Capacity and outage analysis of a dual-hop decode-and-forward relay-aided NOMA scheme
Md. Fazlul Kader, Mohammed Belal Uddin, S.M. Riazul Islam, Soo Young Shin
CCapacity and outage analysis of a dual-hop decode-and-forwardrelay-aided NOMA scheme
Md. Fazlul Kader ∗ , Mohammed Belal Uddin , S. M. Riazul Islam , Soo Young Shin Department of Electrical and Electronic Engineering, University of Chittagong, Chittagong-4331, Bangladesh. Department of IT Convergence Engineering, Kumoh National Institute of Technology, Gumi 39177, South Korea Department of Computer Science and Engineering, Sejong University, Seoul 05006, South Korea
Abstract
Non-orthogonal multiple access (NOMA) is regarded as a candidate radio access technique for the next gen-eration wireless networks because of its manifold spectral gains. A two-phase cooperative relaying strategy(CRS) is proposed in this paper by exploiting the concept of both downlink and uplink NOMA (termed asDU-CNOMA). In the proposed protocol, a transmitter considered as a source transmits a NOMA compositesignal consisting of two symbols to the destination and relay during the first phase, following the principleof downlink NOMA. In the second phase, the relay forwards the symbol decoded by successive interferencecancellation to the destination, whereas the source transmits a new symbol to the destination in parallel withthe relay, following the principle of uplink NOMA. The ergodic sum capacity, outage probability, outagesum capacity, and energy efficiency are investigated comprehensively along with analytical derivations, un-der both perfect and imperfect successive interference cancellation. To inquire more insight into the systemoutage performance, diversity order for each symbol in the proposed DU-NOMA is also demonstrated.The performance improvement of the proposed DU-CNOMA over the conventional CRS using NOMA isproved through analysis and computer simulation. Furthermore, the correctness of the author’s analysis isproved through a strong agreement between simulation and analytical results.
Keywords:
Cooperative relaying, Downlink, Ergodic capacity, Non-orthogonal multiple access,Successive interference cancellation, Uplink.
1. Introduction
To deal with the high data rate requirements of the next generation wireless networks, integration ofmultiple technologies is anticipated [1, 2]. Cooperative relaying strategy (CRS) is an important technologyfor wireless networks to improve system capacity, combat fading, and extend service coverage [3, 4, 5, 6].In addition, non-orthogonal multiple access (NOMA) has garnered substantial attention from the industry and academia to meet with the large data rate requirements of 5G and beyond [7, 8, 9, 10]. In this paper,cooperative diversity and NOMA are integrated, which can be a promising approach to meet the capacitydemands for future wireless networks [11, 12, 13].A lot of different varieties of NOMA can be found in the literature [14]. Among them, cooperativeNOMA (C-NOMA) is one of the most dynamic areas of research [11, 12, 13, 14, 15, 16]. Based on the direction of data transmission C-NOMA can be further classified as uplink C-NOMA [17, 18] anddownlink C-NOMA [19, 20, 21]. In [19], a cooperative relaying scheme (CRS) using NOMA (termed as ∗ Corresponding author
Email addresses: [email protected] (Md. Fazlul Kader ), [email protected] (Mohammed Belal Uddin ), [email protected] (S. M. Riazul Islam ), [email protected] (Soo Young Shin ) Preprint submitted to Digital Signal Processing February 22, 2019 a r X i v : . [ c s . I T ] F e b RS-NOMA) was proposed to improve the spectral efficiency over independent Rayleigh fading channels,where a source (S) transmits a superposition coded composite signal to the relay (R) and the destination (D),during the first time slot. Then, R decodes the symbol to be relayed by performing successive interference cancellation (SIC), whereas D decodes own symbol considering other signal as noise. In the subsequenttime slot, R retransmits the decoded symbol with full power to D. The outcome of CRS-NOMA [19] demon-strates that CRS-NOMA can achieve better sum capacity than traditional decode-and-forward [3] for a highsignal-to-noise ratio (SNR) ρ , but shows worse performance for a low ρ . In [20], the performance of CRS-NOMA [19] was investigated over Rician fading channels. A novel detection scheme for CRS-NOMA [19] was proposed in [21] (termed as CRS-NOMA-ND), where D uses maximal-ratio combining (MRC) andanother SIC to jointly decode transmitted symbols by source. It was shown that CRS-NOMA-ND [21] out-performs CRS-NOMA [19], particularly when the link between S and R is better than the R to D link. Notethat only achievable average rate was analyzed in [19, 20, 21]. In [22, 23], the authors considered both up-link and downlink NOMA under non-cooperative scenario, whereas [24, 25] exploited the concept of both uplink and downlink NOMA under cooperative scenario. In [24], a cooperative relay sharing network wasproposed, where multiple sources can communicate with their corresponding destination simultaneouslythrough a common relay. A C-NOMA scheme considering both downlink and uplink transmission systems,was proposed in [25], where a strong user works as a cooperative relay for the weak user.Unlike the existing works, in this paper, a CRS-NOMA scheme using the concept of downlink and uplink NOMA (termed as DU-CNOMA) is proposed. In the proposed DU-CNOMA, S transmits a super-position coded composite signal consisting of two symbols s and s to D and R, according to the principleof downlink NOMA as in [19, 20, 21], during the first time slot. However, in the subsequent time slot,unlike [19, 20, 21], S transmits a new symbol s and R transmits decoded symbol s to D simultaneously,according to the principle of uplink NOMA [17, 22, 23]. Furthermore, unlike [19, 20, 21], where only per- fect SIC is considered, we consider both perfect and imperfect SIC by taking into account a more realisticscenario. Principal contributions of this paper are outlined as follows:1. A dual-hop CRS by taking into account NOMA is proposed and investigated over independentRayleigh fading channels.2. The closed-form expressions of the ergodic sum capacity (ESC), outage probability (OP), and outage sum capacity (OSC) of DU-CNOMA are derived under both perfect and imperfect SIC. The analyticalresults are validated by Monte Carlo simulation. To look into more insight of the proposed DU-NOMA system, diversity order (DO) for each symbol is also investigated.3. The energy efficiency (EE) of DU-NOMA is computed. Moreover, for the purpose of comparison,EE of CRS-NOMA [19] and CSR-NOMA-ND [21] is also computed.
