A Coordinated Direct AF/DF Relay-Aided NOMA Framework for Low Outage

This paper investigates the performance of a framework for low-outage downlink non-orthogonal multiple access (NOMA) signalling using a coordinated direct and relay transmission (CDRT) scheme with direct links to both the near-user (NU) and the far-user (FU). Both amplify-and-forward (AF) and decode-and-forward (DF) relaying are considered. In this framework, NU and FU combine the signals from BS and R to attain good outage performance and harness a diversity of two without any need for feedback. For the NU, this serves as an incentive to participate in NOMA signalling. For both NU and FU, expressions for outage probability and throughput are derived in closed form. High-SNR approximations to the outage probability are also presented. We demonstrate that the choice of power allocation coefﬁcient and target rate is crucial to maximize the NU performance while ensuring a desired FU performance. We demonstrate performance gain of the proposed scheme over selective decode-and-forward (SDF) CDRT-NOMA in terms of three metrics: outage probability, sum throughput and energy efﬁciency. Further, we demonstrate that by choosing the target rate intelligently, the proposed CDRT NOMA scheme ensures higher energy efﬁciency (EE) in comparison to its orthogonal multiple access counterpart. Monte Carlo simulations validate the derived expressions.


I. INTRODUCTION
The proliferation of internet of things (IoT) and massive machine type communication has augmented the demand for higher data rates, low latency and high bandwidth efficiency in beyond 5G (B5G) and of the incoming signal, and c) incremental selective DF relaying where the relayed link is used opportunistically, and requires a three-bit feedback. Further, in [27], performance of fixed-gain AF relay based CDRT NOMA was investigated in the presence of the BS-FU link assuming sub-optimal selection combining at the FU.

A. Motivation and Contribution
Due to participation in NOMA signalling, NU needs to decode the FU symbol first to perform SIC (complexity of the NU receiver clearly increases) before it can decode its own symbol. Depending on the channel condition as well as the target rate and power allocation factor, NU might occasionally fail to decode its own symbol due to insufficient signal-to-noise ratio (SNR) or unsuccessful decoding of the FU symbol. In such a scenario the BS has to re-transmit the superimposed symbol, which causes reduction in SE as well as energy efficiency (EE). In C-NOMA NU incurs loss in SE (due to allocation of power to the FU symbols, and use of two signalling phases), and EE as well (it is required to expend energy for relaying the FU symbol).
All the aforementioned works [10], [13], [15]- [17], [21]- [24], [26], [27] have laid a solid foundation for the use of C-NOMA and CDRT to improve the FU's performance, but there has been little effort to to improve the NU's performance. Several multimedia-type applications impose a low outage QoS, and it might not be possible to satisfy NU's constraints using these CDRT approaches (they only guarantee a diversity of one at the NU [21]). However, considering an AF or DF relay to assist FU as well as NU with optimal combining at both users not only improves the NU diversity, but also results in improved QoS at both the users. The NU will be required to perform combining with SIC (in a framework discussed in this paper), but attains much better performance, which is required in many scenarios. We also discuss optimization of NU performance while ensuring a desired performance at FU . The key contributions of this paper are as follows: • Considering both AF and DF relaying, we investigate the performance of a new framework for CDRT based downlink NOMA network with direct link to both NU and FU. In the considered framework, BS transmits NOMA signal to relay, NU and FU in the first signalling phase, while in the second signalling phase, R communicates to both NU as well as FU. The NU combines the incoming signals from BS and relay to enhance its performance as an incentive for its participation in NOMA signalling.
