Abstract
In this paper, we consider a dual-user nonorthogonal multiple access (NOMA) with the help of full-duplex decode-and-forward (DF) relay systems with respect to Nakagami-m fading channel environment. Especially, we derive the analytical expressions to evaluate system performance in terms of outage probability, achievable throughput, and energy efficiency. The main investigation is on considering how the fading parameters and transmitting power at the base station make crucial impacts on system performance in the various scenarios. Finally, simulations are conducted to confirm the validity of the analysis and show the system performance of NOMA under different fading parameters of Nakagami-m fading channels.
1. Introduction
With the fast growth related to cellular networks and WiFi network-aware transmission techniques, several wireless facilities to support smart devices are becoming more widespread trend. Massive connections and huge multimedia streaming are adapted to satisfy an explosive growth in the wireless data traffic transmission. As a widely recognized key technology for the fifth-generation (5G) mobile communication systems, nonorthogonal multiple access (NOMA) paradigm is proposed to support the tremendous demands on data traffic. NOMA recently investigated and the related novel architectures for NOMA have drawn great considerations in both academy and industry [1–3]. In the conventional orthogonal multiple access (OMA) schemes, in which at signal domains (i.e., frequency, time, or space), the different orthogonal channels are allocated for accommodated users. In contrast, NOMA assigns the same channel for such users. More specifically, different power levels are nominated to different data flows with assistance of the superposition coding (SC) at the transmitter. At the receiver, the successive interference cancellation (SIC) is deployed to detach separated signals. As a result, main advantages including massive connections, reduced communication latency, and increased spectral efficiency can be achieved by the deployment of NOMA [1, 2].
More recent works have considered the integration of cooperative relaying transmission with energy harvesting in systems [4–8] and with NOMA systems in [9–11]. The crucial advantage of the combined model is that users need the help of the dedicated relays cooperative in NOMA systems to further expand both transmission reliability and energy efficiency [12–20]. Specifically, users with strong channel conditions proceeded as relays to assist the users with weak channel conditions in a cooperative NOMA (C-NOMA) scheme proposed in NOMA-based cellular network [10]. Other trends are applications for wireless power transfer to NOMA as interesting investigation in [6, 8]; that is, simultaneous wireless information and power transfer (SWIPT) technique was used in relaying systems, in which trade-offs between outage performance and energy harvesting coefficients are examined. Additionally, the overlay cognitive radio (CR) networks can require C-NOMA, where a secondary transmitter [12] or a secondary receiver [13] helps as a relay and supports transmitting the primary messages, and hence, the primary network assigned the same frequency band can be able to deliver multiple access capabilities. To expand the performance, a dedicated relay can be employed in NOMA systems [14–20]. In [14, 15], the classical three-node cooperative relaying system (CRS) was applied in NOMA, where the source transfers two symbols with dissimilar power levels possessing superposition coding to a dedicated half-duplex relay so that the acquired symbols corresponding to two time slots are forwarded to the destination. In [16, 17], to increase the performance of the user with the poor channel condition, two-user NOMA systems were measured in two scenarios, including deploying a dedicated half-duplex relay [16] and deploying a dedicated full-duplex relay [17]. Additionally, a variable gain relay was presented to simplify the transmission between the source and NOMA users to serve multiusers in NOMA systems in the case of nonexistence of direct link transmissions as in [18]. System performance such as exact and asymptotic high signal-to-noise ratio (SNR) expressions were presented to illustrate the superiority of NOMA over orthogonal multiple access (OMA) with respect to applied Nakagami-m fading channels [20]. While a fixed gain relay and direct link transmissions were considered to examine performance in concerned NOMA-based relaying networks [18, 19]. With regard to wireless power transfer, a SWIPT-based decode-and-forward (DF) relay was considered in NOMA-based relaying network [21].