4. The performance improvement of the proposed DU-CNOMA over CRS-NOMA [19], and CSR-NOMA-ND [21] is manifested through analysis and simulation. The outcomes of this paper demon-strate that the proposed DU-NOMA is more spectral and energy efficient as compared to CRS-NOMA [19] and CSR-NOMA-ND [21].The rest of this paper is organized as follows. The system model with detailed description of the proposed protocol is provided in Section 2. The channel model is also demonstrated in this section. The closed-formexpressions of the ESC, OP, and OSC are presented in Section 3, 4, and 5, respectively. In Section 6, EE isinvestigated. The numerical results that are validated by Monte Carlo simulation are provided in Section 7,and finally, the conclusion is drawn along with future recommendations in Section 8.
2. Network architecture and protocol descriptions A half-duplex cooperative relaying protocol exploiting the concept of both downlink and uplink NOMAis proposed. The system architecture consists of a source (S), a DF relay (R), and a destination (D), as drawnin Fig. 1. Fig. 1 (a) shows the system architecture considered in [19, 20, 21], whereas Fig. 1 (b) shows thesystem architecture of the proposed DU-NOMA, with related illustrations. All the links (i.e., S-to-R, S-to-D, and R-to-D) are considered available and subjected to independent Rayleigh fading. Channel coefficient (a) CRS-NOMA [19, 20, 21] S D Z Z s R (a) CRS-NOMA [19, 20, 21] S D Z Z s (b) Proposed DU-NOMA Phase-1 Phase-2Phase-1 Phase-2 • S→R, D • SIC at R to decode s • D decodes s • R→D • D decodes s CRS-NOMA [19, 20]CRS-NOMA [21]Phase-1 Phase-2Phase-1 Phase-2 • S→R, D • SIC at R to decode s • D decodes s • R→D • S→D • SIC at D to decode s RS D Z Z s s RS D Z Z s s • S→R, D • SIC at R to decode s • D conserves y D1 • R→D • MRC at D to decode s • SIC at D to decode s • S→R, D • SIC at R to decode s • D conserves y D1 • R→D • MRC at D to decode s • SIC at D to decode s Fig. 1: System model: (a) CRS-NOMA [19, 20, 21] and (b) Proposed DU-CNOMA. with zero mean and variance λ i = d − ν i is represented by h i ∼ CN ( , λ i ) , where d is the distance, ν is thepath loss exponent, and i ∈ { , , } . Parameters h , h , and h refer to the respective complex channelcoefficient of S-to-D, S-to-R, and R-to-D links. Without loss of generality, it is assumed that λ < λ and λ < λ , under statistical channel state information [25]. The data transmission in the proposed protocol isperformed by two cooperative phases as follows. ) At the first phase of the transmission, the source S transmits a composite NOMA signal Z = √ φ P s s + √ φ P s s consisting of two symbols s and s to D and R simultaneously as per law of downlink NOMA.The symbols s and s are corresponded to D and R, respectively. The total transmit power of S, the powerallocation factor with s , and the power allocation factor with s are respectively denoted by P s , φ , and φ wherein φ > φ and φ + φ =
1. Thus, the received signals at D and R are respectively written as y D = h (cid:112) φ P s s + h (cid:112) φ P s s + η , (1) y R = h (cid:112) φ P s s + h (cid:112) φ P s s + η , (2)where η and η are the complex additive white Gaussian noise (AWGN) at D and R, respectively withzero mean and variance σ .Upon receiving the signal, firstly, R extracts s by treating s as noise. Then, it performs SIC to cancelout the extracted information from the received signal and thus it extracts s . For a clear understanding,the SIC process at R following the principle of downlink NOMA, is pictorially represented in Fig. 2 (a).The received signal-to-interference plus noise ratios (SINRs) at R for symbols s and s are respectively3 ecoding of s treating s as noiseDecoding of s s s - (a) Decoding of s treating s as noise Decoding of s s s - (b) Fig. 2: SIC process (a) at R following the principle of downlink NOMA and (b) at D following the principle of uplink NOMA, inDU-NOMA. represented by γ t s → s = φ P s | h | φ P s | h | + σ = φ ρ | h | φ ρ | h | + , (3) γ t s = φ ρ | h | φ ρ | ¯ h | + , (4)where ¯ h ∼ CN ( , κ λ ) , ρ (cid:44) P s σ is the transmit SNR of S and σ is the noise variance. It is noted thatseveral potential implementation issues (i.e, error propagation and complexity scaling) with the use of SIC may lead to errors in decoding even under the perfect channel estimation assumption. As a result theinterference may not be removed completely and there exists residual interference [17, 24, 26]. Hence,in the proposed DU-NOMA, the parameter κ (0 < κ ≤