• For both NU and FU, considering both AF and DF relaying, we present expressions for outage probability and throughput in closed-form. Unlike other works [28], [29] on AF CDRT NOMA where (for analytical simplicity) the harmonic to min approximation is used, we derive the exact outage probability in closed form.
• Our simulations show that the performance of NU with AF and DF relaying is almost the same throughout the range of SNRs. For FU, in the presence of BS-FU link, DF performs better than that of AF at low SNRs and at high SNRs, both achieve similar performance. However, DF always outperforms AF in the absence of the BS-FU link. We also demonstrate that CDRT NOMA with AF relaying allows a wider range of valid power allocations in comparison to DF relaying for both NU and FU.
• We also derive highly accurate high-SNR expressions for the outage probability to demonstrate that combining direct and relayed signals at NU as well as FU (while performing SIC at NU) allows both NU and FU to harness a diversity of 2 with both AF and DF relaying. Clearly, the NU is rewarded for participation in NOMA signalling. However, in the absence of the BS-FU link, FU attains a diversity of only one.
• Next, We show that how the choice of power allocation coefficient and target symbol rates are crucial to maximize the NU throughput while guaranteeing a desired target throughput at FU.
We also present an approximate closed-form expression for power allocation coefficient that maximizes NU throughput for a given FU throughput requirement. In addition to this, we also formulate a NU throughput maximization problem and determine the optimal NU and FU target rate pair. • We also observe that in DF-assisted CDRT NOMA (unlike in the AF case), both BS and R transmit the superimposed symbols (combination of NU and FU symbols) in first and second phase of signalling, respectively. However, the power allocation at BS significantly affects the system performance in comparison to the power allocation at R.
• Further, we observe that the proposed scheme (without using any feedback) always outperforms SDF CDRT-NOMA [26] in terms of outage probability, sum throughput and energy efficiency by a huge margin and also achieves better diversity at both the users.
• Moreover, we compare the performance of the proposed CDRT-NOMA framework to its OMA counterpart (with relaying) and observe that the proposed system ensures higher energy efficiency (EE). We further observe that the availability of BS-FU link helps in achieving a higher EE in comparison to the case when BS-FU link is absent. Also, optimal rate selection is important to maximize the EE.
The rest of this paper is structured as follows. Section II elaborates on the system model for AF as well as DF relay assisted CDRT NOMA framework. Section III analyzes the performance with the proposed framework in terms of outage probability. Section IV discusses NU throughput and energy efficiency maximization. Numerical results based on mathematical analysis are compared to computer simulations in Section V. Finally, Section VI concludes this paper.
Notations: C N (0, σ 2 ) represents a zero-mean complex Gaussian distribution with variance σ 2 . f X (x) and U(·) respectively denote the probability density function (PDF) of a random variable (RV) X and the unit step function. E 1 (·), K 1 (·, ·) and Γ(a, x; b) denote the exponential integral of type 1, the modified Bessel function of the second kind and the generalized incomplete gamma function, respectively.

