Performance of Energy and Spectrally Efficient AF Relay-Aided Incremental CDRT NOMA-Based IoT Network With Imperfect SIC for Smart Cities

High spectral and energy efficiencies are vital for the implementation of smart cities. To this end, this article investigates the performance of an amplify-and-forward (AF) relay-aided coordinated direct and relay transmission (CDRT) protocol in a downlink nonorthogonal multiple access (NOMA)-based Internet of Things (IoT) network in which the source shares the direct as well as the relayed links to the IoT near-user (NU) and the far-user (FU). Different from the existing literature, we exploit incremental relaying (IR) along with combining at the NU (and not just at the FU) to achieve a 20% increase in FU throughput while ensuring the desired performance at NU. Considering practical imperfect successive interference cancelation (SIC), we analyze the throughput performance. Both NU and FU accrue large throughput gains, and doubling of the energy efficiency (EE) is achieved over the nonincremental AF CDRT NOMA scheme and its relayed orthogonal multiple access counterpart. We accomplish this by intelligently exploiting feedback bits in the second phase of signalling to avoid unwanted relaying, which saves energy and improves EE, which is very much required from the perspective of IoT-based energy-efficient smart cities. It is seen that the proper choice of the power allocation coefficient and the target information rate is crucial for maximizing the sum throughput and EE of the considered IoT Network. Finally, we validate the correctness of the theoretical analysis and the superiority of the proposed scheme through Monte Carlo simulations.

Abstract-High spectral and energy efficiencies are vital for the implementation of smart cities.To this end, this article investigates the performance of an amplify-and-forward (AF) relay-aided coordinated direct and relay transmission (CDRT) protocol in a downlink nonorthogonal multiple access (NOMA)based Internet of Things (IoT) network in which the source shares the direct as well as the relayed links to the IoT near-user (NU) and the far-user (FU).Different from the existing literature, we exploit incremental relaying (IR) along with combining at the NU (and not just at the FU) to achieve a 20% increase in FU throughput while ensuring the desired performance at NU. Considering practical imperfect successive interference cancelation (SIC), we analyze the throughput performance.Both NU and FU accrue large throughput gains, and doubling of the energy efficiency (EE) is achieved over the nonincremental AF CDRT NOMA scheme and its relayed orthogonal multiple access counterpart.We accomplish this by intelligently exploiting feedback bits in the second phase of signalling to avoid unwanted relaying, which saves energy and improves EE, which is very much required from the perspective of IoT-based energy-efficient smart cities.It is seen that the proper choice of the power allocation coefficient and the target information rate is crucial for maximizing the sum throughput and EE of the considered IoT Network.Finally, we validate the correctness of the theoretical analysis and the superiority of the proposed scheme through Monte Carlo simulations.

