Computers, Materials & Continua DOI:10.32604/cmc.2021.018351 

Article 
Capacity and Fairness MaximizationBased Resource Allocation for Downlink NOMA Networks
Department of Computer Engineering, College of Computers and Information Technology, Taif University, Taif, 21944, Saudi Arabia
*Corresponding Author: Mohammed AbdElnaby. Email: maahmed@tu.edu.sa
Received: 04 March 2021; Accepted: 05 April 2021
Abstract: Nonorthogonal multiple access (NOMA) is one of the leading technologies for 5G communication. User pairing (UP) and power allocation (PA) are the key controlling mechanisms for the optimization of the performance of NOMA systems. This paper presents a novel UP and PA (UPPA) technique for capacity and fairness maximization in NOMA called (CFMUPPA). The impact of the power allocation coefficient and the ratio between the channel gains of the paired users on the sumrate capacity and the fairness in NOMA is firstly investigated. Then, based on this investigation, the PA and UP algorithms of the CFMUPPA technique are proposed. The power allocation coefficient of the proposed PA is formulated as an exponentially decaying function of the ratio between the channel gains of the paired users to maximize the capacity and the fairness, and its maximum value is adjusted to guarantee the successive interference cancellation (SIC) constraints. The proposed UP is based on selecting the user that has the highest channel gain per subcarrier as the strong user to maximize the capacity and selecting the user that has the closest lower channel gain to the strong user’s channel gain as the weak user to improve the fairness and capacity. The performance evaluation of the proposed CFMUPPA technique in terms of capacity, fairness, and outage probability demonstrates that its performance significantly outperforms that of the orthogonal multiple access (OMA) system and that of the NOMA system with random UP. Also, the simulation results demonstrate the efficiency of the proposed PA in improving the performance of other UP algorithms, such as the random UP algorithm.
Keywords: 5G; nonorthogonal multiple access; user pairing; power allocation; capacity; fairness
The rapid development of multimedia applications and the applications of the Internet of Things (IoT), in addition to the huge increase in the number of wireless and mobile devices, paved the way for the emergence of the 5G communication networks. NOMA has emerged as a promising access technology for capacity enhancement in 5G networks by enabling multiple users to use the same subcarrier at the same time with the aid of successive interference cancellation (SIC) technique implemented at the receiver to detect the user data. The performance optimization of NOMA strictly depends on the efficiency of user pairing (UP) and power allocation (PA) mechanisms. UP and PA mechanisms are responsible for controlling all performance metrics of NOMA, such as system capacity, fairness among users’ equipment (UE), and data rate outage probability [1–5].
Existing UP and PA mechanisms try to improve NOMA performance, but most of them succeeded focus on in improving the system capacity at the expense of the other important metrics such as the fairness among users and the outage probability. Also, most of the existing researches require exhaustive searching and high computational complexity to provide a nearoptimal solution for the UP and PA problems. So, in this paper, a novel capacity and fairness maximizationbased UP and PA (UPPA) technique called (CFMUPPA) is proposed for downlink NOMA. The main contributions of the proposed CFMUPPA technique can be summarized as follows:
1. An extensive investigation of the impact of the power allocation coefficient and the ratio between the channel gains of the paired users (i.e., paired UEs) on the sumrate capacity and the fairness in NOMA is presented. Also, the investigation results are analyzed to clarify how to adjust the power allocation coefficient using the PA algorithm and select the channel gains of the paired UEs using the UP algorithm to maximize the capacity and fairness.
2. Then based on the investigation results, the PA algorithm of the CFMUPPA technique, which is called capacity and fairness maximizationbased PA (CFMPA) is proposed. The power allocation coefficient of CFMPA is formulated as an exponentially decaying function of the ratio between the channel gains of the paired UEs to maximize the capacity and the fairness, and its maximum value is adjusted to guarantee the SIC constraints.
3. The UP algorithm of the CFMUPPA technique, which is called capacity and fairness maximizationbased UP (CFMUP) is based on selecting the user that has the highest channel gain per subcarrier as the strong user to maximize the capacity and selecting the user that has the closest lower channel gain to the strong user’s channel gain as the weak user to improve the fairness and capacity.