II. SYSTEM MODEL
As depicted in Fig. 1, we consider a CDRT downlink NOMA framework consisting of a base station B, a near user U N , a far user U F and a relay station R. Both U N and U F have stringent outage QoS constraints. All nodes operate in the half-duplex (HD) mode and are equipped with a single antenna.
Communication to U N and U F takes place in two signalling phases. In the first phase, B communicates to U N , R and U F over direct links, while in the second phase communication from R to U N as well as U F takes place using either AF or DF mode of relaying.
The channel coefficients h i j ∼ C N 0, 1/λ i j with i ∈ {B, R}, j ∈ {R, N, F} are assumed to be independent and of quasi-static Rayleigh fading type, where λ i j = d m i j , and m is the path-loss exponent. The additive zero-mean complex Gaussian noise at all the receiving nodes is assumed to be of variance σ 2 . Superscript "I" and "II" are used to represent first and second phase quantities.
In case of AF relaying

A. Amplify-and-Forward Relaying
In the first phase, B transmits a superposition of unit-energy symbols s N and s F (of information rates R N and R F ) intended respectively for U N and U F . The transmit power P B is apportioned to U N and U F symbols in the ratio α B : (1 − α B ). Thus, the superimposed symbol can be expressed as  [30]. Using (1), the signal-to-interference-plus-noise ratio (SINR) Γ I NF to decode s F , and the signal-to-noise ratio (SNR) Γ I N to decode s N at U N after SIC, are expressed as where ρ B = P B /σ 2 represents the transmit SNR at B and γ F = 2 R F − 1 represents the threshold SNR at U F . Using (1), the SINR Γ I FF to decode s F at U F can be expressed as Let P R denote the available transmit power at R. In the second phase, R amplifies the incoming signal from the first phase and then forwards s R = βy I R to U N and U F as shown in Fig.1 The signals received at U N and U F in the second phase are given by respectively, where w II N and w II F are the additive noise samples at U N and U F . Similar to the first phase, using (4) the SINRs Γ II NF and Γ II NN to decode s F and s N (after SIC) are expressed as Using (4), the SINR to decode s F at U F is given by The signals from first and second phases are combined at U F . In this paper, we use an approach that deviates from all existing works to date and enable U N to combine the signals in the two phases at each stage of the SIC. We show that this enables U N to attain very good performance and harness a diversity of two without any need for feedback. This allows the network to be used for multimedia and other applications that impose strict outage QoS constraints. It is emphasized that none of the techniques suggested so far [21], [26] can ensure a diversity of two at the near-user in the absence of 7 any feedback 1 . This improvement in diversity as well as in throughput performance also serves as an In the second phase, based on the decoding status of s N and s F , R transmits either superimposed signal s R or only the far user symbol s F as shown in Fig.1 (b). If R decodes both s N and s F successfully 2 , then it forwards the superimposed signal s R = P R α R s N + P R (1 − α R )s F to both U N and U F , where α R and (1 − α R ) denotes the portion of power allocated to U N and U F , respectively. Note that DF relaying (unlike its AF counter part) allows different NOMA power allocations at B and R. The signals received at U N and U F can be expressed as y II N−S = s R h RN + w II N and y II F−S = S R h RF + w II F , where −S in the subscript is used to emphasize that a superposed signal is transmitted by R. Using y II N−S , the respective SINRs before and after SIC (Γ II NF−S and Γ II NN−S ) to decode s F and s N at U N are Using y II F−S , the SINR Γ II FF−S at F to decode s F is However, if R fails to decode s N then it forwards only s F . Now, the received signals at U N and U F are expressed as y II N−F = P R s F h RN + w II N and y II F−F = P R S F h RF + w II F respectively, where the subscript −F is used to emphasize that R merely transmits s F . Using y II N−F and y II F−F , the respective SINRs Γ II NF−F and Γ II FF−F to decode s F at U N and U F can be expressed as In this paper we compare performance of the proposed scheme with a relayed OMA scheme described below.

C. Relayed OMA Scheme
In the considered relayed OMA system, B transmits x F to U F , U N and R in the first signalling phase.
In the second signalling phase R forwards either the amplified (with AF relaying) or the decoded (with DF relaying) FU symbol, while B transmits x N to NU. Using the decoded FU symbol in the first phase, NU cancels the interference caused by transmission by R before decoding. However, if NU fails to decode x F in the first phase, then the signal received from R in the second phase acts as interference at U N and x N transmitted from B acts as interference at FU. Note that NU receives symbols in both time-slots in this OMA scheme with relaying. It can therefore be expected to attain high throughput.
We observe in Section V that the proposed scheme yields much better throughput performance as compared to its relayed OMA counterpart.