I. INTRODUCTION
T HE ADVANCEMENT of Internet of Things (IoT)   systems for the betterment of lifestyle requires IoT applications, such as smart cities [1], smart homes, smart wearables, smart grids, industry 4.0, structural health monitoring, smart education, and smart transportation [2].The change in the communication paradigm of fifth-generation (5G) and beyond 5G networks necessitates massive connectivity and low latency along with higher spectral and energy efficiencies [3], [4].Throughout the history of wireless communication, multiple access techniques have had a dominating influence on the capacity of wireless networks.Orthogonal multiple access (OMA) techniques, such as time-division multiple access (TDMA), frequency-division multiple access (FDMA), orthogonal FDMA (OFDMA), and code-division multiple access (CDMA) have all played an important role in the evolution from 1G to 5G [5].The central idea of OMA is to avoid interference by using orthogonal resources.The proliferation of IoT, massive machine-type communication (mMTC), and wireless services has increased the need for efficient utilization of the limited radio resources [6], [7] as well as the available energy.The fifth and the sixth generation (6G) networks are expected to be key enablers for spectral as well as energyefficient smart cities [1].Over the last few years, a new Third Generation Partnership Project (3GPP) radio access technology termed narrowband IoT (NB-IoT) [4], [8], [9] (which is a low-power and wide-area (LPWA) technology), has attracted much attention from academia as well as industry.Presently, NB-IoT exploits OMA, i.e., single-carrier FDMA (SC-FDMA) for uplink and OFDMA for downlink [8], and is therefore unable to accommodate a massive number of IoT connections [9].The application of nonorthogonal multiple access (NOMA) to improve connectivity in NB-IoT networks has been studied in depth [8] due to its promise of improving spectral efficiency, reducing latency, and supporting massive connectivity, all of which are very much essential from the perspective of smart cities being planned around the globe [1], [10].In accordance with the concept of smart cities, the deployment of more than 200 000 IoT devices per square kilometer is expected in the near future [11].Therefore, the use of NOMA in IoT networks is very much essential to fulfil the objectives of smart cities.By virtue of superposition coding at the transmitter and successive interference cancelation (SIC) at the receiver, NOMA allows multiple users to exploit the same frequency, time, or code resource block concurrently, thereby increasing spectral efficiency [12] and providing improved connectivity for IoT devices.
Due to the advancements and positive experimental outcomes, NOMA has also been considered in some recent standards.Recently, NOMA has been considered as multiuser superposition transmission (MUST) in Release-13 long-term evolution (LTE) of 3GPP, which mainly focuses on downlink mobile broadband (MBB) services [13].Releases 14 and 15 of 3GPP are based on the new radio (NR) system and are focused on uplink transmissions [14] to provide massive connectivity while enabling the newly defined grant-free transmission procedures to support ultrareliable low-latency communication (URLLC).Recently, layered-division multiplexing (LDM) has been accepted by the next-generation American digital TV broadcasting system (Advanced Television Systems Committee (ATSC) 3.0) as a baseline physical-layer technology [15], [16].

A. Related Work
To extend the range, reliability, and Quality of Service (QoS) of the conventional NOMA network, both cooperative NOMA [17], [18], [19], [20] and relayed NOMA has been investigated [21], [22], [23] in the existing literature.In cooperative NOMA [17], the near-user (NU) assists information transmission to the far-user (FU), whereas in relayed NOMA [21] a dedicated relay is used for the exchange of information between source and users.In [18], the performance of amplify-and-forward (AF) protocol-based cooperative NOMA has been investigated, and better outage performance is shown to be achieved in comparison to its decode-and-forward (DF) protocol-based cooperative NOMA counterpart.Bapatla and Prakriya [20] studied an energy-buffer-aided spectral and energy efficient cooperative NOMA network, which is well suited for IoT networks.The performance of both half duplex and full duplex (HD and FD) cooperative NOMA has been studied in [19], and closed-form expressions were derived for the outage probability, ergodic rate, and energy efficiency (EE).It is shown that FD NOMA outperforms HD NOMA in terms of EE (in delay-limited transmission mode) in the low signal-to-noise ratio (SNR) region whereas HD NOMA provides better EE (in delaytolerant transmission mode) in the high SNR region.In [17] and [21], it is shown that the relay/user selection helps to improve the performance of the cooperative/relayed NOMA network.Abbasi et al. [22] studied the outage performance of an AF relay-aided NOMA network and showed that outage performance improves with decreasing distance between the relay and the user.The performance of a relayed NOMA-based IoT network in which an IoT node relays the information has been investigated in terms of outage probability, throughput, and EE in [23].
To further improve the range and reliability, the use of coordinated direct and relay transmission (CDRT) in the NOMA network has been shown to be a promising and practical approach [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34].The use of a CDRT NOMA-based downlink network significantly improves the FU performance [24].The performance of HD DF relay-based uplink CDRT NOMA has been investigated in [25].In contrast, the performance of a wireless-powered HD DF relay-based downlink CDRT NOMA network has been analyzed in terms of outage probability in [26].A joint uplink-downlink CDRT NOMA network is considered in [27] and its performance is investigated for both the case of perfect and imperfect SIC.Closed-form analytical expressions are also derived for the outage probability, ergodic sum capacity, and EE.Xu et al. [28] studied and compared the performance of hybrid multiple access with CDRT and showed that NOMA-based CDRT outperforms the hybrid multiple access in terms of ergodic sum capacity at the cost of increased complexity.In all the above-mentioned works, the source shares the direct link only to the NU, and communication to the FU is assisted by a DF relay.The performance of an HD DF relay-aided NOMA network in which the source shares a direct link to both the NU and the FU has been investigated in [29] while considering three modes of relaying, i.e., fixed DF, selective DF, and incremental selective DF.The performance of an HD DF relay-aided conventional CDRT NOMA network with direct link to FU has been investigated in [31], and closed-form expressions are derived for the users' outage probability and throughput.In [31] and [30], it is shown that combining at NU with SIC in addition can further enhance throughput.AF relays are preferred in practical implementations due to the lower complexity.However, the performance of CDRT NOMA with AF relays has received very little attention.Yue et al. [32] investigated the performance of an HD fixed-gain AF relay-aided NOMA network in terms of outage probability and throughput while considering suboptimal selection combining at the user end.A summary of related works and their comparison with our work is presented in Table I on the top of the next page.