4. Both CFMPA and CFMUP can be considered as nonexhaustive searching algorithms. Also, unlike the proposed CFMPA, most of the existing PA algorithms are exhaustive searching algorithms and have no closedform equation for the power allocation coefficient for the maximization of capacity and fairness.
5. The performance of the proposed CFMUPPA technique in terms of capacity, fairness, and outage probability is evaluated, and the simulation results show that its performance significantly outperforms that of the OMA system and that of the NOMA system with random UP. In addition, the proposed CFMPA is applied to the random UP to demonstrate its efficiency in improving the performance of other UP algorithms.
The paper is organized as follows. Related work is discussed in Section 2. The system model and capacity are outlined in Section 3. The impact of the power allocation coefficient and the ratio between the channel gains of the paired UEs on capacity and fairness in NOMA is presented in Section 4. The proposed CFMUPPA technique is provided in Section 5. Section 6 presents the results, comparison, and discussion. Finally, Section 7 concludes the paper.
Resource allocation in terms of UP and PA plays the main role in improving the performance of NOMA especially in terms of the network capacity. However, the traditional UP and PA methods succeeded in improving the capacity of NOMA with different degrees, they fail in improving other important performance metrics such as fairness among UEs and outage probability at the same time. Besides, computational complexity is another important parameter that should be carefully considered in the design of resource allocation mechanisms since it reduces computational efficiency and the speed of allocation decisions [6–9].
A deep neural network (DNN) based resource allocation technique is proposed in [10] to handle the complexity problem of traditional resource allocation methods since DNN can perform the realtime allocation. Generic DNN is trained to approximate the interior point method (IPM) for PA to improve the computational efficiency and increases the capacity of the system. In [11], a joint dynamic PA and UP algorithm is proposed for powerefficient and delayconstrained hybrid OMA/NOMA systems. In this hybrid system, UP determines if the UE will be served by OMA or NOMA. Both queue state information and the channel are observed, and the PA and UP optimization framework is proposed to minimizes the average transmit power while guaranteeing minimum data rates and decreasing the queueing delay.
In [12], multiobjective optimization is used for resource allocation in multiuser downlink NOMA systems to improve spectrum efficiency and energy efficiency. A joint spectrum and energy optimization problem is formulated and solved using dual decomposition while guaranteeing the SIC process by preserving the constraint of the minimum gap among UE transmit powers. In [13], a joint UP and PA algorithm for uplink NOMA systems is proposed to improve the proportional fairness of UEs. A basic scenario in which UEs are distributed in a single base station (BS) and a complex scenario in which the interfering UEs users are randomly distributed outside BS is considered. Tabu search is used to provide a nearoptimal solution for the UP problem in the basic scenario and the PA problem in the complex scenario is solved using stochastic programming.
Many research works have investigated the NOMA capacity improvement in heterogeneous networks [14–19]. The selection of the UP method for NOMA according to the network load to make a tradeoff between the capacity gain and the complexity of the UP method is presented in [14]. Gale–Shapley, Hungarian, random, and exhaustive methods are considered for UP with dynamic PA, and the results show that for equally loaded cells, the nearoptimal UP methods provide the highest network capacity gain (22%–24%). While for unequally loaded cells, simpler UP methods provide higher capacity gains (approximately 29%).
Also, many researchers investigate resource allocation in MIMO based NOMA systems [20–24]. A greedysearchbased UP and a minimum mean square error (MMSE) based PA is proposed in [20] to maximize the sumrate of a downlink NOMA network. Also, the transmitted power of all UE pairs and that of each UE in each pair are optimized and an iterative procedure is used to solve the PA problem. Performance improvement of Multicell MIMONOMA networks is investigated in [25,26]. In [25], to improve system data rate, the resource allocation problem is divided into NOMA mobile user clustering and the base station selection. A new objective function is proposed to integrate mobile user fairness into system data rate optimization. Moreover, a closedform solution of MIMONOMA resource allocation for a single cluster is derived and a new twoside coalitional matching approach to jointly optimize MIMO NOMA clustering and BS selection is proposed. An analytical framework for exploring the benefits of applying MIMO NOMA clustering in dense wireless networks is developed in [26]. With the aid of stochastic geometry, a new explicit expression for percluster average data rates are derived, and the analysis and optimization of area spectral efficiency are considered.
