(6) (7)

2

where g˜21 = |h˜ 21 | . At the cooperative phase, the user U3 receives the signal transmitted from U2 that is given by y3 [t ] = h23 sr [t − ν] + n3 [t ],

(8)

where n3 is the AWGN at U3 . U3 decodes its information s3 by treating s2 as noise. Thus, the related SINR for s3 at U3 is given as in [14, eq. (3)] s

γ233 =

θ3′ ρu g23 . θ2 ρu g23 + 1

y2d [t ] = h2d sr [t − ν] + hbd sc [t ] + nd [t ],

(11)

where nd is the AWGN at D1 . In both cases, first, D1 needs to decode s3 by treating s2 as noise. Then, after performing SIC process, it decodes its own information s2 . Hence, in case #1, SINRs related to s3 and s2 at D1 can be respectively expressed as 1,s

γ2d 3 = 1,s

θ3′ ρu g2d , θ2 ρu g2d + 1

(12)

γ2d 2 =θ2 ρu g2d .

(13)

In case #2, during the decoding of s3 and s2 , D1 experiences interference from BS, wherein s3 is known as a priori and is removable by using the side information s3 [t − ν] [23,25]. However, D1 cannot remove s1 as this information is unknown. Considering imperfect cancellation of s3 and no cancellation of s1 , the channel coefficient of the interference link from BS to D1 can be modeled as h˜ bd ∼ CN(0, (ς1 θ1 + ς3 θ3 )λbd ), where the parameters ς1 (=1) and ς3 (0 ≤ ς3 ≤ 1) refer to the degree of residual interference. Thus, in case #2, SINRs related to s3 and s2 at D1 can be respectively given by 2,s

θ3′ ρu g2d , θ2 ρu g2d + ρb g˜bd + 1 θ2 ρu g2d . = ρb g˜bd + 1

γ2d 3 = 2,s

γ2d 2

(14) (15)

By using (7), (13), and (15), the achievable rate of U1 , D1 in case #1, and D1 in case #2 are respectively written by

(

s

(

1,s2 2d

R1 =log2 1 + γb11 ,

)

(16)

)

=log2 1 + γ , ( ) 2 ,s R2d =log2 1 + γ2d 2 .

R1d

(17) (18)

The achievable rate of a multi-hop communication system is determined by the rate of the bottleneck hop [26]. In a DF relay assisted protocol, the cooperative transmission is analogous to a series network that refers to the rate is dominated by the weakest link [27]. Therefore, the lower bound of the capacity is achieved in a DF relay deployed network. The lower bound of U3 will be the minimum of BS-to-U2 and U2 -to-U3 link rates. Further, s3 [t − ν] needs to be decoded at U1 and D1 to perform the SIC process. Moreover, for case #1, the achievable rate of U3 can be obtained by using (4), (6), (9), and (12) as

(

s

s

s

1,s

)

R13 = log2 1 + min{γb23 , γb13 , γ233 , γ2d 3 } .

(19)

Accordingly, for case #2, the lower bound of U3 can be obtained by using (4), (6), (9), and (14) as

(

s

s

s

2,s

)

R23 = log2 1 + min{γb23 , γb13 , γ233 , γ2d 3 } .

(20)

Finally, the overall achievable capacities of the proposed DFCNOMA under case #1 and case #2 will be lower bounded as 1 1 R1,p cap. =R1 + Rd + R3 ,

(21)

.

(22)

R2,p cap.

=R1 +

R2d

+

R23

(9) 3. Performance analysis

D2D user D1 also receives the transmitted signal from U2 at cooperative phase. In addition, D1 faces no interference from BS in case #1, whereas it faces interference from BS in case #2. Hence, the received signal at D1 for case #1 and case #2 are respectively represented as y1d [t ] = h2d sr [t − ν] + nd [t ],

3

(10)

3.1. Capacity analysis Ergodic capacities (ECs) of users and the ESC of the proposed DFC-NOMA over the Rayleigh fading channel are studied in this section.