1) represents the level of residual interferenceat R because of imperfect SIC. As a particular case, κ = κ = performed at R at all, which means that R has to consider s as interference to decode s .On the other hand, D decodes s by recking of s as noise. So, the received SINR regarding symbol s at D is obtained as γ t s = φ ρ | h | φ ρ | h | + . (5)4 .2. Phase-2 (t ) During the second phase, according to the law of uplink NOMA, R retransmits the decoded symbol s and S transmits a new symbol s to D at the same instant of time. The respective assigned powers with s and s are √ P r ϑ and √ P s ϑ , respectively. The total transmit power of R, the power allocation factor with s , and the power allocation factor with s are respectively denoted by P r , ϑ , and ϑ wherein ϑ > ϑ . Thereceived signal at D is therefore given by y D = h (cid:112) ϑ P r s + h (cid:112) ϑ P s s + η , (6)where η is the complex AWGN at D during t with zero mean and variance σ . As the information relatedto s is dominant over s at the destination, D first decodes s by considering s as noise. After then, byapplying SIC procedure, it subtracts the decoded information to get s . For a clear understanding, the SICprocess at D following the principle of uplink NOMA is pictorially represented in Fig. 2 (b). The receivedSINRs concerning s and s at D are respectively given by γ t s = ϑ P r | h | ϑ P s | h | + σ = ϑ ρ | h | ϑ ρ | h | + , (7) γ t s = ϑ ρ | h | ϑ ρ | ¯ h | + , (8)where ¯ h ∼ CN ( , κ λ ) , ρ (cid:44) P r σ is the transmit SNR of R, and κ represents the level of residual interfer-ence at D. Note that κ shows similar behavior like κ . The end-to-end data rate of a multi-hop cooperative network is determined by the weakest link. So, theachievable rate related to s is depicted by C =
12 log (cid:0) + min (cid:0) γ t s → s , γ t s (cid:1)(cid:1) , (9)The achievable rate associated with s is dependent on (4) and (7), which can be denoted by C =
12 log (cid:0) + min (cid:0) γ t s , γ t s (cid:1)(cid:1) , (10)By using (8), the achievable rate related to s is given by C =
12 log (cid:0) + γ t s (cid:1) , (11)Therefore, the sum capacity of the proposed DU-CNOMA system can be calculated by summing up (9),(10), and (11) as follows C propsum = C + C + C . (12)
3. Capacity analysis
The closed-form ESC expression of the proposed DU-CNOMA is derived over independent Rayleighfading channel, in this section. 5 .1. Ergodic capacity related to s The achievable rate of (9), can be simplified as [19, eq. (8)] C =
12 log (cid:0) + min {| h | , | h | } ρ (cid:1) −
12 log (cid:0) + min {| h | , | h | } ρφ (cid:1) , (13)Let W (cid:44) min (cid:0) | h | , | h | (cid:1) . Applying PDF f | h ι | ( w ) = ( / λ ι ) e − w / λ ι for ι ∈ { , } , the CDF of W is derivedas F W ( w ) = − e − w (cid:16) λ + λ (cid:17) . Then, the probability density function of W is derived by taking the derivativeof F W ( w ) as f W ( w ) = (cid:18) λ + λ (cid:19) e − w (cid:16) λ + λ (cid:17) (14)Now, using (13) and (14), the EC associated with s can be obtained as¯ C ex1 = E { C } = (cid:90) ∞ { log ( + ρ w ) − log ( + ρ w φ ) } f W ( w ) dw (15)Using log ( x ) = ln ( x ) ln2 , (15) can be written as¯ C ex1 =
12 ln 2 (cid:90) ∞ { ln ( + ρ w ) − ln ( + ρ w φ ) } f W ( w ) dw (16)By applying (cid:90) ∞ e − mw ln ( + nw ) dw = − m e m / n Ei ( − m / n ) [27, eq. (4.337.2)],¯ C ex1 = −
12 ln 2 e ρ (cid:16) λ + λ (cid:17) Ei (cid:18) − ρ (cid:18) λ + λ (cid:19)(cid:19) +