B. Motivation and Contribution
In this work, our main objective is to assist future networks in achieving the goal of spectral and energy-efficient smart cities.By exploiting the feedback from users, incremental relaying (IR) can potentially increase spectral efficiency [33].The integration of IR with cooperative NOMA further improves the spectral efficiency, which is well justified in the existing literature [35].On the other hand, AF relays are simple and easy to implement as compare to its DF counterpart.AF relays are preferred due to their simplicity, and the performance of incremental CDRT signalling with such AF relays is of interest.To the best of our knowledge, this has never been studied before, and needs to be explored for efficient utilization of the radio resource.
In IR signalling, the relay only cooperates when the direct links fail-otherwise, new bits are transmitted in the second phase of signalling.Clearly, this can enhance spectral efficiency and improve EE.Therefore, the design of power control specific to IR signalling to favor direct decoding in one phase is required.Combining at NU like in this article can allow more power to be allocated for FU, thereby increasing the chances of signalling being completed in one phase itself (this increases EE).Therefore, the choice of power control to maximize FU performance while guaranteeing desired NU performance is of utmost importance.Motivated by the above, we consider incremental AF relay-aided CDRT NOMA with direct links to both users, which is important for the implementation of smart cities, but has not been investigated so far.
The key novel contributions of this article are as follows.
1) We analyze the performance of IR AF relay-aided CDRT-NOMA-based IoT network with direct links to both NU and FU.In the considered IoT network, the source broadcasts the NOMA signal which is received Based on the feedback received from both the NOMA users, either the source transmits a new set of symbols (in case of positive feedback from both the NOMA users) or the relay forwards the amplified signal (in case of negative feedback from NU and/or FU).Combining of the direct and the relayed signal takes place at both NU and/or FU to improve the performance (and not just at the FU as in most work to date).
2) Different from the existing works in which fixed-gain AF, suboptimal selection combining, and harmonic-min approximation are used to simplify the analysis [36], we consider a channel-dependent amplification factor with optimal combining at NU as well as FU, and derive a closed-form expression for throughput of both NU and FU while considering the effect of imperfect SIC (which is essential from the practical point of view) without using the harmonic-min approximation.3) We also derive an expression for the EE using the derived throughput expressions and demonstrate that the throughput and EE of the proposed scheme are vastly superior to that with nonincremental AF CDRT NOMA and its relayed OMA counterpart.It is also demonstrated that the combining at both NOMA users like in this article, helps to achieve over 20% gain in FU throughput while guaranteeing the desired throughput at NU.

4)
We demonstrate that the use of IR provides 60% gain in terms of sum throughput and almost doubles the EE in comparison to its nonincremental counterpart.5) Next, we demonstrate that the proper choice of the power allocation coefficient and target information rates is essential to maximize the sum throughput and EE.
In addition, we show that the choices of target rates and power allocation coefficient are also important to maximize the FU throughput while ensuring the desired throughput at NU. 6) In conjunction with this, an FU throughput maximization problem is formulated to obtain the optimal power apportioning parameter along with the optimal NU and FU target information rate pair.7) Finally, we present Monte Carlo simulations for validation of the derived analytical closed-form expressions and to demonstrate the superiority of the considered scheme.