4

M.B. Uddin, Md. Fazlul Kader and S.Y. Shin / Physical Communication 38 (2020) 100914

3.1.1. Ergodic capacity of U1 θ ρ g Let Q ≜ ρ 1g˜ b +b11 . By using the definition of cumulative distriu 21

θ ρ g

bution function (CDF), FQ (q) = Pr{ ρ 1g˜ b +b11 < q}, the CDF of Q can u 21 be derived as

)−1 ) ( ρu ς2 θ2 + ς3′ θ3′ λ21 q − θ ρ qλ FQ (q) = 1 − e 1 b b1 1 + . (23) θ1 ρb λb1 ( ) Considering α = θ ρ1λ , β = ρu ς2 θ2 + ς3′ θ3′ λ21 , and putting 1 b b1 ∫ ∫∞ ∞ 1−FQ (q) dq, the closed-form in 0 log2 (1 + q) fQ (q) dq = ln12 0 1+q (

solution of U1 ’s EC can be calculated as 1 R¯ 1 =

∫

∞

1 − FQ (q)

dq =

∫

1

∞

ln2 0 1+q ln2 0 (1 + q) (1 + αβ q) [ ) ] ( 1 log2 e 1 = e β Ei − − eα Ei (−α) , 1 − αβ β

e

−α q

dq

(24)

ea −∞ a

R¯ ∞ 1

] α Ec + ln (αβα α ) − , = log2 e β (1 − αβ) (1 − αβ) Ec − ln (β)

[

(25)

where Ec represents the Euler constant. 1,s2

= θ2 ρu g2d , the CDF FT1 (t1 ) can be obtained

as t

FT1 (t1 ) = 1 − e

− A1

d

,

(26)

where Ad = θ2 ρu λ2d . Using (17) and (26), the EC of D1 in case #1 is written as R¯ 1d =

1

∞

∫

ln 2

1

(1 + t1 )

0

t − A1 d

e

FW1 (w1 ) = 1 − e (

1

) ( 1 1 . dt1 = − e Ei − 1 Ad

ln 2

e

1+

1

){

( Ec + ln

Ad

Ad

′

FL1 (l1 ) = 1 − e−l1

D=

2,s2

=

as t − θ ρ 2λ 2 u 2d

FT2 (t2 ) =1 − e

(

θ2 ρu g2d , ρb g˜bd +1

(

1

ρb

1

1 Ad

)}

.

(28)

∞

)−1 (29)

(1 + t2 ) (1 + αb βb t2 ) [ ( ) ] 1 1 αb βb = e Ei − − e Ei (−αb ) . 1 − α b βb βb Let X ≜

Y ≜

θ3′ ρu g2d , θ2 ρu g2d +1

(30)

θ3 ρb gb1 , θ1 ρb gb1 +ρu g˜21 +1

Z ≜

θ3′ ρu g23 , θ2 ρu g23 +1

W1 ≜ and L1 ≜ min (X , Y , Z , W1 ). The CDF of X, Y, Z, and W1 are respectively calculated as −

x

FX (x) = 1 − e (θ3 −θ1 x)ρb λb2

( 1+

1

)

λb1

(35)

, A = θ3 ρb λb2 , B = θ3 ρb λb1 ,

El1

+

(θ3′(−θ2 l1 ) , E = ρ1 λ1 + u 23

)

1

, G = ς22 ρu λ22 − θ1 ρb λb2 ,

λ2d

represented as

R13

¯ =

ln2

Dl1

−

El1

−

′ (θ3 − θ1 l1 )2 t ′ e (θ3 −θ1 l1 ) (θ3 −θ2 l1 ) dl1 , (1 + l1 ) {A + G′ l1 }{B + (β − J ) l1 }

∞

∫

1

0

(36)

where t ′ = ρb2 λb1 λb2 and G′ = G − H. However, the closed-form solution of (36) is not tractable [23]. Rather, it can be evaluated through numerical integration. To find out the asymptotic solution, consider ρb = ρu = ρ , ρ (→ ∞, θ1 =) θ2 , θ3 = (θ3′ , and )

θ3 , θ3 gb1 ≈ min θθ3 , N θ1 θ1 gb1 +g˜21 1 g (θ −θ n) perfect SI cancellation. Using n = b1 g˜3 1 , the CDF of 21 nβ be written as FN (n) = ρ λ (θ −θ n)+nβ . Using this CDF and u b1 3 1

under N can

following [14], the asymptotic EC of U3 in case #1 can be derived as 1,∞ R¯ 3 =

∞

∫

( log2

θ3 θ1

θ3 θ1

θ3 1+ θ1

)

θ3 θ1

∫ fN (n) dn +

log2 (1 + n) fN (n) dn

0 θ3 θ1

χ − ψn dn + n) (1 + n) (χ 0 ( ) ( )} θ3 θ3 = ψ1 ln + 1 − ψ2 ln +1 , (37) ln2 ψθ1 θ1