12 ln 2 e φ ρ (cid:16) λ + λ (cid:17) Ei (cid:18) − φ ρ (cid:18) λ + λ (cid:19)(cid:19) (17)where E {·} and Ei {·} denote the expectation operator and exponential integral function, respectively [27]. Let U (cid:44) γ t s , V (cid:44) γ t s , and Z (cid:44) min ( U , V ) . The CDF of U and V can be respectively written as [24, eq.(7)] F U ( u ) = − φ λ φ λ + φ κ λ v e − v φ ρλ = − pp + u e − u φ ρλ , (18) F V ( v ) = − ϑ λ ϑ λ + ϑ λ v e − v ϑ ρλ = − gg + v e − v ϑ ρλ , (19)6here p = φ λ / φ κ λ and g = ϑ λ / ϑ λ . Using (18) and (19), the CDF of Z can be obtained as F Z ( z ) = − pg ( p + z )( g + z ) e − qz , (20)where q = φ ρλ + ϑ ρλ . So, the exact EC related to s is derived as¯ C ex2 = E { C } = (cid:90) ∞ log ( + z ) f Z ( z ) dz . (21)Applying (cid:82) ∞ log ( + z ) f Z ( z ) dz = (cid:82) ∞ − F Z ( z ) + z dz , (21) can be represented as¯ C ex2 =
12 ln 2 (cid:90) ∞ pg ( + z ) ( p + z )( g + z ) e − qz dz = p log e ( p − ) (cid:90) ∞ (cid:20) ( + z ) − gg + z − ( p + z ) − gg + z (cid:21) e − qz dz = p log e ( p − ) (cid:20) gg − (cid:26) − e q Ei ( − q ) + e gq Ei ( − gq ) (cid:27) − gg − p (cid:26) − e pq Ei ( − pq ) + e gq Ei ( − gq ) (cid:27)(cid:21) . (22)Note that (22) is derived by considering imperfect SIC (i.e., 0 < κ ≤ s underperfect SIC is derived as follows.With perfect SIC, Z (cid:44) min ( U , V ) can be written as Z (cid:44) min (cid:0) φ ρ | h | , V (cid:1) . The CDF of Z is thereforegiven by F Z ( z ) = − gg + z e − qz , (23)The exact EC related to s under perfect SIC, is derived as¯ C ex2 , p = (cid:90) ∞ log ( + z ) f Z ( z ) dz = log e (cid:90) ∞ g ( + z ) ( g + z ) e − qz dz = g log e ( g − ) (cid:90) ∞ (cid:18) + z − g + z (cid:19) e − qz dz = g log e ( g − ) {− e q Ei ( − q ) + e gq Ei ( − gq ) } . (24) Let Y (cid:44) γ t s . So, the CDF of Y is derived as F Y ( y ) = − ϑ λ ϑ λ + ϑ κ λ y e − y ϑ ρλ . (25)7o, the exact EC associated with s is obtained as¯ C ex3 = E { C } = (cid:90) ∞ log ( + y ) f Y ( y ) dy = log e (cid:90) ∞ ( + y ) − ϑ λ ϑ λ + ϑ κ λ y e − y ϑ ρλ dy = log e (cid:20) ϑ λ ϑ λ − ϑ κ λ × (cid:26) (cid:90) ∞ ( + y ) − − (cid:90) ∞ ϑ κ λ ϑ λ + ϑ κ λ v (cid:27) e − y ϑ ρλ dy (cid:21) = log e (cid:20) ϑ λ ϑ λ − ϑ κ λ × (cid:26) − e ϑ ρλ Ei ( − ϑ ρλ ) + e ϑ κ ρλ Ei ( − ϑ κ ρλ ) (cid:27)(cid:21) . (26)Note that (26) is derived by considering imperfect SIC (i.e., 0 < κ ≤ s under perfect SIC is derived as follows.With perfect SIC, Y (cid:44) γ t s can be written as Y (cid:44) ϑ ρ | h | . The CDF of Y is therefore given by F Y ( y ) = − e − y ϑ ρλ . (27)Hence, the exact EC associated with s is obtained as¯ C ex3 , p = log e (cid:90) ∞ − F Y ( y )( + y ) dy = − log e e r Ei ( − r ) , (28)where r = ϑ ρλ . Using (17), (22), and (26), the exact closed-form expression of ESC of the proposed DU-CNOMAprotocol under imperfect SIC can be written by¯ C propsum, ip = ¯ C ex1 + ¯ C ex2 + ¯ C ex3 . (29)Conversely, using (17), (24), and (28), the exact closed-form expression of ESC of the proposed DU-CNOMA protocol under perfect SIC can be written by¯ C propsum, p = ¯ C ex1 + ¯ C ex2 , p + ¯ C ex3 , p . (30)
4. Outage probability analysis
According to the required quality of service, C t , C t , and C t are assumed to be the predetermined target date rate thresholds of the symbols s , s , and s , respectively. The closed-form expressions ofoutage probabilities related to s , s , and s are provided over independent Rayleigh fading channel in thefollowing subsections. 8 .1. Outage probability of symbol s The OP of symbol s is given by P out , s = P r { γ t s < R t } = − e − Rt λ ρ ( φ − φ Rt ) , (31)where R t = C t − R t R t + < φ < The OP of symbol s is given by P out , s = − P r { min ( γ t s , γ t s ) > R t } P r { γ t s → s > R t } = − φ λ ϑ λ ( φ λ + φ κ λ R t )( ϑ λ + ϑ λ R t ) × e − Rt φ ρλ − Rt ϑ ρλ − Rt λ ρ ( φ − φ Rt ) , (32)where R t = C t −
1. Now, by putting κ =0, the OP of s under perfect SIC can be expressed as P pout , s = − ϑ λ ( ϑ λ + ϑ λ R t ) e − Rt φ ρλ − Rt ϑ ρλ − Rt λ ρ ( φ − φ Rt ) (33) The OP of symbol s is given by P out , s = − ϑ λ ϑ λ + ϑ κ λ R t e − Rt ϑ ρλ , (34)where R t = C t −
1. Now, by putting κ =0, the OP of s under perfect SIC can be expressed as P pout , s = − e − Rt ϑ ρλ . (35) To investigate more insight into the system outage performance, this section demonstrates DO for eachsymbol in the proposed DU-NOMA. By using lim ρ → ∞ − log P out log ρ [28] in the high SNR regime, DOs related to each of the symbols can be computed according to the following Lemma. Lemma 4.1.