Owing to the important role of cognitive radio as promising solutions to provide high spectral efficiency for future wireless networks, the resource allocation problem in cognitive NOMA Networks is investigated recently in many studies [27–29]. In [27], an uplink IoT device scheduling and power allocation problem based on imperfect spectrum sensing and imperfect channel state information (CSI) is investigated for cognitive heterogeneous NOMA networks. The outage performance of an overlay cognitive NOMA system with imperfect successive interference cancellation (SIC) is investigated in [28]. Closed forms of the outage probability of primary user and secondary user are derived, and an optimal power allocation coefficient is proposed to maximize the system throughput. NOMAassisted overlay cognitive radio network in which the communication between the pair of primary users is achieved with the aid of the secondary transmitter (ST) is considered in [29]. The authors aim to minimize the outage probability of the secondary system under qualityofservice (QoS) constraints of the primary system by jointly optimizing the decoding order at the receivers and the power allocation factor at ST.
A downlink NOMA system is considered, which consists of a base station (BS), multiple subcarriers, and multiple users (i.e., multiple UEs) as shown in Fig. 1. The set of subcarriers donated by m = 1,…, M }, and the set of UEs donated by k = 1,…, K }. The paired UEs transmit over the same subcarriers, and for a subcarrier m it is assumed that UE1’s channel gain is the larger one. Since
On subcarrier m, the BS transmits a superimposed signal for the paired UEs as
where
The received signals for both UEs are
where
By assuming that the transmission bandwidth per subcarrier is normalized to 1 Hz. Then the achievable data rates of the paired UEs are
So, the sumrate capacity per subcarrier m for NOMA is
The achievable data rate of the UEi on subcarrier m in an OMA system is given by
So, the sumrate capacity per subcarrier m for OMA is
4 The Impact of ϡ and μ on Capacity and Fairness of Paired UEs in NOMA
In this section, the capacity (i.e., sumrate) and fairness of paired UEs in NOMA will be presented as a function of both the power allocation coefficient (α) and the ratio of UE2’s channel gain of to UE1’s channel gain of (μ). Eq. (3) presents the achieved data rate of strong UE (
The Jain fairness index (FI) presented in Eq. (7), which measures of the fairness among the achieved users data rate
The performance is investigated at SNR per subcarrier
Fig. 3 shows that the fairness performance significantly deteriorates as μ becomes lower than 0.5 and as α increases. On the other hand, the fairness performance significantly improves as μ increases (i.e., the channel gains of the paired UEs converge) and with the use of small values of α. The obtained results in Fig. 3 can be more clarified by looking to Figs. 4 and 5, which present the achieved data rate of weak UE and the achieved data rate of strong UE. For weak UE, the achieved data rate sharply increases as μ increases, and α decreases, as shown in Fig. 4. On the other hand, the achieved data rate of strong UE independents on μ and increases as α increases as shown in Fig. 4.
The results presented in Figs. 6–9 show that increasing the channel gain of the strong UE to 2 (hm,1 = 2) significantly increases the capacity of paired UE as shown in Fig. 6. This is because the achieved data rate of both weak UE and strong UE is considerably increased as shown in Figs. 8 and 9, respectively. Also, it is shown that the capacity decreases as μ considerably decreases especially at small values of α. So. α should be increased as μ decreases to increase the capacity. On the other hand, increasing hm,1 makes the fairness performance deterioration more sensitive to the increase of the value of α, and the FI considerably decreases as α increases especially at low values of μ as shown in Fig. 7.
From the analysis of the investigation results, we can conclude the following concepts:
• To increase the capacity, α should be increased as μ decreases and vice versa. Since the capacity decreases as μ decreases especially at small values of α.
• The fairness performance significantly improves as μ increases (i.e., the channel gains of the paired UEs converge) and with the use of small values of α.