∫

1

1 − FN (n)

ln2 0 { 1

1+n

ψ(1+χ) , ψ2 1−ψ

where ψ1 =

dn =

=

1

∫

ln2

(ψ+χ) ,ψ 1−ψ

=

θ3 ρu λb1 , β−θ1 ρu λb1

ς22 ρu λ22 x (θ3 − θ1 x) ρb λb2

)−1

,

(31)

θ3′ ρu g2d , θ2 ρu g2d +ρb g˜bd +1

and χ =

and L2 ≜ min

(X , Y , Z , W2 ). The CDF of W2 is calculated as ( )−1 w − ′ 2 βb w2 θ3 −θ2 w2 )a ( ) FW2 (w2 ) = 1 − e 1+ ( ′ , θ3 − θ2 w2 a

(38)

where a = ρu λ2d . Using (31), (32), (33), and (38), the CDF of L2 is written as −l′2

] ( ) (θ3 − θ1 l2 )2 θ3′ − θ2 l2 ρb2 ρu λm , (A + Gl2 ) (B + ηl2 ) (θs a + βb l2 )

Dl2

+

[

3.1.4. Ergodic capacity of U3 in case #1 θ3 ρb gb2 , θ1 ρb gb2 +ρu g˜22 +1

] (θ3 − θ1 l1 )2 ρb2 λb1 λb2 , {A + Gl1 }{B + ηl1 }

Let X , Y , Z as earlier, W2 ≜

dt2

ln 2 0 log2 e

(34)

3.1.5. Ergodic capacity of U3 in case #2

ρb (ς1 θ1 + ς3 θ3 ) λbd t2 1+ θ2 ρu λ2d

e−αb t2

.

the CDF FT2 (t2 ) can be obtained

where βb = ρb (ς1 θ1 + ς3 θ3 ) λbd and αb = θ ρ λ . By using (18) 2 u 2d and (29), the EC of D1 in case #2 is written as

∫

[

Dl1

θ1 ρu λb1 . β−θ1 ρu λb1

1

1

)

(θ3 −θ1 l1 )

+

λb2

=

=1 − e−αb t2 (1 + αb βb t2 )−1 ,

R¯ 2d =

(32)

η = β − J, and J = θ1 ρb λb1 . The EC of U3 in case #1 can be

(27)

3.1.3. Ergodic capacity of D1 in case #2 Assuming T2 ≜ γ2d

,

Using (31), (32), (33), and (34), the CDF of L1 is written as

As applied for R1 , the asymptotic EC of D1 in case #1 can also be obtained as follows.

( )(

)−1

(33)

w1 θ3′ −θ2 w1 ρu λ2d

−

¯∞

1,∞ R¯ d = log2

βy (θ3 − θ1 y) ρb λb1

L1 ≜ min (X , Y , Z , W1 ) ≈ min

3.1.2. Ergodic capacity of D1 in case #1 Assuming T1 ≜ γ2d

1+

z

−

∫y

where Ei (y) = da expresses the exponential integral function [28]. In case of high SNR (ρb → ∞ and ρu → ∞), Ei (−x) ≈ Ec + ln (x) and ex ≈ 1 + x can be applied to derive the asymptotic EC of U1 as follows [28].

(

′ FZ (z) = 1 − e (θ3 −θ2 z )ρu λ23 ,

where l′1 =

1

y

−

FY (y) = 1 − e (θ3 −θ1 y)ρb λb1

FL2 (l2 ) = 1 − e where l′2 =

(θ3 −θ1 l2 )

El2

(θ3′ −θ2 l2 )

(39)

, λm = λ2d λb1 λb2 , and θs = θ3′ −θ2 l2 .

The EC of U3 in case #2 can be represented as R¯ 23 =

1 ln 2

∞

∫ 0

1 − FL2 (l2 ) 1 + l2

dl2 .

(40)

The closed-form solution of (40) is not tractable [23]. Therefore, it will be evaluated through the numerical integration.