C. Structure of This Article
The remainder of this article is organized as follows.The proposed system model as well as the transmission scheme for incremental AF relaying protocol-based downlink CDRT NOMA network are discussed in Section II.Section III analyzes the throughput performance of the proposed IoT network.
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II. SYSTEM MODEL
As depicted in Fig. 1, we consider a downlink NOMA 1 based typical IoT communication scenario comprising of a source denoted by S, an IoT NU and an FU (denoted by U 1 and U 2 , respectively), as well as an AF relay [23] denoted by R. Both IoT nodes U 1 and U 2 possess a direct link to S, and R opportunistically assists the information transmission to both U 1 and U 2 using the IR protocol.All the IoT nodes are of HD type and possess a single antenna.The quasi-static Rayleigh fading channel coefficient between node S and R, S and U k , and R and U k are denoted by Rk ), respectively, where k ∈ {1, 2}, λ ab = d ϕ ab with ϕ denoting the path-loss exponent, and d ab is the distance between node a and b.There is zero-mean additive white Gaussian noise (AWGN) at all receiving nodes, and after matched filtering and sampling, the noise samples are zero-mean Gaussian RVs of variance N o .
We also consider the effect of SIC errors in NOMA, which is unavoidable in the practical implementation of IoT systems.

A. Transmission Scheme
In the proposed system model, each signalling interval consists of two phases. 2As illustrated in Table II, in the first phase, S transmits a superposition of unit-energy symbols x 1 and x 2 over the direct links to IoT nodes U 1 and U 2 at information rates R 1 and R 2 , respectively, as depicted in Fig. 2. The threshold SNR at U 2 and U 1 are γ 2 = 2 R 2 − 1 and γ 1 = 2 R 1 − 1, respectively.In the second phase, either transmission takes place from R to U 1 and U 2 or from S to R, U 1 and U 2 , depending on the decoding status of U 1 and U 2 .The total transmits power P S at S is allocated in the ratio of α S and ᾱS for the transmission of U 1 and U 2 symbols, respectively.Both α S and ᾱS lie between 0 and 1 such that α S + ᾱS = 1.The superimposed symbol ( √ P S α S x 1 + √ P S ᾱS x 2 ) transmitted from S is received at R, U 1 and U 2 .The received signals at U 1 , U 2 , and R are expressed as respectively, where and For ease of exposition, we consider   SIC to decode x 1 .The signal-to-interference-plus-noise ratio (SINR) I 12 to decode x 2 at U 1 and the SINR I 11 to decode x 1 (after SIC) 3 at U 1 are expressed as where ρ S = (P S /N o ), and ε denotes the portion of residual interference caused by imperfect SIC and varies from zero to one, i.e., ε ∈ [0, 1).Likewise, the SINR at U 2 to decode x 2 is expressed as After the completion of the first phase of signalling, both U 1 and U 2 send one-bit feedback denoted by f 1 and f 2 , respectively.The feedback bit f 1 and f 2 denotes the decoding status of U 1 and U 2 , i.e., 1 for successful decoding; otherwise, 0. If both U 1 and U 2 correctly decode their own symbols (f 1 = 1 and f 2 = 1), S transmits a new set of symbols, and R remains silent (it saves power by eliminating unwanted relaying) in the second phase as shown in Fig. 2(a).Otherwise, R transmits the amplified signal to both U 1 and U 2 in the second phase, and S remains silent as shown in Fig. 2(b).The amplified signal transmitted from R is expressed as where ρ R = (P R /N o ) and β is the channel-dependent amplification factor which is obtained by equating the total transmit and receive power at R. The signals received at U 1 and U 2 are respectively, where N II are AWGN samples at U 1 and U 2 , respectively.Similar to the first phase, the SINR II 12 and II 11 to decode x 2 and x 1 (after SIC) at U 1 in the second phase are (10) respectively.The SINR to decode x 2 at U 2 is expressed as After substituting for β in ( 9)- (11), we obtain Depending on the decoding status of both U 1 and U 2 , combining of the first and the second phase signals takes place at U 1 and/or U 2 as listed in Table III.
Remark 1: It can be clearly seen from the transmission process shown in Fig. 2 that the IR in the considered system is basically a positive and negative feedback-based switching Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

