Non-orthogonal multiple access (NOMA) has been seen as a promising technology for 5G communication. The performance optimization of NOMA systems depends on both power allocation (PA) and user pairing (UP). Most existing researches provide sub-optimal solutions with high computational complexity for PA problem and mainly focuses on maximizing the sum rate (capacity) without considering the fairness performance. Also, the joint optimization of PA and UP needs an exhaustive search. The main contribution of this paper is the proposing of a novel capacity maximization-based fair power allocation (CMFPA) with low-complexity in downlink NOMA. Extensive investigation and analysis of the joint impact of signal to noise ratio (SNR) per subcarrier and the channel gains of the paired users on the performance of NOMA in terms of the capacity and the user fairness is presented. Next, a closed-form equation for the power allocation coefficient of CMFPA as a function of SNR, and the channel gains of the paired users is provided. In addition, to jointly optimize UP and PA in NOMA systems an efficient low-complexity UP (ELCUP) method is proposed to be incorporated with the proposed CMFPA to compromise the proposed joint resource allocation (JRA). Simulation results demonstrate that the proposed CMFPA can improve the capacity and fairness performance of existing UP methods, such as conventional UP, and random UP methods. Furthermore, the simulation results show that the proposed JRA significantly outperforms the existing schemes and gives a near-optimal performance.

Non-orthogonal multiple access (NOMA) arises as the reliable multiple access technique for the fifth-generation (5G) communication systems to provide the required high data rates and massive connectivity [

The conventional OMA techniques such as orthogonal frequency division multiple access, which are categorized cannot support massive connectivity since each subcarrier can be allocated to a single user to avoid multiple access interference [

Resource allocation represented in power allocation (PA) and channel assignment or user pairing (UP) are the keys to optimize the performance of NOMA systems. The optimal PA was only existed for users on a single channel and only for the maximization of the sum rate. Furthermore, in most of the existing works, the fairness performance was not taken into account, and the PA only depends on the channel gain of the paired users [

The main contributions of this paper are as follows:

Extensive investigation and analysis of the joint impact of SNR per subcarrier and the paired users’ channel gains on the performance of NOMA is presented.

A novel capacity maximization-based fair power allocation (CMFPA) with low-complexity in downlink NOMA is proposed, which represents the main contribution of this paper. In CMFPA, a closed-form equation is proposed for the power allocation coefficient as a function of SNR per subcarrier and the channel gains of the paired users.

In addition, efficient low-complexity UP (ELCUP) method is proposed to be incorporated with the proposed CMFPA to compromise the proposed joint resource allocation (JRA) for the optimization of capacity and fairness performance of NOMA systems with a significantly low computational complexity.

Compared to the existing schemes, CMFPA can significantly improve the capacity and fairness performance of existing UP methods such as conventional UP, and random UP methods.

Finally, simulation results show that the proposed JRA outperforms the existing schemes and gives a near-optimal performance.

The rest of the paper is organized as follows. A discussion of related work is presented in Section 2. Section 3 presents the system model. In Section 4, the investigation and analysis of the joint impact of SNR per subcarrier and the paired users’ channel gains on the performance of NOMA and the proposed CMFPA are provided. The ELCUP method is given in Section 5. The simulation results and discussion are introduced in Section 6. Finally, the conclusion is given in Section 7.

PA in NOMA depends on several aspects such as the channel conditions and signal-to-noise ratio (SNR), which is related to the total power restriction. The main aim of PA in NOMA is the maximization of the sum-rate (capacity), and there are many related works [

In [

In [

However, the objective of these researches is the maximization of the sum rate and energy efficiency, where fairness among users is not considered, which is an important issue for NOMA networks. Several works considered the fairness issue in NOMA, e.g., [

Joint sub-channel and power management for downlink heterogeneous NOMA networks were investigated in [

A single-cell based downlink NOMA system scenario is considered, where a base station (BS) simultaneously transmits information to K users (i.e., users’ equipment (UEs)) over M subcarriers, as illustrated in

For a subcarrier m, the channel gain of the user1 (UE-1) which is called strong UE is assumed to be larger than the channel gain of the user2 (UE-2), which is called weak UE

On a subcarrier m, the superimposed signal transmitted from BS to the paired UEs is

The received signals of the paired UEs are

Since

So, the sum-rate over a subcarrier m (i.e., the subcarrier capacity) for NOMA system is

The achievable rate of the UE-

So, the sum-rate over a subcarrier m for OMA system is

In this section, extensive investigation and analysis of the joint impact of SNR per subcarrier and the channel gains of the paired users on the performance of NOMA with respect to the capacity and the user fairness are firstly introduced in Section 4.1. After that, the proposed CMFPA, which is based on this investigation, will be presented in Section 4.2 as a function of the following three parameters:

SNR per subcarrier (

The channel gain of strong UE (

The ratio of the channel gain of weak UE to the channel gain of strong UE (

In this section, the joint impact of subcarrier's SNR and the channel gains of the paired UEs with the power allocation coefficient

The subcarrier capacity (i.e., _{k} is the achieved data rate of the k^{th} UE and K is the number of UEs.

During the analysis and discussion of results, we will refer to _{1} for simplicity. The impact of channel gains on NOMA performance is represented in term of the impact of both h_{1} and μ (i.e.,

§ To show the joint impact of both SNR and h1 with

§ To show the impact of μ, the investigation results are taken at a large value of μ (μ = 0.9), a medium value of μ (μ = 0.5), and a small value of μ (μ = 0.1).