M.B. Uddin, Md. Fazlul Kader and S.Y. Shin / Physical Communication 38 (2020) 100914

3.1.6. Ergodic sum capacity By summing up (24), (27), (36) and (25), (28), (37), the exact and approximate ESC of the proposed system in case #1 can be obtained, respectively. For case #2, the exact ESC can be found by adding (24), (30), and (40). On the contrary, ESC of FD cooperative NOMA proposed in [23] is computed by adding [23, eq. (20)] and [23, eq. (21)]. Note that ESC was not computed in [18]. However, for the purpose of comparison, the ESC of D2D-NOMA strategy proposed in [18], can be computed by using SINR equations [18, eq. (3)], [18, eq. (4)], and [18, eq. (8)] as follows: [18]

[18]

[18]

R[18] sum = log2 (1 + γ1,1 ) + log2 (1 + min(γ1,2 , γ2,MRC )), [18]

ρb θ3 gb2 ρb θ1 gb2 +1

ρb θ1 gb1 , ρ1 g11 +1

] γ1[,18 = 2 + ρ1 g12 . Note that ρ1 =

where γ1,1

=

ρb θ3 gb1 , ρb θ1 gb1 +ρ1 g11 +1 p1

σ22

(41) [18]

and γ2,MRC =

, g11 is the channel gain of

residual SI at U1 , σ22 denotes noise variance, and p1 is the transmit power of U1 . For a fair comparison between the proposed DFCNOMA and [18], it is considered that the BS, U1 , and U2 in [18] are located at the position of BS, U1 , and U2 , respectively in the proposed DFC-NOMA. It should be mentioned that U1 employs FD strategy to relay the decoded signal of U2 in [18], whereas U2 employs FD strategy in DFC-NOMA and a dedicated FD relay was used in [23]. Hence, to make consistency it is assumed that g11 = g˜22 , g12 = |h12 |2 , h12 ∼ CN(0, λ21 ), and ρ1 = ρu . 3.2. Outage probability and diversity order 3.2.1. Outage probability of U1 Let r1 , r3 , rd are the threshold data rates below which outage occurs for U1 , U3 , and D1 , respectively. Outage will occur in U1 either if it cannot decode the information s3 or if it decodes s3 but fails to decode s1 . Thus, the OP of U1 can be expressed as [23] s

s

(

(( =1−P

(

)

(

ϖ ρb gb1 ,

θ1 ρb gb1 Λ1

θ3 −θ1 Λ3 , Λ3

r1

where ϖ =

)

( > ρu g˜21 + 1

)

)

) )

,

(42)

Λ1 = 2 − 1, and Λ3 = 2 − 1. It is noted θ by analyzing (27) that for Λ3 > θ3 , the OP becomes PO,1 = 1 and 1 θ3 for Λ3 < θ , it takes the following form 1 ( ) ϕρb λb1 − ϕρ 1λ b b1 PO,1 = 1 − e , (43) ϕρb λb1 + β ( ) θ −θ Λ θ where ϕ = min 3 Λ 1 3 , Λ1 . 3

r3

s

s

PO,3 =1 − P log2 1 + γb23 > r3 , log2 1 + γ233 > r3 ,

(

)

(

)

)

( ) =1 − P ϖ ρb gb2 > ρu g˜22 + 1, ℵρu g23 > Λ3 , where ℵ = θ3′ − θ2 Λ3 . From (29), if Λ3 >

(

)

θ3 θ1

the OP becomes PO,3 = 1, whereas for Λ3 < can be expressed as Λ − ℵρ λ3 − ϖ ρ 1λ u 23 b b2

PO,3 = 1 − e

P1O,d = 1 −

(

) θ3′ ρu g2d > Λ3 , θ2 ρu g2d > Λd , θ2 ρu g2d + 1

where Λd = 2rd − 1. For Λ3 >

Λ3 <

θ′

3

θ2

θ3′ , θ2

, P1O,d is given below Λ

Λ

− ℵρ λ3 − θ ρ dλ u 2d 2 u 2d

P1O,d = 1 − e

.

(47)

Similarly, the OP of D1 in case #2 for Λ3 > θ3′ , θ2

whereas for Λ3 < P2O,d

1 1+

ς22 λ22 ρu ϖ ρb λb2

.

and Λ3 > θ3 , θ1

(44) θ3′ θ2

and Λ3 <

(46)

the OP becomes P1O,d = 1. For

θ′

3

θ2

becomes unity,

it is obtained by using (14) and (15) as

( ) 2,s 2,s = 1 − γ2d 3 > Λ3 , γ2d 2 > Λd ( −

=1−e [{

Λ3 θ ′ −θ Λ

(3

)

2 3 a

+αb Λd

)

} ]−1 βb Λ 3 ) . 1+ ( ′ (1 + αb βb Λd ) θ3 − θ2 Λ3 a

×

(48)