III. THROUGHPUT ANALYSIS
In this section, the performance of the considered IR AF relay-aided CDRT-NOMA-based IoT network is analyzed.We derive the closed-form expressions for the throughput of both U 1 and U 2 in what follows.
1) Throughput at U 1 : Based on the decoding status of IoT nodes U 1 and U 2 given in Table III, the throughput at U 1 can be mathematically defined as (the terms in τ inc 1 below correspond to Rows 1-6 of Table III) where C 12 = I 12 + II 12 and C 11 = I 11 + II 11 represent the combined SINRs to decode x 2 and x 1 at U 1 .Using the basic probability theory, τ inc 1 in ( 15) can be further expressed as We present an expression for τ inc 1 in the following theorem.
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Proof: Refer to Appendix A. Part of the gain in throughput with the proposed scheme is because of IR, and a part due to use of the unique combining at the NU.CDRT techniques proposed in the literature do not use combining at the NU like in this work.To show that the combining at NU is helpful for obtaining a better performance at FU while guaranteeing a desired performance at NU, we derive the expression for throughput at NU in what follows for the case when combining does not take place at NU (denoted by τ inc 1nc ).Similar to τ inc 1 in ( 16), τ inc 1nc can be mathematically expressed as Lemma 1: The expression for throughput at U 1 for the case in which no combining (NC) takes place at U 1 (τ inc 1nc ) is given by where A 1 and A 2 , are as in (39), (19) and, A a 3 and A a 4 are as follows: where Proof: To obtain the expression for τ inc 1nc , we substitute U = 0 in (13) and ( 14 2) Throughput at U 2 : Similar to U 1 , the throughput at U 2 can be mathematically defined as (the terms in τ inc 2 below correspond to Rows 1-6 of Table III) where C 22 = I 22 + II 22 denotes the combined SINR to decode x 2 at U 2 .Using the basic probability theory along with the independence of RVs, τ inc 2 in (15) can be rewritten as After simplification, we present τ inc 2 in the following theorem.
Theorem 2: Throughput at U 2 with the IR AF relaying protocol in the CDRT-based downlink NOMA network is given by where A 1 and A 2 are as in ( 39) and ( 19), respectively, and A 5 is expressed as in (32), shown at the bottom of the next page.
Proof: Refer to Appendix C for the detailed proof.Remark 2: The closed-form expressions for both the NU and FU throughput for the case of perfect SIC can be readily obtained by substituting for ε = 0 in the analytical expression obtained in the case of imperfect SIC.

A. Far-User Throughput Maximization
It can be seen from ( 17) and ( 31) that the choice of α S , R 1 , and R 2 is pivotal in attaining large throughput at both the IoT nodes U 1 and U 2 .Since the S-U 1 channel is stronger than the S-U 2 channel, it is reasonable to maximize throughput at U 2 while guaranteeing the desired target throughput at U 1 .It can be shown that τ inc 1 is a concave function of α S .When α S is small, x 2 cannot be decoded by U 1 (and, hence, x 1 detection fails), and when α S is close to 1, x 1 cannot be decoded.For any specified τ that is smaller than the maximum τ inc 1 , α S can take Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
values only in a range.Denote the minimum and maximum α S range by α min S and α max S , and the range of values by A. U 2 throughput should be optimized for α S ∈ A. The optimization problem is formulated as It is analytically very difficult to solve the above joint optimization problem due to the complex nature of the resulting mathematical expressions.However, numerical search can readily be used to pick the optimal information rates (R * 1 &R * 2 ) and optimal power apportioning parameter α S (α * S ) while guaranteeing a minimum throughput of U 1 .

IV. ENERGY EFFICIENCY
For energy-constrained next-generation communication systems with a large number of connected IoT devices, EE is a fundamental metric, and it is defined as the ratio of sum throughput (denoted by τ inc sum ) to total energy consumption [19], [39], [40].Using the throughput expressions derived for the IoT nodes U 1 and U 2 (τ inc 1 and τ inc 2 ), given in ( 17) and ( 31), the EE of the proposed system is mathematically expressed as where Q is the total energy consumption of the considered IoT network in a signalling interval of duration T and can be expressed as when cooperation from the relay node is not required, and as when relaying is required.Remark 3: It can be clearly seen from ( 34) that EE is a scaled version of sum throughput.It follows then that the values of power allocation coefficient and target information rates that maximize throughput also maximize the EE.

