Performance Analysis of MIMO-NOMA Systems Based on Dynamic User Pairing Scheme

Multiple input multiple output (MIMO) structure can enhance the total capacity of the modern communication systems without using consuming excess power or bandwidth. Non-orthogonal multiple access (NOMA) configuration is a good nominee to accommodate with MIMO structure to fulfil the demands to extra user data rates and enriched spectral efficiencies. The dynamic uniform channel gain difference (DUCGD) user pairing technique plays an important role to maximize the capacity of all the paired and served users. The DUCGD is implemented by calculating the channel gain of every prospected user and sorting it in descending order to pair ones with the highest difference in channel gains to be functioned together. In this paper, the performance analysis of MIMO-NOMA systems by means of DUCGD is presented. The numerical analysis showed that, the increase of the number of users leads to an increase in the systems’ gain and the total achieved sum rates. This improvement is shown to be due to using DUCGD and an increased number of transmitting and receiving antennas, jointly.


Introduction
User pairing in non-orthogonal multiple access (NOMA) enables more than one user to share their resources using superposition coding (SC) in the power domain. Where each user can take a proportion of the transmitted power according to a sharing factor called power coefficient [1], it plays a promising procedure in the next mobile generation due to its higher spectral capacities [2] [3]. The uniform channel gain difference (UCGD) pairing technique depends on fixed power coefficient and neglects channel gain differences between users. This UCGD maximizes the capacity of the selected paired users [4], consequently channel gain calculated at every frame to decide which users can be paired to obtain maximize the capacity of all paired and served users.
In 5G wireless communication system, its' main target is getting the largest number of users and the fastest data speeds with good bit-error-rates (BER). The multiple-input multiple-output (MIMO)-NOMA has been a hopeful technique to fulfil this targets due to its superior spectral efficiency (SE) and higher capacities without consuming excess power or bandwidth [5] [6]. To utilize the user pairing (UP) manner in MIMO-NOMA procedure, the base station (BS) supposed to pick which users thought to be paired to share the similar band in advance, since the clustered users should have a major variance between there channel gains to raise the systems' whole rate [2].
In [7], The influence of the pairing techniques on the feasible sum rates of NOMA has been practiced with stationary power allocation but not a dynamic one. A new algorithm advances to acquire extraordinary properties of the interference signal cancellation at NOMA method studied in [8]. In [9], traditional NOMA apportions more power to the served users with low channel gains to escalate their throughput. The closed-form globally-optimal solution in [10] acquired to fix user pairing and power allocation problem with least rate compel for each user in NOMA scheme. In [11], an extra consideration about UP in the cognitive radio applications inspired from NOMA scheme is presented, where the achievable sum rate could be amplified with a costumed matched distributed algorithm. In [12], a user pairing and pair scheduling for massive MIMO-NOMA schemes expanded the throughput by alleviating the inter-pair interference. The issue of ergodic capacity expansion MIMO-NOMA systems with the Rayleigh fading channel is illustrated in [13], and submit both optimal and suboptimal power allocation schedule to settle this optimization problem. Finally, in [14] the new algorithm for power allocation can improve the achieved overall rate of NOMA method.
In this paper, the performance of different types of MIMO-NOMA pairing schemes were compared by calculating their total sum rate at various cases. The study considered a constant users' number and utilizing 2, 4 and 8 transmitting (Tx) and receiving (Rx) antennas. When DUCGD pairing scheme is utilized, the system resulted highest sum rates with increasing of the number of utilized antennas. As well as, the cumulative distribution function (CDF) investigation proved that the probability of higher total sum rate is greater than the probability of lower ones at various user's number in the same mentioned case. When the number of utilized MIMO antennas is fixed, the gain due to NOMA pairing schemes is increased with the increase of number of users. Due to the benefits of DUCGD over conventional schemes, it suggested to utilize it in MIMO-NOMA systems with increased numbers of users and massive numbers of antennas.
This paper is structured as follows. Second section portrayed user pairing in MIMO-NOMA. Third section explains the considered MIMO-NOMA system model. Furthermore, the results of the simulation and considerations are executed in the fourth Section. Finally, the conclusion is presented in fifth section.