3.2.4. High SNR approximation Considering high SNR (ρb → ∞), and ρu = ερb , the OP can be evaluated in the high SNR regime where ε (0 < ε ≤ 1) is a relay transmit power controlling variable [23]. Under all interference cancellation (IC) conditions, OPs of U1 , U3 , and D1 are respectively approximated as P∞ O,1 =

P∞ O,d

⎧ ⎪ ⎨

(

1− 1+

β ϕρb λb1

)−1

for

0 < ς3′ ≤ 1

(49)

( )−1 ⎪ ⎩1 − 1 + ες2 θ2 λ21 , for ς3′ = 0 ϕλb1 ⎧ ( )−1 ⎨1 − 1 + ες22 λ22 for 0 < ς22 ≤ 1 ϖ λb2 = Λ3 ⎩ 1 + ϖ ρ λ , for ς22 = 0 ℵρu λ23 b b2 { 1 − {(1 + F ) (1 + H )}−1 for case#2 = Λ3 + θ ρΛudλ , for case#1 ℵρu λ2d 2 2d

where F =

ξ , εℵλ2d

H =

ξ Λd , θ2 ελ2d

(50)

(51)

and ξ = (ς1 θ1 + ς3 θ3 ) λbd Λ3 .

Imperfect IC (ipIC) causes the OPs of U1 and U2 to maintain constant values that create error floors (EFs). In addition, the interference from BS to D1 in case #2 causes its OP to attain a − log P constant value that creates an EF. Using limρb →∞ log ρ O in (49), b

(50), and (51), DOs of U1 , U3 , and D1 in case #1 under ipIC and perfect IC (pIC) are respectively found as

1

3.2.2. Outage probability of U3 If U2 fails to decode s3 or U2 can decode but U3 cannot, then outage occurs in U3 . Hence,

(

3.2.3. Outage probability of D1 The D2D user will be in outage under two conditions; i.e., i. D1 fails to decode U3 ’s information and ii. D1 decodes s3 but fails to decode s2 . Thus, the OP of D1 in case #1 can be obtained as

P∞ O,3

PO,1 = 1 − P log2 1 + γb13 > r3 , log2 1 + γb11 > r1 ,

5

∞ ∞ D∞ O,1 = 0; DO,3 = 0; DO,d = 1

for

0 < ς22 , ς3′ ≤ 1,

∞ ∞ D∞ O,1 = 0; DO,3 = 1; DO,d = 1

for

ς22 = ς3′ = 0.

(

)

(52)

For case #2, the DO of D1 in case #2 will be zero due to the interference from BS. Unknown interference at U1 makes its DO zero for both pIC and ipIC. Similar to [23], U3 ’s DO is unity under pIC and zero under ipIC. There exists no interference other than intended NOMA user interference on D1 in case #1 that results in DO unity.

exist, θ3′ , θ2

it

(45)

4. Numerical results The performance in terms of EC, ESC, and OP is evaluated in this section. The fixed power allocation technique and the normalized collinear distance are assumed for simplicity [14,18,23]. All simulations are executed by considering ρb = 2ρu , ρb = 40 dB,

6

M.B. Uddin, Md. Fazlul Kader and S.Y. Shin / Physical Communication 38 (2020) 100914 Table 1 Simulation parameters. Parameter

Value

Number of channel realization SNR ρb , ρu , respectively Normalized node distances db3 , dbd , db2 , db1 , db3 − db2 , dbd − db2 , db2 − db1 , respectively Path loss exponent ϑ Variance λ22 Power allocation factor θ1 = θ2 , θ3 = θ3′ , respectively Residual interference ς = ς3 = ς3′ = ς22 Outage threshold r1 = r3 = rd

10 000 0 to 60 dB, 0 to 30 dB 1, 0.8, 0.6, 0.2, db3 − db2 , dbd − db2 , db2 − db1

Fig. 2. ESC vs. ρb under pIC.

4 0.3 [0, 0.5], [0.5, 1] [0,1] 0.75 bps/Hz

Fig. 4. EC vs. relay position under pIC.

4.1. Ergodic capacity

Fig. 3. ESC vs. ρb under ipIC.

ϑ = 4, db3 = 1, dbd = 0.8, db2 = 0.6, db1 = 0.2, d23 = db3 − db2 , d2d = dbd − db2 , d21 = db2 − db1 , λ22 = 0.3, θ1 = θ2 = 0.15, ς = ς3 = ς3′ = ς22 , and θ3 = θ3′ = 0.85, unless specified otherwise. Besides, all simulation parameters are precisely noted in Table 1. For notational simplicity, case #1 and case #2 are denoted as C1 and C2 in all graphs, respectively. The concordance between the analytical and simulation plots verifies the accuracy of analyses.