Recently, due to its potential to double the spectral efficiency, full-duplex (FD) wireless communication has attracted substantial attentions by permitting concurrent downlink (DL) and uplink (UL) transmission in the same frequency band [22–24]. The two-way communication links in a two-user FD scheme were inspected in terms of the rate region and the achievable sum rate [25, 26], respectively. Most of the researches on NOMA schemes rely on the Rayleigh fading channel model. Nevertheless, Rayleigh fading is considered as the special case of fading channels. Alternately, it is the most effective way to consider influences of Nakagami-m fading channels in the outage performance evaluation of NOMA with regard to the line of sight (LoS) transmission. To our best knowledge, the wide-ranging topic-related wireless analysis, i.e., Nakagami-m fading channels in relaying-aware NOMA, has not been well considered yet in the previous literature. In [18], the closed form and lower and upper bounds on the ergodic sum rate together with the outage probability have been provided in amplify-and-forward (AF) relaying over Nakagami-m fading channels, whereas the achievable rates over Rayleigh fading channels in the decode-and-forward (DF) scheme have been explored in [27]. Contrasting with the case single of antenna equipped in all nodes as recent works [18, 27], the outage performance analysis over Rayleigh fading channels deploying multiple antennas has been assigned for the source and all destinations in [28]. Furthermore, by resolving the combined power allocation and relay beamforming scheme, the maximum sum rate has been attained in the case of multiple antennas equipped in the relay, while the single antenna is equipped in source and all destinations [29]. In [30], the authors studied the performance of the cooperative relay scheme with a single relay over Nakagami-m fading channels in terms of downlink in NOMA, in which both DF and AF protocols are examined. To determine the decoding order of cell-edge users’ data, they adopt statistical channel state information (CSI) for such system and the closed form of the ergodic sum rate and outage probability are derived. In a similar trend, the authors in [19] developed new closed-form expressions of both precise and approximate outage probabilities of fixed gain AF relaying in NOMA.
In this study, we consider a different model compared with [19, 30], where an FD relay supports transmission data from the base station (BS) in the scenario of NOMA to serve two NOMA users with different locations assigned, including the users at the cell center and the other one located in the cell edge. It is worth noting that our work considers the same architecture as that in [9, 17]. However, compared to work in [9] which considered the Rayleigh fading environment, our investigation generalizes in the complex case of Nakagami-m fading condition. Furthermore, research [17] is assumed under perfect co-channel suppression at user and modelled nonfading self-interference channel as a Gaussian noise for convenience in analysis. These assumptions are extended in this work by exploiting more practical scenario of imperfect channel estimation and self-interference cancellation scheme. Unlike the conventional NOMA performed in previous works [19, 30], this investigation mainly focuses on two cases of relay where single antenna or dual antenna are equipped at relay to perform forwarding NOMA signals to destination. The contributions are summarized as follows:(i)We investigate the outage performance for NOMA systems with the proposed FD relaying strategy, and it is derived in the closed form for the considering scenario. On the contrary, the performance comparisons among proposed NOMA, with FD and half-duplex (HD) relaying schemes are also provided.(ii)We examine the achievable throughput based on the derived outage probability. To look insights regarding energy, we consider energy efficiency performance for the proposed system model.(iii)Computer simulations are conducted to verify the accuracy of the theoretical analyses. Main results show that NOMA with the higher fading parameter and higher transmitting power of the BS outperforms the remaining cases in terms of outage performance and throughput. Such results exhibit a better behavior in NOMA with the improved channel condition, especially in the high transmitting power region.
The remaining of this paper is organized as follows. The overall system model and assumptions are introduced in Section 2. In addition, Sections 3 and 4 represent the detail analytical derivations of the outage probability for FD and HD transmission mode, respectively. In Section 5 provides simulation results, and Section 6 provides a conclusion for this research.