Consider ρ → ∞ and e − x = − x in the high SNR regime. Hence, DOs of s , s , and s arerespectively expressed as D s = , D s = (cid:40) , imperfect SIC0 , perfect SIC D s = (cid:40) , imperfect SIC1 , perfect SIC (36)9 roof. In high SNR, the OP related to symbol s can be approximated as P ∞ out , s = R t λ ρ ( φ − φ R t ) ≈ ρ . (37)So, the DO related to symbol s is derived as D s = lim ρ → ∞ − log 1 − log ρ log ρ = . (38)Moreover, the OP related to symbol s for large ρ under imperfect and perfect SIC can be respectivelyapproximated as P ∞ out , s = − φ λ ϑ λ ( φ λ + φ κ λ R t )( ϑ λ + ϑ λ R t ) , (39) P p , ∞ out , s = − ϑ λ ( ϑ λ + ϑ λ R t ) . (40)Imperfect SIC and inter-symbol interference effects cause the OP related to s settling in the high SNRthat creates error floor. Using (39) and (40), the DO related to symbol s under imperfect and perfect SICrespectively can be found as D s = lim ρ → ∞ − log P ∞ out , s log ρ = , (41) D p s = lim ρ → ∞ − log P p , ∞ out , s log ρ = . (42)Lastly, in high SNR, the OP related to symbol s under imperfect and perfect SIC can be respectivelyapproximated as P ∞ out , s = − ϑ λ ϑ λ + ϑ κ λ R t , (43) P p , ∞ out , s = R t ϑ ρλ ≈ ρ . (44)Therefore, the DO related to s under imperfect and perfect SIC can be respectively computed by using (43)and (44) as D s = lim ρ → ∞ − log P ∞ out , s log ρ = , (45) D p s = lim ρ → ∞ − log P p , ∞ out , s log ρ = lim ρ → ∞ − log 1 − log ρ log ρ = . (46)The DO related to s under realistic imperfect SIC assumption becomes zero whereas it becomes one underperfect SIC assumption.
5. Outage capacity analysis
This section presents analytical derivation of OC for each symbol in the proposed DU-CNOMA over independent Rayleigh fading channels. The OC is defined as the data rate that can be attained if a systemis allowed to be in outage with probability ϒ . For wireless environments with deep fading situation, it is a10ritical performance metric. The OC of each symbol can be derived from their corresponding OP by using[29, eq. (2.68)] as shown in the following subsections. The OC C t related to s , with specified OP ϒ can be computed from (31) as ϒ = − e − Rt λ ρ ( φ − φ Rt ) e − Rt λ ρ ( φ − φ Rt ) = − ϒ − R t λ ρ ( φ − φ R t ) = ln ( − ϒ ) { ( λ φ ρ ln ( − ϒ ) − } R t = λ φ ρ ln ( − ϒ ) C t − = λ φ ρ ln ( − ϒ )( λ φ ρ ln ( − ϒ ) − C t =
12 log (cid:18) + λ φ ρ ln ( − ϒ )( λ φ ρ ln ( − ϒ ) − (cid:19) . (47) Using e x ≈ + x at high ρ , the OC C t related to s , with specified OP ϒ can be computed from (32) as ϒ = − φ λ ϑ λ ( φ λ + φ κ λ R t )( ϑ λ + ϑ λ R t ) × (cid:18) − R t φ ρλ − R t ϑ ρλ (cid:19) ϒ = − GH ( G + IR t )( H + JR t ) (cid:18) − R t G ρ − R t H ρ (cid:19) , (48)conditioned on γ t s → s > R t , where G = φ λ , H = ϑ λ , I = φ κ λ , and J = ϑ λ . After some algebraicsimplifications, (48) can be rewritten as IJ ρ ( − ϒ ) R t + { ( GJ + HI ) ( − ϒ ) ρ + H + G } R t + ( − GH ρ ϒ ) = KR t + LR t + M = K = IJ ρ ( − ϒ ) , L = ( GJ + HI ) ( − ϒ ) ρ + H + G , M = − GH ρ ϒ are assumed. Solving (49) andconsidering feasible root, C t can be obtained as R t = − L + √ L − KM K C t − = − L + √ L − KM KC t =
12 log (cid:32) + − L + √ L − KM K (cid:33) (50)11n the other hand, the OC C t under perfect SIC can be computed from (33) as ϒ = − ϑ λ ( ϑ λ + ϑ λ R t ) (cid:18) − R t φ ρλ − R t ϑ ρλ (cid:19) = − H ( H + JR t ) (cid:18) − R t G ρ − R t H ρ (cid:19) R t = GH ρ ϒ GJ ρ ( − ϒ ) + G + HC t =
12 log (cid:18) + GH ρ ϒ GJ ρ ( − ϒ ) + G + H (cid:19) (51) Using e x ≈ + x at high ρ , the OC C t related to s , with specified OP ϒ can be computed from (34) as ϒ = − ϑ λ ϑ λ + ϑ κ λ R t ( − R t ϑ ρλ ) ϒ = − ϑ λ ( ϑ ρλ − R t )( ϑ λ + ϑ κ λ R t ) ϑ ρλ ϒ = ϑ κ λ R t ρ + R t ( ϑ λ + ϑ κ λ R t ) ρ R t = ϑ λ ρ ϒ + ϑ κ λ ρ − ϑ κ λ ρ ϒ C t =
12 log (cid:18) + ϑ λ ρ ϒ + ϑ κ λ ρ ( − ϒ ) (cid:19) (52)On the other hand, the OC C t under perfect SIC can be computed from (35) as ϒ = − e − Rt ϑ ρλ e − Rt ϑ ρλ = − ϒ R t = − ϑ ρλ ln ( − ϒ ) C t = − ϑ ρλ ln ( − ϒ ) C t =
12 log ( − ϑ ρλ ln ( − ϒ )) (53) Using (47), (50), and (52), the OSC of the proposed DU-CNOMA under imperfect SIC is given by C outsum, ip = ( ) + ( ) + ( ) . (54)Conversely, Using (47), (51), and (53), the OSC of the proposed DU-CNOMA under perfect SIC is givenby C outsum, p = ( ) + ( ) + ( ) . (55)12 SNR [dB] E r god i c s u m c apa c i t y ( b i t s / s e c / H z ) CRS-NOMA [Sim.]CRS-NOMA-ND [Sim.]DU-NOMA [Sim.]DU-NOMA [Anl.]