Considering the pIC condition, capacity versus ρb behavior is plotted in Fig. 2. The outcome demonstrates that the ESC increases with the increase in ρb , wherein the ESC of DFC-NOMA in case #1 labeled as C1 outperforms both of DFC-NOMA in case #2 labeled as C2 , [18] and [23] protocols. At the second hop, NOMA exploited simultaneous transmission for D2D receiver (D1 ) and cellular user (U3 ) benefits DFC-NOMA achieving higher ESC than [18] and [23]. Although case #2 outstrips [18] and [23] until ρb = 18 dB, it falls behind [18] and [23] beyond that and gets saturated at high ρb . The interference signal from BS to D1 in case #2 causes the decreasing SINR than that of [18] and [23] with the increase in ρb , which results in the lower ESC for case #2 than [18] and [23]. For both cases, the similar ESCs by corresponding analytical and simulation results justifies the analysis. It is also found that [18] outperforms [23] at low ρb region, whereas at high ρb region both show almost similar capacity performance. Under ipIC in DFC-NOMA and FC-NOMA protocols, the capacity response with ρb is demonstrated in Fig. 3. It is clear that the higher residual interference causes lower ESC in all protocols. For ς = 0.033 , case #2 and [23] outperform each another alternately from low-to-medium and medium-to-high SNR. Conversely, for ς = 0.32 , both cases of the DFC-NOMA achieve better ESC than [23] that proves the efficacy of the proposed cases under high residual interference effect. In FC-NOMA, the SINR of the NU becomes affected with the increase in residual interference. As the NU contributes significantly to the sum capacity of FCNOMA, the ESC of this protocol gets lower due to the high residual interference effect. Though the NU of DFC-NOMA also gets equally

M.B. Uddin, Md. Fazlul Kader and S.Y. Shin / Physical Communication 38 (2020) 100914

7

Fig. 5. ESC vs. relay position under ipIC.

Fig. 7. ESC vs. θ1 under ipIC.

Fig. 6. ESC vs. θ1 under pIC.

Fig. 8. OP vs. ρb under pIC.

affected by the residual interference, the NOMA exploited transmission at the second hop of DFC-NOMA helps it achieve better ESC than FC-NOMA under higher residual interference. Assuming pIC, the EC of all users associated with DFC-NOMA is shown with the change of relay position in Fig. 4 for both cases. The result refers to the achievable ECs of all users become higher as the relay moves farther from the BS wherein D1 (case #1) outperforms all remaining users. All other users obtain comparatively nearby values due to the interference impact. The more U2 becomes close to D1 , the more the channel between them becomes better, which helps D1 (case #1) achieve better EC than others. However, the interference from BS to D1 results in D1 (case #2) having degraded EC compared to D1 (case #1). As there is no impact of interference from BS to D1 on the EC of U1 , it becomes same for both cases. Moreover, even if there is an impact of interference from BS to D1 on the EC of U3 , since it has no effect on bottleneck link’s SINR, EC of U3 remains same for both cases. Owing to the subjection to interference, cellular users (U1 and U3 ) achieve lower capacity than the D2D user (D1 ) of the system.

ESC versus db2 is plotted under ipIC as shown in Fig. 5. ESC increases with the increase in db2 where FC-NOMA [23] attains a saturated value when U2 moves farther than a certain value from BS. With the movement of U2 towards U3 , the rate related to BSto-U2 link becomes lower, which defines the data rate and causes the system to attain the saturated value. For all U2 positions, ESC under ς = 0.033 is higher than the respective ESC under ς = 0.32 . Under comparatively less residual interference (ς = 0.033 ), when db2 < 0.5, [23] shows better ESC than any of the cases of DFC-NOMA, but for db2 > 0.5, case #1 shows better ESC than [23], and for db2 > 0.6, case #2 shows better ESC than [23]. When U2 moves towards D1 , the EC of D1 becomes better, and hence, DFC-NOMA shows better ESC for higher db2 . Under comparatively high residual interference (ς = 0.32 ), both case #1 and case #2 achieves better ESC than [23]. Under any of the residual interferences, case #1 outperforms case #2. Interference from BS to D1 at case #2 is responsible for this phenomenon. Considering pIC, the change in achievable capacity with the change in allocated power to the symbols is demonstrated in Fig. 6 for ρb = 15 and 45 dBs, where θ1 = θ2 . It is obvious that the

8

M.B. Uddin, Md. Fazlul Kader and S.Y. Shin / Physical Communication 38 (2020) 100914

Table 2 A comparative study between the proposed DFC-NOMA, [18], and [23]. Item

FD D2D-aided cooperative NOMA [18]

NOMA with cooperative FD relaying [23]

Proposed DFC-NOMA

System model

In [18], to improve the performance of a NOMA FU, a cooperative NOMA scheme consisting of a base station (BS), a NU, and a FU is proposed, where direct link between BS and FU is active.