III. OUTAGE PROBABILITY ANALYSIS
In this section, the outage performance of coordinated direct AF/DF relay assisted downlink NOMA is analyzed. We derive closed-form expressions of near and far user outage probabilities considering AF or DF relaying. In order to determine the diversity order for U N and U F , the asymptotic expressions of user outage probabilities are also derived. For ease of exposition, we define |h BR | 2 = X (λ BR = λ x ), A. Amplify-and-Forward Relaying 1) Far user outage probability: The outage probability of U F can be written as p AF (3) and (7), p AF F can be expressed as The sign of (γ F −ρ B W φ) depends on the range of W and different values of Table I, wherein can be expressed as After some mathematical rearrangement (13) can be expressed as We first solve for I 1 as follows: Entire range of W, X and Y Substituting x = x − ζ F 1 (w) in the above and re-arranging terms, we get Solving for3he inner integral using [31, 3.324.1], we obtain where . Following a similar approach, we derive an expression for I 2 . p AF F can then be expressed as where . Unfortunately, the integrals in (18) do not admit a closed form.
We therefore present a highly accurate approximate expression for P AF F in the following theorem.
Theorem 1. An accurate closed-form expression for FU outage probability with AF relaying is given by Proof. Refer to Appendix A.
Using the expression obtained in (19), it is extremely difficult to establish the diversity order. We therefore derive a high-SNR approximation to p AF F in the following Lemma.
Proof. Refer to Appendix B.
Remark 1. In the absence of direct link to U F , the outage probability of U F can be readily derived by substituting W = 0 into (12). After using a procedure similar to that used to derive (18), we obtain an exact closed-form expression for p AF F as follows: The above equality holds only for α B < 1 1+γ F , otherwise p AF F = 1. Note that for higher values of ρ B and ρ R , µ F and χ F are very small. Therefore, applying K 1 (θ) 1 2 Γ(1)( θ 2 ) −1 [32, 9.6.9] in (21), we obtain Using e −θ 1 − θ in the above, a high SNR approximation to p AF F is given by 2) Near user Outage Probability: Due to the manner in which SIC is performed with combining, the outage probability of U N is Theorem 2. The near user outage probability can be written as follows: where Proof. Using (2), (5) and (6) into (24), we obtain Outage always occurs In the above, depending on values of α B and γ F , two ranges of  Table II. Now, p AF N can be expressed as where χ N 1 (Z), χ N 2 (Z), ζ N 1 (X, Z), ζ N 2 (X, Z), χ F , χ N and φ are defined in the line following (25). After performing mathematical rearrangements in (27) we obtain (25).
Theorem 3. An accurate closed-form expression for p AF N is given by where Proof. Refer to Appendix C.
Lemma 2. The diversity orders D AF F and D AF N achieved at U F and U N are given by Proof. To derive the diversity order for U F and U N , we use the high-SNR expression of p AF F and p AF N given by (20) and (28), respectively. We consider ρ B = ρ R = ρ without loss of generality. The diversity orders attained by U F and U N are given by D For ρ → ∞, we use e −θ = 1 − θ and substitute for χ F and ξ 1 . After neglecting higher order terms of 1 ρ , we obtain diversity order as expressed in (29). The detailed proof is omitted due to paucity of space.
Remark 2. The fact that the near-user also attains a diversity of two is significant, and motivates it to participate in NOMA signalling.
Remark 3. In the absence of direct link to U F , the diversity order D AF F is obtained by using ρ B = ρ R = ρ into (23). The diversity order D AF F can be expressed as However, the diversity order for U N remains the same as expressed in (29).
B. Decode-and-Forward Relaying 1) Far user outage probability: Let Γ COM FF−S = Γ I FF + Γ II FF−S and Γ COM FF−F = Γ I FF + Γ II FF−F . FU is not in outage when a) both s F and s N are decoded at R (Γ I RF ≥ γ F , Γ I RN ≥ γ N ) and FU SNR after combining is sufficient (Γ COM FF−S ≥ γ F ), b) s F can be decoded at R, but not s N but SNR after combining is sufficient at FU (Γ COM FF−F ≥ γ F ), and c) s F cannot be decoded at R but Γ I FF ≥ γ F . The outage probability for U F can be formulated as In the following, we present closed-form expressions for FU outage.
Theorem 4. The exact closed-form expression of the outage probability for U F is given by Proof. Refer to Appendix D.
The expressions obtained in (32) involve the generalized incomplete gamma function due to which the diversity cannot readily be established from them. We therefore present a highly accurate high-SNR approximation to p AF N in the following Lemma.
Lemma 3. A high SNR approximation to p DF F is given by Proof. Refer to Appendix E.

Remark 4.
In the absence of the direct link to U F , we can use W = 0 in (31) to get After solving (34) as in Theorem 4, an exact expression for p DF F is given by Using e −θ 1 − θ in above and neglecting higher order terms of 1 ρ R , a high-SNR approximation to p DF F is given by 2) Near user outage probability: NU is not in outage when a) R decodes both s F and s N Γ I RF ≥γ F , Γ I RN ≥γ N and SNRs at NU (after combining) are sufficient to decode both s F and s N Γ COM NF−S ≥γ F , Γ COM NN−S ≥ γ N , b) R decodes s F but fails to decode s N Γ I RF ≥γ F , Γ I RN <γ N , and SNRs to decode s F (after combining) and s N (from first phase) are sufficient at NU Γ COM NF−F ≥ γ F , Γ I NN ≥ γ N , and c) R fails to decode s F Γ I RF <γ F , but the first phase SNRs are sufficient to decode both s F and s N at NU Γ I NF ≥ γ F , Γ I NN ≥ γ N . The outage probability for U N can be formulated as where Theorem 5. The exact closed-form expression of the outage probability for U N is given by where Proof. Refer to Appendix F.
In the following lemma, we present a high-SNR approximate expression for p DF N to obtain the diversity order at NU.