2. System and Signal Model
2.1. Network Topology and Channel Assumptions
2.1.1. Network Topology
The considered FD cooperative relaying NOMA network is depicted in Figure 1, where a base station assigned with single antenna, denoted by B, transfers the information toward two single antenna equipment users, and , by exploiting the power domain division technique, namely, NOMA. In such a model, it is assumed that existence of the link can be seen due to nearer distance, while the connection of link is nonexistence. Hence, B directly transmits messages to and indirectly sends to with help of the intermediate relay node which is denoted by . Specially, in order to enhance the spectral efficiency, is designed to operate in the full-duplex mode and thus facilitates two antennas as assumed in [9, 17]. It is worth noting that the multiple antenna relay node can further mitigate the self-interference power; however, this approach leads system to be more complex [31]. Thus, we assume the single antenna for transmitting and receiving at terminals in this work. It can refer as a typical situation of a multiantenna scheme as investigated in [9, 17].
2.1.2. Outdated Channel Model
In practice, because of estimation errors, it is highly difficult to estimate the perfect channel state information (CSI) of wireless network. Thus, the outdated channel coefficient is modelled as follows [32, 33]:where represents the outdated CSI at the transceiver with variance , whereas is the perfect channel coefficient, and denotes the estimated channel error which can be approximated as a Gaussian random variable with zero mean and variance , and [33], respectively. In fact, the known channel factor at the transmitter is a feedback from receiver after estimating the period; hence, the CSI at the transmitter is outdated.
2.1.3. Channel Statistic Distribution
In this work, all estimated channel coefficients are modelled under Nakagami-m fading condition. Although the Rician fading environment is more suitable to examine the self-interference (SI) link due to the short distance between antennas, its complicated distribution functions prevent to give the analytical expressions. Fortunately, the Nakagami-m fading distribution provides an alternate approximation to the Rician distribution. Inspired by this, and to simplify the analysis, we have adopted the Nakagami-m fading to model the SI channel as in this paper and recent works [6, 22]. Thus, the probability density function (PDF) and cumulative distribution function (CDF) of their gains follow gamma distributions with mean and integer severity factor m and, respectively, formulated aswhere and present the fading severity factor and mean, respectively. In this paper, we also assume is an integer number and . When , the channel environment returns to the Rayleigh fading channel. It implies that the considered Nakagami-m fading channels are more general than the previous Rayleigh fading condition. The equality in (3) is achieved by applying an equivalent relationship in Eq. 8.352.6 of [34].
Additionally, the channel coefficients are denoted as follows: the channels from B to and from B to are and , respectively. The connection between (or ) and be (or ), while the self-interference link at and interference of link are symbolized as and , respectively. In general, the channel gain follows the gamma distribution with parameter and with .
Remark 1. It is noted that, although the considered system in this study is as same as in [9, 17], the channel conditions investigated in our system undergo imperfect knowledge of the Nakagami-m fading environment. Since such channel condition is more general than the Rayleigh fading environment in [9], and this research can be considered as a generalized version of previous work in [17] when considering nonideal interference cancellation hardware for both co-channel interference at and self-interference at , taking imperfect CSI noise into account.
Remark 2. In this paper, the severity fading parameter, i.e., m, is strictly supposed as an integer value. Thus, the analytical expression is only true for such considerations. The general case of noninterger values of m is beyond the scope of this study.
2.2. Full-Duplex NOMA Relaying Scheme and Signal Analysis
2.2.1. Cooperative NOMA FD Relaying Scheme
In this part, we adopt cooperative FD relaying NOMA network considered in [9, 17]. The modelling signal can be formulated as follows. In the block time t, B sends a superimposed mixture of the signals intended for both and , thanks to the power domain division:where and are two allocated power parameters for and messages, respectively, with and, . As aforementioned, we assume that is the near user and is the far user, thus it satisfies . The notations , , and are analogously and and superimposed NOMA data symbols, with zero mean and variances of unit.
Firstly, we consider the signal associated with . According to link, the received signal at under imperfect CSI is thus given bywhere and are B and transmission powers, respectively. denotes the additive white Gaussian noise (AWGN) at with zero mean and variance . Besides, denotes the residual interference coefficient after using interference cancellation technique in the FD mode. It is worth pointing out that user must first detect message for SIC purpose so, therefore, user can theoretically remove interference signal which was sent from the relay node. However, the interference part cannot completely suppress due to the limitation of mitigation level and imperfect CSI. Then, they are treated as residual interference signals at as that in [9]. We use to represent the delay time for signal processing. Its value is small compared to time block and can be ignored in analysis as that in [9].
