Resource allocation algorithm in Heterogeneous Network Based on Non-orthogonal Multiple Access

The proposed resource allocation algorithm with joint power control and user pairing addresses the problem of degraded uplink user fairness due to cross-cell interference in NOMA uplink and improves user fairness. In the power control section, by decoupling power control from user pairing, the WOA algorithm is proposed in the statistical channel state scenario to solve the nonconvex optimization problem of intra-user pair fairness; in the user pairing section, the PTS algorithm is proposed to introduce randomness into the algorithm to improve the algorithm’s global search performance, solve the local optimum problem of integer programming, and improve inter-user pair fairness. Simulation results show that relative to the α-fairness comparison algorithm, the algorithm in this paper can improve fairness by about 5% under different interfering user densities, cell coverage radius, and tiny area transmit power.


Introduction
In order to achieve higher system throughput, higher user rates, and more simultaneous users, Non-Orthogonal Multiple Access (NOMA) [1], [2] and Heterogeneous Network (HetNet) [3], [4] have been widely discussed.The combination of NOMA and HetNet enables the multiplexing of spectrum resources in the power domain and the multiplexing of spectrum resources in the air domain, thus increasing the multiplexing rate of spectrum resources and the number of users served.However, it introduces more interference, which may result in the reduction of the system's maximum sum rate, user transmission rate, and inter-user fairness.In the uplink, numerous users simultaneously transmit data to the base station using the same resource as transmitters, and the base station receives a superposition of data from numerous users.Additionally, the user's transmit power and channel state are both factors that affect the decoding order.The effect of user pairing on system performance is examined in [5].For single-antenna and multiple-antenna cells, the best user pairing technique is discovered, respectively.[6] examines first how the performance of the system is impacted by the order in which user information is decoded.Then, an optimization algorithm based on Lagrangian pairwise joint channel assignment and power control is proposed to enhance the system's maximum sum rate.[7] proposes a user scheduling strategy with the goal of proportional fairness, in which the user with the least amount of delivered information is selected to communicate at each moment, thus ensuring fairness among users.[8] proposes a new optimization algorithm for power control and joint resource allocation.The optimization problem is difficult, so the algorithm must be solved in two steps.First, resource allocation is performed by a designed many-to-many matching algorithm under the assumption of full power emission.Then, the power control is optimized by geometric planning based on the resource allocation results.
It has been commonly assumed in existing studies that the base station is able to obtain real-time perfect channel state information (CSI) for every user.However, in real systems, the channels obtained by the base stations are non-perfect due to receiver performance limitations, extended processing, and delivery of signaling, pilot frequency pollution, user mobility, and other factors [9], [10].Therefore, the case where only statistical CSI can be obtained needs to be studied during resource allocation.In the uplink, user fairness is affected by user pair selection as well as cross-cell interference.

NOMA uplink communication signal transmission model in cellular heterogeneous networks
In this paper, we consider an uplink network for a cellular heterogeneous network with NOMA.It is assumed that M users exist within a tiny area, and cross-cell interference users are randomly distributed with out-of-cell in a spatial Poisson point process.The users in the microcell are denoted as , {1,2, , } , respectively, and their sets are U .The spectrum resource of the system consists of N sub-channels, the total system bandwidth is B , and the sub-channel bandwidth is 0 B .A single antenna is used for transmission at both the base station and the user side, and the total amount of NOMA multiplexed users is limited to 2 because this SIC requires high receiver performance and the superposition of too many signals will lead to low SINR and cannot be decoded.

Rate model for the uplink
Taking users i u and j u as an example, assuming that i u has a higher channel gain, it is necessary to control j u to transmit at high power and transmit at low power if we want to control i u message to be decoded first at the base station end.We let i p and j p represent the power that is transmitted of users i u and j u , as well, on a unit sub-channel with the maximum value max P .The respective rates of users i u and j u when paired as a pair are expressed as where i h and j h represent the channel gains within the base stations i u and j u , respectively, I is the total power of the interfering signal received by the base station per unit sub-channel, and 2 0  is the total noise power per unit sub-channel.The channel contains two components: Rayleigh fading g and path loss r   . is the path loss coefficient.0 B is the bandwidth per unit sub-channel.

Question formulation
We let , i j  be the user pairing factor, , {0,1} . Therefore, it is possible to express the rate of user i as and the rate of user j as In this paper, Jain's fairness index is used as the objective function, and for the selection of the concave function f(x) [11].This paper proposes to construct the utility function with ( ) 2 x f x  and establishes the fairness utility function as the optimization objective to improve the system fairness under the guarantee of user SINR demand through power control and user pairing.The optimization objectives are shown below.
Equation (3a) indicates the range of values of the power control coefficient for the post-decoded users.Equations (3b) and (3c) indicate that the SINR of the first and second decoding users meet the decoding threshold, respectively.Equation (3d) indicates the range of values of user pairing coefficients.Equation (3e) indicates that each user can only be paired with one other user.In the actual system, perfect real-time channel state information and real-time interference information cannot be obtained due to receiver performance limitations, inaccurate channel estimation, frequency guide pollution, random arrival of user services, and other factors.Consequently, to optimize the system in this paper, statistical channel state information and statistical interference information are used.The objective function is defined as where outage Pr (1, ) i is the interruption probability,  is the interruption probability threshold, and , is the anticipated rate of user information consumption.In an effort to improve optimization outcomes, the original problem is decomposed into two separate suboptimization problems iteratively solved in this paper.In the power control subproblem, the optimal power control solution is found for each possible user pairing method; in the user pairing subproblem, on the basis of the power control best solution and the corresponding transmission rate, the close to ideal user linking method is identified.