Perfect SICImperfect SIC=0.02 =0.04 =0.08 Fig. 3: ESC comparison between CRS-NOMA [19], CRS-NOMA-ND [21], and proposed DU-CNOMA w.r.t SNR ρ . φ =0.9, φ =0.1, ϑ =1, and ϑ =0.7. Distance between S and R, d SR (in meters) E r god i c s u m c apa c i t y ( b i t s / s e c / H z ) CRS-NOMA [19]CRS-NOMA-ND [21]DU-NOMA =35 dB=45 dB
Fig. 4: ESC comparison between CRS-NOMA [19], CRS-NOMA-ND [21], and proposed DU-CNOMA w.r.t distance (in meters)from S to R, d SR under perfect SIC. φ =0.9, φ =0.1, ϑ =1, and ϑ =0.7.
6. Energy Efficiency
To study the performance of future wireless networks, EE can be another important performance metric.Hence, in this section, we demonstrate EE of the proposed DU-NOMA protocol. The expression of EE η can be written by η = Total data rate of the NOMA systemTotal energy consumption . (56)13 .05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Power allocation coefficient E r god i c s u m c apa c i t y ( b i t s / s e c / H z ) CRS-NOMACRS-NOMA-NDDU-NOMA =35 dB=45 dB
Fig. 5: ESC comparison between CRS-NOMA [19], CRS-NOMA-ND [21], and proposed DU-CNOMA w.r.t power allocation coef-ficient φ under perfect SIC. ϑ =1 and ϑ =0.7. Now, using (29) and (30), EE of DU-NOMA considering ESC or delay-tolerant transmission mode underimperfect SIC and perfect SIC can be respectively given by [26] η ESCDU-NOMA, ip = ¯ C propsum, ip T P s + T P r = C propsum, ip T P s + T P r , η ESCDU-NOMA, p = ¯ C propsum, p T P s + T P r = C propsum, p T P s + T P r . (57)where T represents the time of a complete transmission. Similarly, using (54) and (55), EE of DU-NOMAconsidering OSC under imperfect SIC and perfect SIC can be respectively given by η OSCDU-NOMA, ip = C outsum, ip T P s + T P r , η OSCDU-NOMA, p = C outsum, p T P s + T P r . (58)Moreover, for the purpose of comparison, EE of CRS-NOMA and CRS-NOMA-ND under perfect SIC canalso be investigated using [19, eq. (10)] and [21, eq. (20)] into (56), respectively considering delay-toleranttransmission mode.
7. Numerical results and discussions
This section presents simulation (Sim.) and analytical (Anl.) results of our proposed DU-CNOMA pro- tocol. In each case, analytical result matches well with simulation result and it confirms the correctness ofthe author’s analysis presented here. For comparison purpose, the simulation results for CRS-NOMA [19]and CRS-NOMA-ND [21] are also presented. It should be mentioned that analytical derivations for OPand OSC are not provided in [19, 21]. Throughout the simulation, it is assumed that ν =2, d SD =10 meters, d SR = d SD / d RD = − d SR , φ =0.9, φ =0.1, ϒ = ϒ = ϒ = ϒ , ϑ =1, ϑ =0.7, and κ = κ = κ , unless otherwise specified. Note that fixed power allocation method as in [19, 20, 21] is assumed for the proposedprotocol. 14 SNR [dB] -3 -2 -1 O u t age p r obab ili t y P out, s [Sim.]P out, s [Anl.]P pout, s [Sim.]P pout, s [Anl.]P pout, s [Sim.]P pout, s [Anl.] C t =0.5 bps/Hz C t =0.75 bps/Hz Fig. 6: OP of the proposed DU-CNOMA w.r.t SNR ρ under perfect SIC. φ =0.9, φ =0.1, ϑ =1, and ϑ =0.7. It should be mentioned that the distance used in the simulations is arbitrary. Although, we have assumedthat the distance between S and D is 10 m, the proposed protocol is viable for any distance between S andD by tuning different parameters such as transmit power, bandwidth, path loss exponent etc. Furthermore, to meet the demanded traffic in 5G or future wireless systems, network densification by the deployment ofultra-dense small cells is one of the most effective techniques. Therefore, small cells with inter-site distanceof 5, 10, 20 m etc. are expected to be common in future wireless systems [30, 31].