Based on NOMA principle, the near user first detects the message by treating symbol as interference, then removes symbol, and finally decodes its own data. Therefore, the signal to interference plus noise ratio (SINR) to decode message at isand the SINR at to detect its own data is given bywhere and are the signal-to-noise ratio (SNR) at B and , respectively, and . It is worth noting that, in (7), we assume the perfect SIC is achieved as that in [9]. The system performance can be degraded since successive interference was cancelled imperfectly. But it is out of the paper scope.
Now, considering the connection, by denoting channel coefficients of , , and relay loop interference links as , , and , respectively, the received signal at is expressed asand the amount of signals received at from relay node could be formulated aswhere and are AWGNs at relay and , respectively, both with zero mean and variance . Since the relay tries to decode the information intended for while treating the symbol of as interference, the SINR is computed to decode the message of , and it can be expressed as
Additionally, from (9), the SNR to detect message at iswhere and .
2.2.2. The Near NOMA User-Aided Cooperative NOMA FD Relaying Scheme
In this subsection, we combine the user-aided relaying architecture in [10] into FD cooperative. This idea exploits the near user as a relay node to forward message to far user . In fact, first decodes symbol for SIC purpose; hence, can forward it to improve decode diversity. In such a suggested scheme, SINRs at for detecting the data becomewhere , with the transmitting power at node X and . In addition, the SINR to detect data at is reexpressed as
According to user-aided transmission, the SINR at relay to determine is now suffered by additive interference intended from caused by FD forwarding and can be rewritten bywhere .
Regarding the link, the SINR at relay and are given by adding the interference from aided user aswhere and .
Moreover, the listened signal at from could be expressed as
Then, the SNR at from user-aided relaying iswith . For simplicity in analysis, it is assumed that the far user exploits the selection combine (SC) approach to process two paths achieved from the relay and user-aided relaying . Hence, the SINR at with the proposed scheme is expressed aswhere and .
In the sequels, the system performance in terms of outage probability will be analysed.
3. Outage Probability Consideration on Full-Duplex Relaying NOMA
3.1. Outage Probability of
3.1.1. Cooperative NOMA FD Relaying Scheme
According to the considered NOMA technique, the outage probability of can be determined as error when recognizing either or its own message. Thus, the meets outage probability, , which is formulated aswhere and are the target rates of and , respectively, and and are the channel capacities at associated with and symbols, respectively.
Proposition 1. Putting and . The outage probability of for such a considered system over the Nakagami-m fading condition is given bywhere , , , and , .
Proof 1. See Appendix.
With the high SNR regime, i.e., , and the approximate expression for , we can achieve the approximation asStarting from (A.2), we can achieve the asymptotic expression asFinally, by applying Eq. 6.455.1 of [34] for the last integral, the asymptotic outage probability of is given bywhere is the Gaussian hypergeometric function [34].
3.1.2. User-Aided Cooperative NOMA FD Relaying Scheme
Similar to that in (19), the outage probability of can be obtained by replacing the corresponding proposed scheme SINR instead and is given by
Substituting (12) and (13) into (24), the outage performance is given in Proposition 2.
Proposition 2. The outage probability of for the user-aided relaying cooperative FD relay system under the Nakagami-m fading environment is determined aswhere is defined in Proposition 1, , , and :
Proof 2. The procedure is similar that in Appendix.
In case of , we get the approximate expression:where
3.2. Outage Probability of
3.2.1. Cooperative NOMA FD Relaying Scheme
Based on the operation of the dual-hop cooperative DF relaying scheme, the outage probability of can be expressed aswhere and are the channel capacities of message associated with hop and hop, respectively. It is worth noting that is defined in Proposition 1.
Proposition 3. We denote , , , and , and the outage probability of is given bywhere and
Proof 3. See in Appendix.