Based on Probability based Tabu Search user matching algorithm
User pairing is encouraged in this section.A user receives different information rates when paired with another user.In the uplink, the priority decoding users are able to communicate at full power without affecting the post-decoding users.To improve user fairness, the optimization objective of user pairing is established as: , s.t.{0,1}, , For the 0-1 integer programming problem in the equation, this section proposes the Probability based Tabu Search (PTS) algorithm based on the probability of user pairing.PTS introduces randomness into the initialization and discovery neighborhood steps, thus extending the search capability of the algorithm.
Each element of the user pair matrix is set to 1 with a certain probability, indicating that any user pair of two users may exist in the optimal solution.This probability is denoted as , ( ) (0,1) i j pr t  , representing the probability that i u and j u will be paired in the t -th iteration., ( ) 0  first requires transforming the 0-1 planning problem into a convex optimization problem and finding its suboptimal solution.To solve this optimization problem, a deformation of ( 5) is required.We make , , , 2 , , introduce the channel variable  , and relax Equation (5a), the transformation of the desired function towards s.t.log / (0,1), , The original issue is changed into a concavity optimization issue that can be resolved using either the interior point strategy or the simplex method.The optimal solution , i i  obtained is a small number, and this value can be used as a probability, , , i j i i pr t    , representing the probability that the user has for ( i u , j u ) to be present in the ideal resolution.The probability will increase the larger this value.

Power control algorithm based on the whale optimization algorithm
This section determines the objective function as follows to determine the best power control strategy for each user: ,  (7d).
The whale optimization algorithm (WOA) is proposed in this section for addressing the power placement problem because the target function is a nonlinear programming problem with equations.However, WOA is primarily utilized for tackling the minimax issue in unconstrained optimization, so an efficient equation handling method is needed to solve the constrained problem.The penalty function method is a straightforward and popular approach.As a result, the purposed function and the processing equations are combined in this work using the penalty function method.Then the objective Equation ( 7) is subjected to the inverse operation and finally solved using WOA.So, the penalty function of this optimization problem can be obtained from Equation (7) as Then the fitness function of WOA can be expressed as The entire algorithm flow is depicted in Table 1 in accordance with the preceding section.Table 1.User pairing and power control iterative optimization algorithm 1: Initialize the position of a single whale, the number of iterations, and a small threshold 0   .6: Solve the power allocation issue with fixed user pairing, per 3.2.7: until convergence 8: Calculate the f for each search agent according to Equation (9).9: Update the probability matrix  and the taboo list.

Simulation results
In this paper, two approaches are chosen for contrast to confirm the efficacy of the algorithm design: the  -fairness algorithm [12], and the maximum-minimum fairness algorithm [5].At a cell radius of 20 m and a user transmit power of 200 mW, the relationship between fairness and the distribution density of interfering users is shown in Figure 1(a).It is evident that as the density of interfering users rises, the fairness of the system decreases.The approach presented in this work can enhance the system fairness under various interference strengths when compared to the a-fairness comparison algorithm.The fairness is improved by about 5% when the expected value of interference user density is 20 users/km 2 .Figure 1(c) demonstrates the association between system fairness and ultimate user transfer power.The fairness of the system grows as well as user transmit power rises.First, when the base station transmitting power increases, the probability of achieving absolute fairness within the user pair increases.In addition, since the user rate is a concave function when the same power is increased, the rate increase of users with lower rates is larger.Therefore, the gap between different user pairs decreases and fairness increases.

Conclusions
This paper addresses the problem of degraded uplink user fairness due to cross-cell interference in NOMA uplink and improves user fairness through the proposed resource allocation algorithm with joint power control and user pairing.When it comes to user linking, this paper proposes the PTS algorithm, which introduces randomness into the algorithm to improve the global search performance of the algorithm, solves the local optimum problem of integer programming, and improves the fairness between user pairs.Then the nonconvex optimization problem of fairness between user pairs is put forth to be solved using the WOA algorithm.Simulation is used to confirm the efficiency of the approach suggested in this chapter.Relative to the α-fairness comparison algorithm, the algorithm in this paper is able to improve fairness by about 5% for different interfering user densities, cell coverage radius, and tiny area transmit power.

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The computation of the initial 1

2 : repeat 3 : 5 :
Set the power control factor's initial value to any workable value.Solve the user pairing under fixed power issue, per 3.1.

Figure 1 .
Figure 1.Comparison of results: (a) Fairness and interference user distribution density (b) Fairness and the range of coverage for small areas (c) Fairness and maximum user transmit power Figure 1(b) depicts the relationship between system fairness and the coverage radius of a small area.It is evident that as the cell radius increases, user fairness declines.Comparing the algorithm for maximum-minimum fairness comparison, the advantage of this paper's algorithm is more obvious when the cell coverage radius increases.Compared with the α-fairness comparison algorithm, this algorithm can improve the fairness of the system by about 5%.Figure1(c) demonstrates the association between system fairness and ultimate user transfer power.The fairness of the system grows as well as user transmit power rises.First, when the base station transmitting power increases, the probability of achieving absolute fairness within the user pair increases.