• The capacity significantly increases as the channel gain of the strong UE (hm,1) increases.
It should be noted that the selection of the value of α is the responsibility of the power allocation (PA) algorithm, while the selection of the values of μ and hm,1 is the responsibility of the user pairing (UP) algorithm.
5 The Proposed CFMUPPA Technique
The proposed CFMUPPA technique consists of capacity and fairness maximizationbased PA (CFMPA) algorithm and capacity and fairness maximizationbased UP (CFMUP) algorithm. Both CFMPA and CFMUP algorithms based on the concepts concluded from the investigation results of the impact of α and μ on capacity and fairness in NOMA which is presented in the previous section. A detailed description of each algorithm is given in the next sections.
5.1 The Proposed CFMPA Algorithm
With respect to the selection of the value of α, which is the responsibility of the PA algorithm, the investigation results presented in Section 4 demonstrate the following:
• To increase the capacity, α should be increased as μ decreases.
• The fairness performance significantly improves with the use of small values of α. In other words, the fairness performance deteriorates as α increases, especially at small values of μ.
So, the objectives of CFMPA are as follows:
1. Increase α as μ decreases to maximize capacity, and this will be at the expense of some degradation in fairness performance at small values of μ.
2. Considerably decrease α as μ increase to maximize both capacity and fairness.
3. Adjust the maximum value of α (
To achieve these objectives, the proposed relation between α and μ is formulated as follows:
where
Eq. (9) for
where
5.2 The Proposed CFMUP Algorithm
With respect to the selection of the values of μ and hm,1 which is the responsibility of the user pairing (UP) algorithm, the investigation results presented in Section 4 demonstrate the following:
• To increase the capacity, μ should be increased. Since the capacity decreases as μ decrease especially at small values of α
• The fairness performance significantly improves as μ increases.
• The capacity significantly increases as hm,1 increases.
So, the objectives of CFMUP are as follows:
1. Increasing the values of μ which results in maximization of both the capacity and fairness. So, CFMUP aims to pair the weak UE that has the closest lower channel gain to the strong UE’s channel gain.
2. Selecting the UE that has the highest channel gain over the subcarrier as the strong UE (UE1) to maximize the capacity of the NOMA system.
The steps of CFMUP are as follows:
1. For each subcarrier, the channel gains of UEs are sorted in descending order, and the highest UE’ channel gain is detected.
2. Sorting the subcarriers in descending order according to its highest UE’s channel gain and follows this order during the UP process in the following steps.
3. CFMUP starts the selection process by selecting the strong UE for each sorted subcarrier (i.e., the subcarrier with highest UE’s channel gain first). The UE that has the highest channel gain over the subcarrier is selected as the strong UE, and each selected UE is discarded from subsequent selection during the UP process since each UE can be paired on a single subcarrier.
4. After completing the selection process of the strong UE for each subcarrier in step 3, CFMUP starts the selection process of the weak UE for each sorted subcarrier. The UE that has the closest lower channel gain to strong UE’s channel gain over the subcarrier is selected as the weak UE, and each selected UE is discarded from subsequent selection during the UP process.
The pseudocode of the proposed CFMUP is shown in Algorithm 1.
6 Results, Comparison, and Discussion
In the simulation, we consider the NOMA system, which is characterized by the frequency selective fading channel with six independent multipath. The fading parameter in the channel model is a random variable and follows the Rayleigh distribution. It is assumed that the transmission bandwidth per subcarrier is normalized to 1 Hz. The results presented below refer to ensemble averages across 5000 channel realizations.