The approximate expression is given asWith the help of equality in Eq. 8.354.2 of [34], since , we can get
3.2.2. User-Aided Cooperative NOMA FD Relaying Scheme
As early assumption, shall exploit the SC technique to choose the best from both signal paths. Additionally, channels are independent with each other, and the outage can be further written as
Proposition 4. The outage probability of for the suggested -aided FD relaying cooperative NOMA system is given bywherewith defined in Proposition 3, , , , , , , , and .
Proof 4. The results can be obtained by similar way in proof 3.
Similar approximating procedure for , the approximate expression for with user-aided relaying is derived.
3.3. Delay-Limited Throughput and Energy Efficiency for FD Relaying NOMA
In the delay-limit transmission mode, the system throughput is given as a function of outage probability [7, 10]. The throughput of the considered FD cooperative relaying NOMA is given by
Besides, for user-aided relaying, cooperative FD NOMA is obtained as
Recently, to adapt deployment for green communications, the energy efficiency becomes a crucial factor to evaluate system efficiency. Normally, the energy efficiency of the considered system is defined as a ratio of throughput to total consumed power. For the aforementioned FD relaying NOMA system, the system energy efficiency can be illustrated as that in [10]:
Similarly, the EE of the user-aided relaying scheme is given by
4. A Comparison Study on Half-Duplex Relaying NOMA
For the comparison purpose, the HD NOMA relaying is represented as a benchmark. Some results for the HD cooperative NOMA system can be addressed in [16]. Unlike the FD NOMA relaying architecture, the HD ones divide a data transmission period into two slots. In the first phase, the source B transmits message to and based on the superposed signal in (4); thus the SINR at for retrieving data and its own data are, respectively, given by and while the SINR at to detect symbol can be expressed as with and .
In the second phase, we consider two scenarios of implementation as in the FD transmission mode, such as conventional and proposed user-aided relaying for the HD cooperative NOMA system. Firstly, for the conventional cooperative NOMA network, the relay regenerates and forwards signal to while the source and remain silent. Thus, the SNR at user from in the latter time slot is given by . Secondly, in the case of user -aided relaying scheme, the SINR at from is with and . Similarly, by exploiting selection combining technique at the far user, the received SINR is given by . It is noted that the SINR of and for the proposed user-aided relaying HD scheme is similar to that for the conventional HD cooperative scheme except that transmitting power is replaced by the corresponding proposed power, i.e., , , and . In what follows, we will study the outage probability of considered HD networks.
4.1. Outage Probability of
Regarding performance, the outage probability for the conventional scheme can be obtained as the expression below. Define and . In the HD transmission mode, the outage probability of user 1 for the traditional cooperative NOMA is given bywhere and .
For the proposed FD user -aided relaying cooperative NOMA system, the outage probability is easily obtained by replacing with .
4.2. Outage Probability of
The outage probability of in HD conventional relaying network is obtained asand the outage for the proposed -aided relaying cooperative HD scheme iswhere and are given in Proposition 3 and
Proof 5. It can be achieved by using the similar analysis that in the FD mode.
5. Numerical Results
In this section, the effectiveness channel factor to the NOMA relaying system is simulated. In the simulation, the noise is normalized, i.e., . The final results are averaged over realization runs. For fairness in comparison, we assume the total power budget to equal ρ, the transmitted power is set up for conventional cooperative NOMA scheme and that for the user-aided relaying scheme . Unless other stated, the target rates of and are set and , respectively. The allocated power fraction be so that . We also set the fading severity parameter as .
The system model is conducted as Figure 2. The distances between nodes x and y are denoted with . We normalize and . The angle between link and link is α. Hence, the space form relay to is and distance between and is . In order to invoke large-scale fading, the channel power mean parameters are set as the following function of distance, such as , , , and . . The power mean of self-interference links at relay and after precancellation is set , where κ is the imperfect CSI level, n is the exponential loss factor, and ε represents the interference mitigation level. Unless other stated, we set , , and .