10 15 20 25 30 35 40 45 50
SNR [dB] -3 -2 -1 O u t age p r obab ili t y =0.02 =0.04 Lines: analytical resultsMarkers: simulation resultsP out, s P out, s Fig. 7: OP of the proposed DU-CNOMA w.r.t SNR ρ under imperfect SIC. φ =0.9, φ =0.1, ϑ =1, ϑ =0.7, and C t =0.5 bps/Hz . ESC versus SNR behavior of DU-CNOMA, CRS-NOMA, and CRS-NOMA-ND is shown in Fig. 3.
Performance of the proposed DU-CNOMA is executed under two conditions, i.e., perfect SIC and imperfectSIC. Note that only perfect SIC is considered in CRS-NOMA and CRS-NOMA-ND. For the case of perfectSIC, it is observed from the figure that DU-CNOMA significantly outperforms all other existing protocols.15
SNR [dB] O u t age s u m c apa c i t y ( bp s / H z ) OSC [Sim.]OSC [Anl.] =0.02 =0.04 =0.08 Imperfect SICPerfect SIC
Fig. 8: OSC of the proposed DU-CNOMA w.r.t SNR ρ . φ =0.9, φ =0.1, ϑ =1, ϑ =0.7, and ϒ =0.1. However, with the increasing amount of residual interference the performance of DU-CNOMA starts de-grading which causes it to exhibit a saturated value at high ρ values. For example, the performance of the proposed protocol becomes worse for κ = . than κ = . . Therefore, at high ρ , the adverse impact ofresidual interference on DU-CNOMA causes it to achieve less ESC than existing methods. Therefore, it issuggested that an efficient interference cancellation technique can significantly improve the performance ofDU-NOMA, particularly at medium to high ρ . Lastly, strong agreement between simulation and analyticalresults verifies the appropriateness of the ESC analysis. ESC behavior for varying relay position between source and destination, d SR (in meters) is demonstratedin Fig. 4, under perfect SIC. ESC versus d SR performance of DU-CNOMA is compared with CRS-NOMAand CRS-NOMA-ND protocols for two different ρ values, i.e., ρ = 35 and 45 dBs. For both cases, proposedprotocol achieves better ESC than existing protocols irrespective of the relay position. In addition, ESC ofDU-CNOMA becomes far better than others for the increasing distance between source and relay. However, the ESC of DU-CNOMA becomes maximum at a certain d SR . For example, this behavior is bounded by amaximum d SR value (e.g., around d SR = 5 for ρ = 35 dB and around d SR = 9.5 for ρ = 45 dB).ESC with respect to (w.r.t) the power allocation coefficient φ is shown in Fig. 5 for two cases of ρ ,where ρ = 35 dB and ρ = 45 dB. It is demonstrated that ESC performance of DU-NOMA degrades with theincrease of φ , whereas φ has a slight impact of the performance of CRS-NOMA and CRS-NOMA-ND. Further, ESC of the proposed DU-CNOMA protocol is higher than existing protocols for all feasible valuesof φ . It is also clear from the figure that ESC of the proposed protocol is higher for ρ = 45 dB than 35 dB.16 Specified outage probability O u t age s u m c apa c i t y ( bp s / H z ) =35 dB [Perfect SIC]=45 dB [Perfect SIC]=35 dB [Imperfect SIC, =0.04 ]=45 dB [Imperfect SIC, =0.04 ] Fig. 9: OSC of the proposed DU-CNOMA w.r.t specified outage probability ϒ under perfect SIC. φ =0.9, φ =0.1, ϑ =1, and ϑ =0.7. Let C t = C t = C t = C t . OP versus SNR performance of the proposed protocol is demonstrated in Fig.6 for two different threshold values of target data rate, i.e., C t = 0.5 bps/Hz and 0.75 bps/Hz. Perfect SIC is considered for analyzing all analytical and simulation results. Coincidence of analytical and simulationresults for each case refers to the accuracy of OP analysis. It is pointed out that OP becomes better withthe increase of SNR. The OPs related to s and s show better than s for a specific C t when ρ ranges frommedium to high. Though OPs related to symbols s and s decrease linearly with the increase of ρ after acertain ρ , OP related to symbol s tends to be saturated for high ρ range. The OPs related to s , s , and s for C t = 0.75 bps/Hz is higher than C t = 0.5 bps/Hz, as expected.By considering imperfect SIC and target data rate C t = 0.5 bps/Hz, OP of DU-CNOMA protocol w.r.tSNR ρ is depicted in Fig. 7. Only OP versus SNR analysis related to s and s are compared as theperformance related to s is not affected by imperfect SIC condition. OP related to s is better than s atany value of ρ for the considered parameters. OP related to any of the symbols is less for small residual interference (i.e., κ = . ) than comparatively large amount of residual interference (i.e., κ = . ).Though OP related to s shows linear behavior even at high ρ as shown in Fig. 6, it tends to be saturated athigh ρ as shown in Fig. 7 due to the impact of residual interference.