V. NUMERICAL RESULTS
This section presents numerical results to verify the analytical expressions, and draw some useful insights.Unless specified otherwise, the default parameter setting for simulations are: and ϕ = 3 and N o is normalized to unity [17].Without loss of generality, we assume P S = P R = P (ρ S = ρ R = ρ) [19], [41] and target information rates [31].Furthermore, we compare the performance of the proposed scheme with nonincremental AF CDRT scheme [31] (throughputs denoted by τ ninc 1 and τ ninc 2 ) and its relayed OMA counterpart (throughputs denoted by τ oma 1 and τ oma 2 ).In the considered relayed OMA scheme, S serves U 1 and U 2 in the first and the second phase, respectively, over the direct link, and R forwards the amplified U 2 symbol in the second phase.The combining of the first and the second phase signal takes place at U 2 , whereas U 1 cancels the interference from R using the decoded U 2 symbol from the first phase.
Figs. 3 and 4 depict the throughput performance of IoT node U 1 and U 2 (τ inc 1 and τ inc 2 using ( 17) and ( 31), respectively) with respect to ρ for R = 1, 1.5 bpcu and α S = 0.25.It is clear from both the figures that the throughput increases with increasing ρ and saturates to R after a certain value of ρ.A huge gain in throughput (almost double) can be clearly observed in comparison to relayed OMA and nonincremental AF CDRT NOMA [31] for both the NU and the FU.This is due to intelligently exploiting the feedback bits received from both NU and FU, which helps to avoid unwanted relaying in the second phase and entire communication takes place in one phase only.In addition, we also demonstrate the effect of SIC error on the throughput performance of both the NU and the FU in Figs. 3 and 4, respectively.It is clear from Fig. 3 that the SIC error does not affect the U 2 throughput performance at low as well as high SNRs, whereas the SIC error degrades the throughput performance of the U 2 in the mid-range of SNR, but the degradation in performance is not significant even with Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.30% of SIC error (ε = 0.3).Similar to U 2 , the U 1 throughput performance remains unaffected at high SNR, whereas the SIC error slightly limits the U 1 throughput at low as well as a mid-range of SNR.It can be clearly seen from both the figures (Figs. 3 and 4) that the effect of SIC error is not significant.Therefore, we have considered ε = 0, i.e., the case of perfect SIC in the remaining figures.Figs. 5 and 6 depict U 1 and U 2 throughput performance (τ inc 1 and τ inc 2 using ( 17) & (31), respectively) with respect to α S for ρ = 35 dB and R = 1, 1.5 bpcu and R * (optimal rate).It is clear from Figs. 5 and 6, that both U 1 and U 2 throughput first increases with increasing α S , attains a maximum value, and then decreases.This is due to the incremental signalling which depends on the decoding status at both U 1 and U 2 , and the unsuccessful decoding of the FU symbol at FU and/or NU after a certain value of α S Fig. 6.U 2 throughput versus α S with ε = 0, 0.15, 0.2, 0.3 and R = 1, 1.5, R * bpcu, and ρ = 35 dB.
(less power allocation to FU).It becomes 0 for ).It is also clear from both Figs. 5 and 6, that the optimal choice of target information rate R (denoted by R * ) helps to achieve a huge gain in throughput at both U 1 and U 2 in comparison to random choice of R. Therefore, the joint selection of optimum power allocation coefficient as well as the optimal target information rate is crucial to ensure better throughput performance at both U 1 and U 2 .Figs. 5 and 6 also show the U 1 and U 2 throughput performance for the case of nonincremental AF CDRT NOMA [31].It can be clearly seen that incremental signalling provides a huge gain in throughput at both U 1 and U 2 in comparison to nonincremental AF CDRT NOMA.Fig. 7 depicts the variation of τ inc 2 [using (31)] with respect to R 2 for τ = 1.6, 1.8 and 1.9 bpcu, ρ S = 35 dB, R 1 = 2, R * 1 and α S = α * S .It is clear that τ inc 2 decreases with increasing τ .We observe that the optimal choice of R 2 (R * 2 ) maximizes τ inc 2 while ensuring desired throughput τ inc 1 = τ at U 1 .In addition, the optimal choice R * 1 of R 1 significantly improves τ inc 2 .Clearly, U 2 attains maximum throughput performance at (R * 1 , R * 2 ), and joint optimization of R 1 and R 2 is very important.It also shows that the combining at U 1 plays a very important role in U 2 throughput performance, which degrades significantly if there is NC at U 1 as in conventional CDRT (denoted by τ inc 2nc in Fig. 7), where combining is performed only at the U 2 .