Figures 3 and 4 plot the impact of the fading parameter m on the outage performance with varying total transmitted power. It is experimentally illustrated that the fading parameters of the transmission links have a great influence on the outage performance. The outage performance with a higher m outperforms the ones with the lower m. This is because a higher m implies a stronger received SNR at destination. Furthermore, the main reason is that a larger fading parameter leads to a higher diversity order for the user, resulting in a lower outage probability [18]. As shown in Figures 3 and 4, analysis results match very well with the Monte Carlo simulation curves.
Performance gap can be seen among three cases of outage probability related to users and . Furthermore, there exists a saturation for the outage probability in the higher transmit power region. One can also observe from Figure 4 that the fading parameters of all links () have crucial impact on the outage performance.
Figures 5 and 6 investigate the impact of imperfect CSI level on the outage performance of the system.
Figure 7 provides a comparison of the achievable throughput by considering two concerned modes at relay. Note that the considered system also gains benefit of the FD scheme and achieves a higher throughput as increasing the fading parameters. However, performance gap as varying fading parameters can be seen clearly in transmitting power ranging from 10 dB to 20 dB for the FD scheme and ranging from 15 dB to 25 dB for the HD scheme. It is worth noting that throughput performance of the HD scheme for the one time slot is lower than the remaining schemes. To sum up, the better channel condition leads to higher throughput can be obtained and such throughput reaches the limited value at a high level of transmitting power at B. Such observations verify the accuracy of our derived expressions.
From Figure 8, we can see that the NOMA using the FD mode always outperforms the NOMA using the HD mode in terms of the optimal energy efficiency. Interestingly, optimal energy efficiency can be achieved at the FD mode and HD mode during the first time slot, but such values can only be found by using the numerical method. Moreover, the low energy efficiency can be seen at high transmitting power of B. The reason is that putting more power at B reduces energy efficiency of the considered system.
Figures 9 and 10 show the variation of outage performance of and under impact of angle α with , , and . As can be seen from Figure 9, the outage probability of FD network decreases when α increases from 0 to π. This is due to the decline of interference from relay to since the distance between these nodes grow. However, performance of the HD scheme does not suffer from this variation. From Figure 10, there are some fluctuations of outage. Outage performance of the proposed user-aided relaying FD scheme outperforms than that of the conventional scheme when . This can be explained that since space between relay and user is large enough, it leads to the small interference between nodes and improves the proposed user-aided relying.
6. Conclusion
In this paper, the system performance of cooperative NOMA networks over imperfect Nakagami-m fading environments has been studied. We have derived the closed-form expressions of the outage probability and delay-limited throughput and energy efficiency for both conventional relaying and near user-aided relaying for the cooperative NOMA system. The numerical simulations have been conduced to verify the exactness of analytical expressions. The results show that the system performance can further be enhanced by improving either severity parameter m or exactness of the channel as imperfect CSI is raised. In addition, the simulation results also reveal that the near user-based relaying for the cooperative NOMA scheme can improve far user performance; however, it degrades that of near user.
Appendix
Substituting (6) and (7) into (19), the outage probability can be simplified after some simple manipulations aswhere is defined in Proposition 1. To tackle (A.1), we consider two scenarios as below.
Case 1. In the case , i.e., , the outage probability is always equal to one, i.e., .
Case 2. In the case , i.e., , (A.1) can be computed asAccording to (2) and (3), (A.2) can be solved aswhere , , and are defined in (20). Step applies in Eq. 1.111 of [34] and step uses equality in Eq. 3.381.4 of [34] . Combining the above two cases, Proposition 1 is derived, and this is the end of perfect explanation for such proposition.
Since and are independent to each other, in (29) can be further simplified asThe item can be revealed as the same as in (A.3) and given byIn addition, the second item, i.e., , can be calculated as follows:Finally, substituting every computed equation into main formula, Proposition 3 is derived. This is the end of the proof.
Data Availability
No data were used to support this study.
Conflicts of Interest
The authors declare that they have no conflicts of interest.