Concerning the capacity,

Concerning the capacity,

Concerning the capacity,

It is worth mentioning that in case of small values of μ, the optimization of both the capacity and the fairness performance cannot be achieved. Therefore, it is better to maximize the capacity and avoid a large loss in the achieved capacity at the expense of the degradation of the fairness performance by setting

Based on the extensive investigation results in previous section, the following concepts can be concluded:

In the case of a large value of μ, no capacity loss occurs as

In the case of a medium value of μ (i.e., μ = 0.5), no significant capacity loss occurs as

In the case of a small value of μ (i.e., μ = 0.1), the best choice is setting α close as possible to its highest possible value (α = 0.5) to maximize the capacity and avoid a large loss in the achieved capacity at the expense of the degradation of the fairness performance.

Since the proposed CMFPA targets to maximize the capacity and to achieve the highest possible FI values without capacity loss,

§ As the value of μ decreases,

§ As the values of SNR and h1 increase,

Based on the concluded concepts from the extensive investigation results in the previous section, the following closed-form equations for the adjustment of

During simulation value of

The proposed equation guarantees that the value of

The UP algorithm is responsible for the selection of the paired UEs according to their channel gains and consequently the selection of _{1}_{2}_{1}_{2}_{1}_{1}_{1}

Maximizing the capacity by increasing the values of _{1}.

Improving the fairness among the paired user by avoiding small values of μ.

Minimizing the computational complexity of the UP process.

The steps of the user pairing process are proceeded as follows:

The average value of the channel gains of all users over each subcarrier is computed to be used as a simple measure of the channel quality per subcarrier, such that, the subcarrier with the highest average value of the channel gains is considered as the best subcarrier.

The order of subcarriers during the UP process is the highest channel quality subcarrier (i.e., the best subcarrier) first.

UP process is performed on two sequential stages; the first stage is the assignment of the strong user for each subcarrier followed by the second stage in which the assignment of the weak user for each subcarrier is performed.

During the strong user assignment stage, the user with the largest channel gain over each ordered subcarrier is assigned as the strong user. The selected user is discarded from the subsequent assignment process.

During the weak user assignment stage, the user with the most convergent channel gain to the strong user's channel gain is assigned as the weak user to avoid small values of μ. The selected user is discarded from the subsequent assignment process.

The pseudo-code of ELCUP is presented in Algorithm 1.

In this section, the performance of the proposed CMFPA and the performance of the proposed joint resource allocation (JRA), which consists of the proposed ELCUP incorporated with the proposed CMFPA are evaluated via simulations. During the simulation, a frequency selective fading channel with six independent multipath is considered with Rayleigh distributed fading parameters. Link level simulations are performed in MATLAB, and 5000 realizations of channel gains are taken to generate each data point on the forthcoming figures.

The simulation results investigate the performance of the proposed CMFPA compared with that of Fractional Transmit Power Allocation (FTPA) [

Random UP is the easiest method for user pairing, in which the users are randomly selected and allocated into a random empty subcarrier. On the other hand, in conventional UP, the user with the best channel gain is paired with the user with the worst channel gain, which needs exhaustive search to assure that the capacity of the NOMA system is larger than that of OMA system. So, the impact of pairing users whose channel gains are more divergent (i.e., small values of μ) can be investigated in case of conventional UP.

The decay factor of FTPA is chosen to be 0.4 to make a compromise between the capacity and the fairness performance. The minimum power gap

One of the important performance metrics is the outage probability which is defined as the probability that the data rate of UE is lower than a certain minimum rate R_{0}_{0 }=_{ }1 bps/Hz and R_{0 }=_{ }2 bps/Hz is presented in _{0 }=_{ }1 bps/Hz and R_{0 }=_{ }2 bps/Hz. Also, it is shown that the outage probability of the random UP using the proposed CMFPA is better than that using FTPA especially at R_{0 }=_{ }2 bps/Hz and is always lower than that of OMA. For conventional UP, it provides the worst (i.e., highest) outage probability at R_{0 }=_{ }1 bps/Hz and the proposed CMFPA can improve its outage probability for R_{0 }=_{ }2 bps/Hz at high SNR’ values to outperform random UP using FTPA.

In this paper, a novel low complexity PA called CMFPA in downlink NOMA is proposed to maximize the capacity while nearly optimize the fairness performance. Extensive investigation and analysis of the joint impact of SNR and paired users’ channel gains on the performance of NOMA is presented. Next, in CMFPA, a closed-form equation is proposed for the power allocation coefficient as a function of SNR and the channel gains of the paired users. In addition, an efficient low-complexity UP (ELCUP) method is proposed to be incorporated with the proposed CMFPA to compromise the proposed joint resource allocation (JRA) for the optimization of capacity and fairness performance of NOMA systems. Compared to FTPC, the proposed CMFPA can significantly improve the capacity and the fairness performance of existing UP methods such as conventional UP, and random UP methods. Also, the proposed JRA outperforms the existing schemes and gives a near-optimal performance.

The authors would like to acknowledge the support received from Taif University Researchers Supporting Project Number (TURSP-2020/147), Taif University, Taif, Saudi Arabia.