In [23], a cooperative NOMA scheme consisting of a BS, an NU, a dedicated relay (Re), and an FU is proposed, where direct link between BS and FU is absent.

• A downlink NOMA is exploited

• A downlink NOMA is exploited

in the direct phase only. In the relaying phase, only NU relays the decoded symbol of FU.

in the direct phase only. In the relaying phase, only Re retransmits the decoded symbol of FU.

• Imperfect SIC in removing the

• Imperfect SIC in removing the

interference from the superposed NOMA symbol is not considered. • Two symbols are transmitted during two phases.

interference from the superposed NOMA symbol is not considered. • Two symbols are transmitted during two phases.

To improve the system performance, a cellular and D2D systems integrated cooperative NOMA (termed as DFC-NOMA) protocol consisting of a BS, a NU, a FU, and a pair of D2D devices is proposed where direct link between BS and FU is absent. • The concept of downlink NOMA is exploited in both phases where the FD relay acting D2D transmitter applies the downlink NOMA strategy to transmit its own and the decoded FU symbols in the cooperative phase. • Imperfect SIC is considered in removing all possible intra-cell interference. • Three symbols are transmitted during two phases.

Users served

2

2

3

Performance metrics

• OP

• OP • ESC

• • • •

Analytical derivations

Analytical derivation for OP is provided.

Analytical derivations for ESC and OP are provided.

Analytical derivations for EC, ESC, OP, and DO are provided.

Numerical results

Simulation results display only OP.

Simulation results display OP and ESC.

Simulation results display OP, EC, ESC, and DO.

Outcomes

[18] shows improved OP than corresponding conventional NOMA and orthogonal multiple access (OMA) schemes.

In the moderate signal-to-noise ratio (SNR) regime, [23] shows better OP and ESC than corresponding half-duplex (HD) protocol.

The proposed DFC-NOMA is more spectral efficient and so it outperforms [23] in terms of ESC. Depending on the amount of residual interference, trade-off happens. Users’ OPs meet the error floor when the DO is zero.

Fig. 9. OP vs. ρb under ipIC.

OP ESC Ergodic capacity (EC) Diversity order (DO)

outperforms [23] in terms of ESC. When ρb = 45 dB, case #1 outperforms [23], and [23] outperforms case #2 in terms of ESC. Under high ρb , if pIC is possible, owing to the non-cancellable interference at D1 in case #2, the SINR gets affected badly by noise, because of which case #2 achieves less ESC than [23] at ρb = 45 dB. It is noted that after an initial increase in ESC with the increase in θ1 for all cases, the ESCs of case #1 and [23] become saturated whereas the ESC of case #2 becomes degraded as the high allocated power to U1 increases the non-cancellable interference at D1 . Considering ipIC, the ESC versus power allocation factor response is shown in Fig. 7 for ς = 0.033 and 0.32 , where θ1 = θ2 and ρb = 45 dB. For all values of θ1 , the ESC of a particular protocol under ς = 0.033 is better than that of ς = 0.32 . This reveals that more residual interference causes more degraded ESC. As previously observed in Fig. 3, both cases of the proposed DFC-NOMA outperform [23] under comparatively high residual interference (ς = 0.32 ), but case #1, [23], and case #2 respectively outperform each other under comparatively less residual interference (ς = 0.033 ) for all θ1 . 4.2. Outage probability

ESCs for ρb = 45 dB is better than the respective ESCs for ρb = 15 dB. However, the ESC of case #2 beyond θ1 = 0.4 becomes similar for both of 15 and 45 dB. The less difference in power allocation factors and the proportionate increase in unavoidable interference with ρb cause similar ESC for low and high ρb in case #2. When ρb = 15 dB, case #1 outperforms case #2, and case #2