In Fig. 8, we plot user fairness 4 versus target information rate R for α S = 0.2, 0.3 and ρ = 25, 30 dB and compares the same with the nonincremental AF CDRT scheme [31] and its relayed OMA counterpart.It can be clearly seen that the user fairness depends on the choice of target information 4 Due to apportioning of power between users, user performance varies in NOMA signalling, and one user can achieve much better performance in comparison to others.For user fairness, performance all the users performance should be similar.Likewise [42], we define the proportional fairness in terms of the ratio of FU to NU throughput as F inc = τ inc 2nc /τ inc 1nc .rate as well as NOMA power allocation factor.It is clear the proposed is very much fair for lower target information rate R and power allocation coefficient α S , and fairness decreases with increasing R and α S .On the other hand, increasing transmit SNR ρ improves the fairness.It is also clear from Fig. 8 that the proposed scheme results in much better fairness in comparison to its relayed OMA counterpart, and provides similar fairness to the nonincremental AF CDRT.
Fig. 9 depicts the variation of sum throughput [using ( 17) and (31)] with respect to R while considering α S = α * S and ρ = 35 dB.It is clear that the sum throughput is a quasiconcave function of R, and an optimal R exists that maximizes the sum throughput.The choice of R is crucial in maximizing the sum throughput performance, which will also be evident in the next figure.Moreover, the proposed scheme outperforms  the OMA as well as fixed AF CDRT NOMA by a huge margin in terms of sum throughput.It also shows that the sum throughput performance degrades significantly (around 10%) if there is NC at NU. Fig. 10, shows the variation of U 1 and U 2 throughput with respect to the ratio of S-R and R-U 1 distances obtained by varying d SR while fixing d S1 = 2.The obtained result provides new insights.U 2 throughput first increases, attains a maximum value, and then decreases to zero.On the other hand, U 1 throughput keeps on decreasing.It is clear that the placement of R significantly affects the throughput performance of both U 1 and U 2 .However, the performance of U 1 is affected less in comparison to U 2 .
In Fig. 11, we plot U 1 and U 2 throughput for various distance conditions, i.e., with respect to the ratio of d S1 to d S2 .We vary d S1 while fixing d S2 = 4 to vary (d S2 /d S1 ).It can be clearly seen from Fig. 11 that U 1 and U 2 throughput increases with increasing d S1 to d S2 ratio, and saturates after a certain value due to the fixed target rate and decreasing d S1 (because S to U 2 distance is fixed, i.e., d S2 = 4).Clearly, the throughput for both U 1 and U 2 increases with increasing transmit SNR ρ.It is also clear that the throughput for both 1 U decreases with increasing α S .This is due to lower power allocation to U 2 with increasing α S , which results in unsuccessful decoding of U 2 symbol at U 1 and/or U 2 .
In Fig. 12, we plot sum throughput [using (17) and ( 31)] versus α S for ρ = 35 dB and different values of R, i.e., R = 1, 1.5 bpcu and R * (optimal R).It is observed that the sum throughput first increases with increasing α S , attains a maximum value, and then decreases (due to unsuccessful decoding of the FU symbol after a certain value of α S ).
).It can be clearly seen that the optimal choice of R ( R * ) provides a substantial gain in comparison to random choice of R. Therefore, the joint selection of optimum R and α S is very important to achieve high sum throughput performance.Fig. 13 depicts EE [using (34)] versus ρ for R = R * , α S = α * S and P = 7, 10 W and compares the same with the nonincremental AF CDRT scheme [31] (EE denoted by ξ ninc = ([τ ninc 1 + τ ninc 2 ]/Q)) and its relayed OMA counterpart (EE denoted by ξ oma = ([τ oma 1 + τ oma 2 ]/Q)).It can be clearly observed that the EE increases with increasing ρ and then saturates.As ρ increases throughput of both U 1 and U 2 increases which in turn increases the sum throughput and, hence, EE increases.It is also observed that EE increases with decreasing transmit power P (for ρ = 42 dB, ξ inc decreases from 0.9516 to 0.6662 when P increases from 7 to 10 W).Clearly, the proposed scheme is much more energy efficient and, hence, can be used in energy-constrained applications.

