# Novel Resource Allocation Techniques for Downlink Non-Orthogonal Multiple Access Systems
## 1 Introduction  
The development of different multiple access techniques for each generation has brought many advantages to wireless cellular communication, such as improving spectral and energy efficiency and achieving a high data rate. The fifth-generation (5G) networks are expected to be used various applications in the future \"smart\" era [1, 2, 3]; they are anticipated to serve a large number of mobile cellular users with huge data traffic transmission. This makes spectrum allocation a challenging issue in wireless communication [4]. Several advanced technologies have been developed to address this problem and achieve high spectral efficiency, such as millimeter wave communication, machine-to-machine communication, network virtualization technology and non-orthogonal multiple access techniques [5, 6, 7]. In this context, power domain non-orthogonal multiple access (PD-NOMA), known simply as NOMA, has arisen recently as one of the promising technologies. NOMA ensures fairness between users and connectivity of a huge number of mobile devices with low-latency transmission [8, 9]. It utilizes power domain or code domain multiplexing to allow many users to share the resources of frequency or time. The assignment of different subchannels to different users allows adaptable bandwidth allocation [10; 11]. NOMA employs two main fundamental techniques for transmitting and receiving user information: superposition coding (SC) and successive interference cancellation (SIC). Since several users are allowed to use the same subchannel, inter-user interference may occur. Thus, in NOMA, different power levels are assigned to the multiplexed users to reduce the interference by allocating more power to the far user and less power to the near user [12]. The best NOMA performance can be achieved by utilizing effective resource allocation and user pairing solutions. Nevertheless, determining efficient resource allocation is a challenging issue and has received significant attention from researchers [13; 14]. Different solutions have been proposed to optimize the subchannel and power allocation in the downlink and uplink NOMA system. Most of works in the literature have measured the achieved sum rate and weighted sum rate of the NOMA system with suboptimal solution and without showing the closed-form solutions for the optimal power allocation. In addition, the ideal energy efficiency of a NOMA system that allows achieving optimal performance is not well studied in the literature. Hence, this paper focuses on proposing optimal solutions for user pairing and power allocation to maximize the system sum rate and energy efficiency performance. This paper extends our work in [15] and proposes novel resource allocation techniques in a downlink single-cell NOMA system using Dinkelbach (PDKL) and Hungarian (HNG) algorithms. The base station (BS) is considered to have a knowledge about channel state information (CSI). To reduce complexity at the receiver, SIC technique is applied for the multiplexed users. The HNG algorithm first pairs two users in a subchannel. Then, equal power allocation is considered for each subchannel. The optimal power allocation technique is applied to achieve the optimal power allocation for each of the multiplexed users in the given subchannel. The major contributions of this work are as follows:  
* An optimal user pairing approach based HNG algorithm is proposed that considers pairing of only two users at each subchannel. This algorithm guarantees an optimal performance of both the sum rate and energy efficiency maximization process in a downlink NOMA system. For comparison, the performance of the proposed algorithm is compared with the center-based user pairing (CEB) method proposed in [16]. * The sum rate maximization problem is formulated by considering SIC for each user in the subchannel in which the constraints are the minimum acceptable data rate and the maximum available transmission power at the BS.