Lemma 4.
A high-SNR approximation to p DF N is given by where Proof. Proof is similar to that used to derive (33), and is therefore omitted.
Proof. The diversity orders for U F and U N are obtained by using high-SNR expressions of p DF F and p DF N given by (33) and (39), respectively. We substitute ρ B = ρ R = ρ and solve for D DF j = − lim ρ→∞ log 2 p DF j (ρ) log 2 ρ , j ∈ {N, F} . Details are omitted due to paucity of space.

Remark 5.
In the absence of direct link to U F , the diversity order D DF F is obtained by using ρ B = ρ R = ρ → ∞ into (35) and using linear approximations to the exponential terms. The diversity order D DF F can be expressed as However, the diversity order for U N remains the same as in (40).

IV. NU THROUGHPUT AND ENERGY EFFICIENCY MAXIMIZATION
NU needs to decode the FU symbol and perform SIC to decode its own symbol, and might therefore incur some performance loss. For this reason, maximizing the NU throughput while guaranteeing a desired FU target throughputτ is well motivated. We do so in this section. The FU and NU throughput in bits per channel use (bpcu) are defined as where p AF F , p AF N , p DF F and p DF N are as in (19), (28), (32) and (38) respectively.
Careful choice of power allocation coefficient α B and symbol rates R F and R N is crucial to attaining good throughput at U N and U F . With DF relays, α R can also be chosen. However it will be demonstrated in Section V that a large range of α R values result in the same throughput performance. The reason for this is that α R is only used when both s F and s N are decoded correctly at R (which in turn depends on α B ). We therefore focus only on choice of α B , R N and R F .
We first consider the case when the B-U F link is absent. Noting that the NU benefits when the maximum value of α B is chosen, we derive α i opt B by using (23) and (36) into (42) to get The NU throughput for AF and DF relaying schemes can be obtained by substituting α B = α i opt B into expressions for τ i N . Clearly, τ i N is now a function only of symbol rates R N and R F (and therefore γ N and γ F ). Thus, careful choice of symbol rates is essential for maximizing the NU throughput. Let R opt N and R opt F denote the optimal symbol rates that maximize τ i N . Now, the optimization problem is formulated as Solving the above joint optimization problem analytically is difficult. However, numerical techniques can be used to pick the optimal R N and R F .
In the presence of the B-U F link, a three-dimensional search is required to determine α B , R N and R F while ensuring that τ i F ≥τ. Energy efficiency is an important performance metric for any communication system. It is defined as [14]: where 'sum throughput' represents the sum of τ i N and τ i F . Let T denote the signalling duration. Let E B = P B T 2 and E R = P R T 2 . Using τ i N , and τ i F from (42), the EE of the system is expressed as Since the sum throughput τ i sum is function of symbol rates R N and R F , careful choice of symbol rates is essential for maximizing the EE. Let R opt N and R opt F denote the optimal symbol rates that maximize The EE optimization problem can be formulated as Obtaining a closed-form solution to the above joint optimization problem is extremely difficult.
However, a two dimensional search can be used to find the optimal R N and R F .