In this section, the performance of the proposed CFMUPPA scheme is evaluated and compared with the performance of the OMA system, as well as that of NOMA utilizing random UP. Random UP is considered as the lowest complexity UP algorithm, which provides suboptimal capacity performance since it is based on the random selection of the paired UEs on each subcarrier without considering the users’ channel conditions [30]. Both the proposed CFMPA and Fractional Transmit Power Allocation (FTPA) [31,32] are used for power allocation for random UP to demonstrate the efficiency of the proposed CFMPA in improving the performance of other UP algorithms. During the simulation, the decay power allocation factor of FTPA is set to be 0.2, and the value of minimum power gap
Firstly, the performance is evaluated as a function of SNR at M = 32 subcarriers (i.e., K = 64 UEs). Fig. 10 shows that the proposed CFMUPPA technique achieves considerably higher capacity than that of random UP and that of OMA. It is clear that the capacity of CFMUPPA is higher by more than 2 bps/Hz than the capacity of OMA and higher by slightly less than 2 bps/Hz than the capacity of random UP for all SNR values.
Despite the good fairness performance is the main feature of NOMA random UP due to its random allocation nature, Fig. 11 demonstrates the efficiency of CFMUPPA in providing a significantly high degree of fairness among UEs compared to NOMA random UP. In addition, Fig. 11 demonstrates the significant efficiency of CFMPA in improving the fairness of random UP compared to the FTPA algorithm. On the other hand, the high FI obtained by OMA is a result of the nonexistence of interference among UEs in OMA and the uniform power allocation.
The probability that UE’s data rate is lower than a minimum data rate R0 is called the outage probability and it is represented in Fig. 12 for R0 = 1 bps/Hz and in Fig. 13 for R0 = 2 bps/Hz. It is shown that CFMUPPA technique provides the lowest outage probability especially at small SNR values and its values are approximately lower by a factor 0.1 than the values of random UP and OMA for most of the SNR values. Also, it is shown that CFMPA efficiently reduces the outage probability of random UP compared to the FTPA algorithm especially at R0 = 2 bps/Hz.
Secondly, the performance is evaluated as a function of the number of UEs at SNR = 20 dB where the number of UEs is double the number of subcarriers. Fig. 14 shows that the capacity of the proposed CFMUPPA outperforms that of OMA by approximately 30% and that of NOMA random UP by approximately 17%. Also, it is shown that the capacity of the CFMUPPA improves as the number of UEs increases, while the capacity of the other algorithms tends to reach its maximum value as the number of UEs becomes greater than 16 UEs. With respect to the fairness performance, Fig. 15 shows that CFMUPPA achieves significantly high FI equals 0.9 compared to 0.63 obtained by random UP with FTPA, and the proposed CFMPA can improve the fairness performance of random UP by 35% (FI = 0.85) compared to the FTPA algorithm. In terms of outage probability, the lowest outage probability for R0 = 1 bps/Hz and R0 = 2 bps/Hz is achieved by CFMUPPA and it slightly improves as the number of UEs increases. on the other hand, the worst outage probability is achieved by random UP with FTPA as shown in Figs. 16 and 17. Also, it is shown that CFMPA considerably reduces the outage probability of the random UP compared to the FTPA algorithm.
Since the performance of the NOMA system is controlled by UP and PA. So, this paper presents a novel UP and PA (UPPA) technique for capacity and fairness maximization called (CFMUPPA). Firstly, the paper investigates the effect of the power allocation coefficient and the ratio between the channel gains of the paired users on the capacity and the fairness of the NOMA systems. Then, capacity and fairness maximizationbased PA (CFMPA) is proposed in which the power allocation coefficient is formulated as a function of the ratio between the channel gains of the paired users, and its maximum value guarantees the SIC constraints. After that, capacity and fairness maximizationbased UP (CFMUP) is proposed to pair the strong user that has the highest channel gain per subcarrier with the weak user that has the closest lower channel gain to the strong user’s channel gain to maximize the capacity and fairness. Simulation results show that the performance of the proposed CFMUPPA technique significantly outperforms that of the OMA system and that of the NOMA system with random UP. Also, applying the proposed CFMPA to the random UP significantly improves its performance.
Acknowledgement: The authors would like to acknowledge the support received from Taif University Researchers Supporting Project Number (TURSP2020/147), Taif University, Taif, Saudi Arabia.
Funding Statement: This research was supported by Taif University Researchers Supporting Project Number (TURSP2020/147), Taif University, Taif, Saudi Arabia.
Conflicts of Interest: The author declares that he has no conflicts of interest to report regarding the present study.
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