User pairing in NOMA
SC used in the NOMA systems to make numerous users sharing the mutual bandwidth with their information by giving each user a part of transmitting power. This process makes these users in a pair. The channel gains are a way to treat M users selected randomly in a cell 1 where m h implying the Rayleigh fading channel gain between the BS and the coordinated th m user and their allocated powers are in the arrangement 1 , respectively. where  represents the transmit signal to noise ratio (SNR). The total achievable data rate of NOMA is calculated by (3) The th m user can achieve m R permanently. The sum data rate of an orthogonal MA technique is calculated by (4) To anatomize DCU pairing in NOMA, the discussion is restricted to use two users per pair for simplification. Combining users from the cell centre (high CQI) and cell edge (low CQI) into pairs can achieve ultimate channel gain difference between them. The difference in the channel gain of the cell mid users (CMU) is very less if there are paired with each other. The likelihood that superior capacity of these pairs are lower than MA systems is studied in [7]. The nearness in the channel gains and the power coefficients lead to the increasing of noise at lower channel gain users and the deficiencies of SIC at higher channel gain users which are the main reasons of decreasing the capacity in these CMU pairs [15]. Therefore, if the CMU are paired, their sum rates could be lower than MA and the small mobility made the difference in gain neglected. For those reasons, dynamic uniform channel gain difference (DUCGD) pairing is used to accommodate the CMU by preserving comparatively DUCGD between paired users of all pairs as shown in figure 1. b. The user's channel gains which existing in the cell are splitted into two combinations by median h , pursued by inter-group paring in such a way that CMU are well adapted.
Consider the channel gains of L users in a cell as    L h  as in (5). The DUCGD can find the users of CMU which can be paired with either the higher channel gain or the lower channel gain users. This implies each time the minimum gain users of each gathering are matched with others, trailed by blending next least clients of the two clusters, etc. The power allocation factor in this method depends on the channel gain as in (6) In this technique, the submitted procedure solved the main reasons of decreasing the capacity in these CMU pairs which discussed previously, that way allowing them to take advantage of MIMO-NOMA pairing techniques by getting higher capacity gain and minimizing the SIC performance issue.

System model
A solitary circular cell MIMO-NOMA broadcast is Imposed scheme with radius R, the BS at the centre serving a total M user [12]. In which every user of the cell has K receiving antennas and BS is supplied with N antennas. Here, M > 2N is expected to confirm that 2N users are chosen from all the users and everyone should have the same frequency band with its paired client. The user terminal (UT) should have a number of antennas greater than that of BS as the required system. The accurate channel state information's (CSIs) of all the users are known for both UTs and BS [12].
The Tx signal for the paired users have with SC at the BS can be shown as (7)  Following the essential rule of NOMA [2], the power allocation coefficients Can be customized as Within a pair, fragmentary transmit power was utilized to characterize 1,i a and 2,i a , so that, the principal user can recognize the subsequent user's signal effectively, and afterward subtracts it from the superposition coded signal by means of the SIC procedure [2]. the sum rate of MIMO-NOMA schemes can be indicated as (9) As a correlation, the sum rate of traditional MIMO-OMA frameworks can be expressed as (10)

Conclusion
In this paper a new proposed method for improving the gain of MIMO-NOMA pairing techniques has been used. The simulation results of this new method has been showed that the gain duo to the DUCGD pairing scheme is improved with the increase of Tx and Rx antennas. It is noticed that higher SNR leads to decrease the gain of DUCGD pairing system. The probability of achieving higher total sum rates in accordance with employing the DUCGD is superior by increasing number of transmitted and received antennas, also the spectral efficiency enhancing proportional to number of users especially for lower values of the SNR. The previous analysis proved that DUCGD suggested to utilize in MIMO-NOMA schemes with increased numbers of users or antennas. Through this paper, it was found that it is possible to use the DUCGD pairing techniques to take the advantage of the features which provided in 5G techniques.