V. SIMULATIONS AND NUMERICAL RESULTS
In this section we present computer simulations to confirm accuracy of the derived analytical expressions and derive useful insights. Unless mentioned otherwise, the considered system parameters are as follows: , and m = 4. Also σ 2 is normalized to unity [15]. Further, we assume that P B = P R = P (ρ B = ρ R = ρ) [14] and symbol rates R N = R F = R (γ N = γ F = γ T ). We also compare the performance of the proposed schemes with its relayed OMA counterpart described in Section II.
In Fig.2    respectively. Also, the approximate high-SNR expressions for outage probability derived in (36) and (33) are quite accurate. A decrease in α B and α R signifies that more power is allocated to U F , and p DF F therefore continuously improves with decreasing α B and α R as shown in Fig.4. Clearly, from  Fig.6 shows the variation of τ i F versus ρ at R = 1, 2. Here, we compare both DF and AF relaying schemes considering optimal power allocation coefficients α B and α R . In the presence of the B − U F link, performance with DF is superior to that of AF for lower SNRs. At high SNRs, the performance of both AF and DF is comparable. However, in the absence of B − U F link, performance with DF is always superior. AF relays are often preferred due to their simplicity, and can be seen to result in good performance except at low SNRs. Fig.7 depicts τ i N versus ρ for R = 1, 2. For fair comparison of AF and DF relaying, optimal power allocation coefficients are used at B and R. We observe that both AF and DF achieve almost similar performance in terms of near-user throughput 3 .  ). Further increase in α B decreases the probability of successful decoding of s F at U N , and τ AF N therefore also decreases.
In Fig.9, τ DF N or τ DF F is plotted versus α B (considering optimal α R ) and α R (considering optimal α B ) for R = 1.5, 2, 2.5. As with AF relaying, τ DF F is maximum at α B = 0 and then decreases to 0 with increasing α B . τ DF N increases initially, attains a maximum value at α B = γ N γ N +γ F +γ F γ N , and then decreases to 0 (the SINR to decode s F at NU decreases). It can be observed that presence of the B − U F significantly improves the FU throughput. Also, both τ DF F and τ DF N change significantly with α B while change in α R does not significantly change the throughput 4 . Hence, an optimal choice of α B is important. For this reason, we study variation of energy efficiency w.r.t α B only. From Fig.8 and Fig.9, it can be clearly seen that CDRT NOMA with AF relaying provides wider range of valid power allocations in comparison to DF relaying for both U N and U F . The presence of the B − U F widens the valid range of power allocations for U F with AF relaying (but not with DF relaying).
In Fig.10, we plot sum throughput τ i sum = τ i F + τ i N versus R = R N = R F using optimal α B and α R . With increase in SNR τ i sum also increases and τ i sum is a quasi-concave function of R, and a unique value R opt exists at which τ i sum is maximum. Clearly, CDRT NOMA with DF outperforms that with AF in terms of sum throughput. P. In addition to this we observe that for mid-SNR range DF outperforms AF, while at low as well as at high SNRs both achieve similar performance in terms of EE. However, in the absence of the B − U F link, DF outperforms AF for a wider range of SNRs and the gap is more as compared to the case when the B − U F link is present.
In Fig.12, we plot η AF E and η DF E versus α B with R = 1 and ρ = 30 dB for P = 1W and P = 2W .
We also compare the EE of NOMA CDRT with its relayed OMA counterpart. It is evident that EE of both AF and DF relay-aided NOMA in CDRT are higher than that of relayed OMA. This is largely because of the fact that the signals from both B and R are combined at NU as well as FU. It can be seen that in the OMA case, EE with DF is better than that with AF, whereas in CDRT NOMA, AF is more energy efficient. We also show that the presence of the B − U F link significantly improves the EE (the gap is larger with AF as compared to DF).
In Fig.13, we plot the variation of η AF E and η DF E versus α B for fixed transmit power (P = 3W ), ρ = 30 dB and R = 1, 2, R opt . Clearly, the energy efficiencies of AF as well as DF increase as we increase the  symbol rate from 1 to 2, and the improvement is huge when the optimal symbol rate (R opt ) is used.
Further, this is true for the entire range of the power allocation parameter. We also observe that EE of relay-aided NOMA CDRT is significantly higher than that of OMA. In case of both DF and AF aided NOMA in CDRT, we observe that by optimally choosing R N , the NU throughput can be maximized while guaranteeing the desired FU throughputτ. Also, selecting an optimal rate (R F = R opt F ) helps to provide huge gain in NU throughput in comparison to any fixed rate R F . Therefore, the NU throughput attains a maximum performance at (R opt N , R opt F ). Clearly, jointly optimizing R N and R F (as in Section IV) is of utmost importance. It can also be observed that presence of the B − U F significantly improves the NU performance.
In Fig.16, Fig.17 and Fig.18, we compare the performance of proposed AF as well as DF relay-aided CDRT NOMA with selective decode and forward (SDF) CDRT NOMA of [26] in terms of outage probability, sum throughput and energy efficiency, respectively. It is clear from Fig.16 that for optimal optimal power allocation, the proposed AF as well as DF relay-aided CDRT NOMA outperform the SDF CDRT NOMA framework of [26] by a huge margin. The SDF CDRT NOMA achieves diversity order of one, whereas, proposed schemes can achieve a diversity of two at both the users. It is clear from Fig.17 that the proposed scheme almost doubles the sum throughput in comparison to SDF-CDRT NOMA framework of [26]. Fig.18 illustrates that the proposed scheme is also more energy efficient.