OP with respect to ρb of DFC-NOMA is shown in Fig. 8 under the assumption of pIC, and r1 = r3 = rd = 0.75 bps/Hz. It is noticed that OPs decrease with the increase in ρb . OPs of U3 and D1 (case #1) decrease linearly with the increase in ρb , whereas OPs of U1 and D1 (case #2) get saturated due to the presence

M.B. Uddin, Md. Fazlul Kader and S.Y. Shin / Physical Communication 38 (2020) 100914

of interference that creates EFs and leads DOs to 0. It should be mentioned that the interference from BS to D1 in case #2 can only affect the OP of D1 , and the others will remain the same as case #1. Though the OPs of U1 and D1 (case #2) are better than U3 at low ρb , these become inferior at mid to high ρb . As the OP of D1 (case #1) depends only on the U2 -to-D1 link and is interference free, it is better than all other OPs. Owing to the subjection to interference from BS, the OP of D1 (case #2) is inferior than that of D1 (case #1). For all users’ OP, the analytical and simulation results match well and the OPs of U1 and D1 (case #2) meet their respective EFs at high ρb , which support the accuracy of the analysis. OP versus ρb of DFC-NOMA is shown in Fig. 9 for two different values of residual interference, i.e., ς = 0.32 and 0.033 . The OP under less residual interference (ς = 0.033 ) is better than the OP under higher residual interference (ς = 0.32 ). The graph trend is similar as Fig. 8. Higher residual interference causes users meeting their respective error floors at higher OP, and vice-versa. To be more specific, for ς = 0.32 , users meet the error floor at higher OP than that of ς = 0.033 . As the OP of D1 in case #1 is independent of residual interference, it remains similar for both ς values. 4.3. Comparative analysis To clarify the novelty and contribution of our work, a summary of comparative study among the proposed DFC-NOMA, D2DNOMA [18], and NOMA with cooperative FD relaying [23] is provided in Table 2. 5. Conclusion A D2D-aided FD cooperative communication protocol using NOMA, i.e., DFC-NOMA, has been proposed and analyzed over Rayleigh fading channels. Considering ipIC, the exact and asymptotic expressions of EC, E-SC, OP, and DO of the system have been analyzed. By the cost of an increased interference at the NU (U1 ) than FC-NOMA and D2D-NOMA schemes, DFC-NOMA facilitates simultaneous data transmission to cellular and D2D users that helps in achieving higher capacity than FC-NOMA and D2D-NOMA schemes. The performance varies depending on the various physical parameters. It is observed that lower residual interference shows better system performance. As the interference influences the performance of NOMA exploited systems, interference mitigation technique for this kind of protocol is kept for future investigation. Besides, to enhance the NOMA user fairness, an optimal power allocation strategy for the proposed protocol will also be investigated in future research. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2019R1A2C1089542).

9

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Mohammed Belal Uddin received the B.Sc. degree in electrical & electronic engineering from the Rajshahi University of Engineering and Technology, Rajshahi, Bangladesh, in December 2014. Recently, he has completed Master’s degree in IT convergence engineering from the Kumoh National Institute of Technology, Gumi, South Korea. His major research interests include 5G, cooperative communications, NOMA, MIMO, cognitive radio networks etc. [email protected]

Md. Fazlul Kader has been a faculty member with the Department of Electrical and Electronic Engineering, University of Chittagong, Bangladesh since 2007, where he is currently an Associate Professor. He received the Ph.D. degree from the Kumoh National Institute of Technology, South Korea in February 2018 with best PhD Thesis Award. He was also selected as a Best Researcher by BK21 project, South Korea in the same year. He is an Associate Editor of the IEEE Access and received Outstanding Associate Editor Award of 2018. Moreover, he regularly serves as a reviewer and TPC member in many reputed journals and conferences. His major research interests include 5G, cognitive radio networks, cooperative communications, MIMO, computer networks, NOMA, spatial modulation etc. [email protected] Soo Young Shin received his B.S., M.S., and Ph.D. degrees in electrical engineering and computer science from the Seoul National University, Seoul, Korea, in 1999, 2001, and 2006, respectively. From July 2006 to June 2007, he was a Visiting Scholar at FUNLab, the University of Washington, Seattle, WA, USA. For 3 years, he was working in the WiMAX Design Lab, Samsung Electronics, Suwon City, Korea and is currently an Associate Professor in the School of Electronics, Kumoh National Institute of Technology, Gumi City, Korea, since September 2010. His research interests include 5G, cognitive radio networks, NOMA, OFDM, signal processing etc. [email protected]