VI. CONCLUSION
In this article, we analyzed the performance of an AF relay-aided CDRT protocol in the downlink NOMA-based IoT network with direct links to both the IoT nodes for the first time assuming incremental signalling.The case of imperfect SIC is considered which is essential for the practical implementation of IoT-based smart cities.It is shown that the use of incremental signalling along with combining at the FU as well as the NU (along with SIC) can provide large gains in terms of throughput and EE in comparison to the nonincremental AF CDRT NOMA and its relayed OMA counterpart.We demonstrated that the optimal selection of the target information rate and power allocations coefficient is very much crucial to maximize sum throughput as well as EE of such an IoT network.The obtained insights confirm that the proposed scheme is useful in energy-constrained higher throughput demanding scenarios like smart cities. Extending the analysis to the scenario of multiple users along with multiple transmit antennas at the source is an open problem.Here, the main focus could be to optimize the power allocation coefficient and the beam forming weights so as to provide massive connectivity.

APPENDIX A
Proof of Theorem 1: To obtain τ inc 1 , we solve for the terms A 1 , A 2 , A 3 , and A 4 in ( 16) one by one.Using (6), A 1 can be expressed as Performing mathematical manipulations, the above can be expressed as Using the PDF of RV Z which is exponentially distributed, the above can be further expressed as Next, we use (5) to express A 2 in (16) as follows: Performing mathematical rearrangements, the above can be expressed as Similar to A 1 , we use the PDF of RV Y to obtain the expression for A 2 as Using ( 5) and ( 13), A 3 in ( 16) can be expressed as After mathematical rearrangements, A 3 can be expressed as where = (γ 1 /[(α S − ε ᾱS γ 1 )ρ S ]) and = (γ 2 /[κ 2 ρ S ( ᾱS − α S γ 2 )]).We use δ = to represent that the holds ( ᾱS −α S γ 2 ) > 0 and (α S −ε ᾱS γ 1 ) > 0; otherwise, A 3 equals 0. The RV X, Y and U are exponentially distributed and, hence, the above can be expressed in integral form as (47) Next, we substitute y + (χ /[ρ S ε ᾱS (χ + α S )]) = y followed by mathematical rearrangements to express the above as follows: Furthermore, we use relation [38, eq. (2.64)] to obtain the closed-form express for A 3 as in (48), shown at the bottom of the next page.Using (5) and ( 13), A 4 in ( 16) can be expressed as Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

Fig. 2 .
Fig. 2. Illustration of the transmission process for the incremental signalling.(a) S-U 1 and S-U 2 transmission are successful in the 1st phase of signalling.(b) S-U 1 and/or S-U 2 transmission is unsuccessful in the 1st phase of signalling.

I 11 .
) which results in C 12 = I 12 and C 11 = For the detailed proof, refer to Appendix B.

TABLE I SUMMARY
OF EXISTING RELATED WORKS AND THEIR COMPARISON WITH OUR WORK at NU, FU, and the relay in the first phase of signalling.

TABLE II DECODING
STATUS-BASED TRANSMISSION IN THE FIRST AND SECOND PHASES OF SIGNALLING

TABLE III DECODING
STATUS-BASED COMBINING OF THE DIRECT AND THE RELAYED SIGNALS AT IOT USERS between the direct NOMA and the Relayed NOMA protocol, respectively.