VI. CONCLUSION
In this paper, we analyzed the performance of new framework for downlink non-orthogonal multiple access (NOMA) in a coordinated direct and relay transmission (CDRT) scheme with direct link to both near-user (NU) and far-user (FU). In this framework, NU performs combining of direct and relayed signals while performing successive interference cancellation, which considerably improves NU outage performance, and enables it to attain a diversity of two without feedback. This scheme is very useful in multimedia and other applications where the NU has stringent outage constraints. The FU also can attain a diversity of two. Considering either amplify-and-forward (AF) or decode-and-forward (DF) relaying, closed-form expressions for outage probability and throughput were derived for both NU and FU. In spite of the fact that DF relaying allows for different choice of power allocation at the relay, performance with simpler AF relays is comparable to that with DF relays. We demonstrate that careful choice of power allocations coefficient and the the target rates is important to maximize throughput and energy efficiency.

APPENDIX B
Proof of Lemma 1: After some mathematical arrangements, (16) can be expressed as For large ρ B and ρ R , we use the linear approximation to the exponential term in denominator to obtain where ξ 2 (w) . Using [31, 3.352.6] in the above, we obtain Further using e ξ 2 (w)λ x E 1 (ξ 2 (w) λ x ) = 1 1+ξ 2 (w)λ x [32, 5.1.19] and simplifying, we obtain Substituting for ζ F 1 (w) from the line following (18) and neglecting higher-order terms of 1/ρ B , we get We use [31, 3.352.1] to obtain Similarly, the expression for I 2 is given by After substituting for I 1 and I 2 from (59) and (60) into (14), the high SNR approximation to p AF F is given by (20).

APPENDIX D
Proof of Theorem 4: Using (3), (8) and (10) into (31), Pr{A 1 } can be expressed as Since the RVs W , X and Y are independent and have an exponential distribution, we obtain After substituting λ w (w + φ R ϑ 1 ) = w and solving, we obtain Using an approach similar to that used to derive (50), we obtain Similarly, the expression for Pr{A 2 } is obtained as Further, using (3) and (8), Pr{A 3 } of (31) can be expressed as Using (73) Solving the above integral using [31, 3.352.3], we obtain At high SNRs, κ ∝ 1 ρ 2

B
. We therefore neglect the product term of κe κ . Now Pr{A 1 } is expressed as Similarly, solving for A 2 , we obtain Substituting for Pr{A 1 } and Pr{A 2 } from (77) and (79) into (31), we obtain p DF F given by (33).

APPENDIX F
Proof of Theorem 5: Using (2) and (8) in (37), Pr{B 1 } can be expressed as Using (37), Pr{B 2 } is given by To satisfy χ N > χ F , max χ N , Using this fact, the above can be simplified as Further, the expression for Pr{B 3 } is calculated as No range of X, V and Z is valid Using the above, the conditions for outage on ranges of X, V and Z with φ > 0 and φ < 0 are listed in Table III. Now, Pr{B 3 } can be expressed as . After averaging over the PDFs of RVs V , X and Z, we obtain where ω = −λ v (γ F −φρ B z) ρ R (φ R +ρ B z(φα R +α B (1−α R ))) ,χ N = min(χ F , χ N , ϑ 4 ). After some mathematical rearrangement, the above can be expressed as λ z e −λ z z dz λ z e −λ z z dz where ε 3 = λ v α R ρ R . Substituting λ z (z + φ R ϑ 1 ) = z, and using [33, eq. (4)], I 8 and I 9 are obtained as . Using I 8 and I 9 from (87) and (88) into (86), Pr{B 3 } is expressed as Substituting (80), (82) and (89) into (37), p DF N is obtained as in (38).