10% OSC of the proposed DU-CNOMA protocol w.r.t SNR ρ is plotted under both perfect and imper- fect SIC conditions in Fig. 8. Three cases of imperfect SIC is considered, i.e., κ = . , κ = . and κ = . . For perfect SIC condition, OSC of the system linearly increases with the betterment of ρ andmaintains it till the high ρ . But, for imperfect SIC condition, OSC of the system tends to be saturated athigh ρ due to the impact of residual interference. If the effect of residual interference increases, OSC ofDU-CNOMA decreases and tends to be saturated at a less value of ρ than for comparatively small residual interference impact.OSC behavior w.r.t specified outage probability ϒ for the proposed DU-CNOMA protocol is demon-strated in Fig. 9. Both perfect and imperfect SIC conditions are taken into account and the performancebehavior is observed for two different values of ρ , i.e., ρ = 35 dB and 45 dB. Fig. 9 depicts that OSC of thesystem increases with the increase of specified outage probability ϒ . In addition, OSC goes high for higher ρ (= 45 dB) than lower ρ (= 35 dB). It is also clear that OSC of DU-NOMA shows better for perfect SICcase than imperfect SIC case for a specific value of ρ .17 SNR [dB] A v e r age ene r g y e ff i c i en cy ( b i t s / J / H z ) CRS-NOMACRS-NOMA-NDDU-NOMA
Perfect SICImperfect SIC=0.08 =0.04 =0.02 Fig. 10: EE comparison between CRS-NOMA [19], CRS-NOMA-ND [21], and proposed DU-CNOMA w.r.t SNR ρ consideringergodic rate or delay-tolerant transmission. φ =0.9, φ =0.1, ϑ =1, ϑ =0.7, T=1 and P s = P r =
10 W.
10 15 20 25 30 35 40 45 50
SNR [dB] A v e r age ene r g y e ff i c i en cy ( b i t s / J / H z ) Perfect SICImperfect SIC =0.02 =0.04 =0.08 Fig. 11: EE of the proposed DU-CNOMA w.r.t SNR ρ considering OSC. φ =0.9, φ =0.1, ϑ =1, ϑ =0.7, T=1 and P s = P r =
10 W.
Fig. 10 shows EE comparison between DU-NOMA, CRS-NOMA, and CRS-NOMA-ND w.r.t. SNRconsidering delay-tolerant transmission mode or ergodic rate. It is observed that DU-NOMA shows sig- nificantly better performance than CRS-NOMA and CRS-NOMA-ND, in terms of EE under perfect SIC.However, under imperfect SIC, the performance gain of DU-NOMA over others depend on the level ofresidual interference, particularly at high ρ . Finally, Fig. 11 shows EE of the proposed DU-NOMA versusSNR considering outage sum rate under both perfect and imperfect SIC. From both figures, it is clear thatperfect SIC case outperforms imperfect SIC case, particularly at medium to high ρ . Finally, a comparative study between the proposed DU-NOMA, CRS-NOMA [19], and CRS-NOMA-ND [21] is summarized in Table 1. 18 . Conclusion and future works
A cooperative decode-and-forward relaying strategy using the concept of downlink and uplink NOMA has proposed and analyzed in this paper. Under both perfect and imperfect SIC, the performance of theproposed protocol has studied comprehensively, in terms of ESC, OP, EE and OSC over independentRayleigh fading channels. The closed-form expressions of these system parameters have derived and vali-dated by computer simulation. To get insight into the systems’s outage performance, DO for each symbol isalso computed. It has shown that the proposed protocol significantly outperforms CRS-NOMA and CRS-
NOMA-ND under perfect SIC, whereas under imperfect SIC, performance gains depends on the level ofresidual interference, particularly at high SNR. Furthermore, hybrid downlink-uplink NOMA for multi-input multi-output systems will be investigated in future works.19 able 1: A comparative study between the proposed DU-NOMA, CRS-NOMA [19], and CRS-NOMA-ND [21].
Item CRS-NOMA [19] and CRS-NOMA-ND [21] Proposed DU-NOMASystemModel A CRS-NOMA consisting of a S, a R anda D is proposed, where direct link betweenS and D is active.• A downlink NOMA is exploited inPhase-1 only. In phase-2, only R re-transmits the decoded symbol to D.• In contrast to CRS-NOMA [19], Duses MRC and another SIC to jointlydecode transmitted symbols by S inCRS-NOMA-ND [21].• Two symbols are transmitted duringtwo phases. A different relaying strategy using NOMA(termed as DU-NOMA) is proposed andinvestigated to further improve the per-formance of CRS-NOMA system as com-pared to [19, 21].• The concept of downlink NOMA isexploited in phase-1, whereas theconcept of uplink NOMA is appliedin phase-2.• Three symbols are transmitted dur-ing two phases.PerformanceMetrics • ESC• Though simulation results for OP isalso shown in [21], [21] did not pro-vide any closed-form expressions forOP. • ESC• OP• OSC• DO and• EEAnalyticalderivations Analytical derivation for ESC is provided. Analytical derivations for ESC, OP, OSC,DO, and EE are provided.Numericalresults Simulation results show only ESC in [19],whereas ESC and OP in [21]. Simulation results show ESC, OP, OSC,and EE.Outcomes CRS-NOMA [19] can achieve morespectral efficiency than the conventionalCRS [3] when the SNR is high, and theaverage channel power of the S-to-R link isbetter than those of the S-to-D and R-to-Dlinks. On the contrary, [21] outperforms[19], particularly when the link between Sand R is better than the R to D link. The proposed DU-NOMA is more spectraland energy efficient as compared to CRS-NOMA [19] and CSR-NOMA-ND [21].
Disclosure statement
The author(s) declare(s) no potential conflict of interest regarding the publication of this paper.
Acknowledgment
This research was supported by the University of Chittagong, in part by the MSIT (Ministry of Science,ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2018-20014-1-00639) supervised by the IITP (Institute for Information & communications Technology Promo-tion). This research was also supported by the Sejong University Research Faculty Program Fund (2019-
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