Robust resource allocation in two-tier NOMA heterogeneous networks toward 5G

Abstract

This paper proposes a framework of users association and power allocation in the two-tier heterogeneous networks with nonorthogonal multiple access (NOMA). Taking account of practical wireless communication environment, the channel uncertainties are considered and described in the form of probability constraint. In order to maximize the total energy efficiency of the system and reduce the intra-cell and inter-cell interference, the joint optimization problem is formulated with the uncertain channel gain. The probability constraint is transformed to the deterministic one based on the integral transformation. With the aid of relaxation variable and successive convex approximation method, the original integer non-convex optimization problem is divided into two solvable convex subproblems. The user association algorithm and power control algorithm are presented to determine the optimal resource allocations. The simulation results show that the proposed algorithm is effective and robust to the dynamic communication environment.

Introduction

In recent years, the exponential growth of smartphones and mobile services has led to increasing demand of high-speed data access, and traditional cellular networks are no longer adequate. In order to improve spectrum and energy efficiency, improve the quality of service(QoS) of user, the fifth generation (5G) mobile communication technology is implemented [1], [2]. Meanwhile, radio access technologies are usually characterized by multiple access schemes. In the fourth generation (4G) mobile communication system, orthogonal frequency division multiple access (OFDMA) mode is mainly used based on the 3rd Generation Partnership Project (3GPP). However, the information theory illustrates that the NOMA technology is generally more effective than the orthogonal multiple access (OMA) technology, when the single cell network system is implemented. Therefore, NOMA is a promising multiple access technology for the fifth generation (5G) communication [3], [4].

In the 5G network, it is necessary to maximize use of spectrum resources, in order to satisfy user needs. More effective receivers can be developed, since the signal processing technologies are more advanced and the hardware facility cost is declining. NOMA with the use of successive interference cancelation (SIC) has become a good solution for 5G network multiple access technology. The approach attempts to differentiate users by sending different power; the approach can be implemented for multi-user communication in the same time domain and the same frequency domain. Therefore, NOMA is able to improve the efficiency of spectrum utilization [5]. In [6], Nguyen et al. considered an FD-NOMA multiuser MISO (MU-MISO) system. On the premise of ensuring the user-specific quality-of-service and total transmit power, the problem of joint optimization of user association (UA) and power control to maximize the overall spectral efficiency (SE) is proposed. In addition, a new transformation method is proposed to solve the problem of mixed-integer non-convex programming. In [7], Islam et al. provided a detailed classification survey of user pairing and power allocation algorithm in the downlink NOMA network, and discusses the key role of resource allocation scheme in realizing the maximum benefit of NOMA network.

The superiority of NOMA system was theoretically demonstrated by a simple case of single base station and dual users in [8]. Fu et al. [9] attempted to minimize the power of single-tier NOMA system. The QoS is guaranteed by ensuring a minimum rate of each user. The simulation results show that NOMA system can provide higher throughput than OFDMA system in the downlink transmission [10]. It has been proved that the single cell downlink NOMA communication system has lower outage probability and higher ergodic capacity than the traditional multiple access technology [11]. In [12], Yang et al. considered the sum rate maximization problem in a downlink single-input single-output NOMA system, and found the global optimal solution. In [13], Yang et al. studied the problem of maximizing the total throughput of multiple users in the visible light communication (VLC) systems with NOMA, and guaranteed the fairness of users. The effectiveness of incomplete SIC technology and perfect SIC technology in NOMA system was studied in [14], [15], [16]. However, only the single-cell or single-tier network model is studied. Development of models in two-tier heterogeneous networks is more complicated, since inter-cell and cross-tier interference is contaminated on the network. Hence, the interference management is essential for the whole network. The two-tier heterogeneous network is able to effectively offload data traffic and power consumption of the network [17], [18], [19]. The signal coverage can be expanded and the system capacity can be increased when a small base station is deployed within the macro base station [20]. Therefore, multi-layer heterogeneous network is the focus of 5G research. In addition, many literature- has made a detailed study on the user characteristics of 5G network. In [21], the authors considered the multiple services for each user in the uplink NOMA network, and the user’s demand for real-time and non real-time services is constructed into two parts of the utility function. A distributed algorithm based on game theory is proposed. In [22], in order to make more effective use of computing resources in 5G network and make resource allocation more flexible, the concept of resource elasticity is put forward.

In the design of NOMA heterogeneous networks, satisfying user association is essential. In NOMA networks, user association determines whether users should be connected to a specified base station to form an user group for superposition transmission [23]. The sequence of successive interference cancelation and the number of decoding users can be determined based on the number of users allocated in the base station. Therefore, the user correlation strategy is significant to spectrum efficiency and energy efficiency. To maximize logarithmic utility, a simple user association strategy is proposed in [24]. A strategy is proposed in [25] to optimize both user association and spectrum allocation. The strategy attempts to maximize the system throughput constrained with the fairness. However, the aforementioned approaches only address the problem of user association in traditional heterogeneous networks, but not in the NOMA networks. Problem of user association is tackled in a single cell NOMA network, and the power control method is used to optimize the whole system [26]. Liu et al. [27] proposed the user association strategies to reduce the system energy consumption. However, these methods are not applicable to solve the user association problem of the two-tier heterogeneous NOMA network.

In the two-tier NOMA heterogeneous networks, the energy consumption cannot be ignored since there are many small base stations engaged with the macro base station. The operational expenditure for the energy consumption is large. Therefore, the energy efficiency is necessary to be improved in the heterogeneous networks. Also, intra-cell interference, inter-cell interference and cross-tier interference coexist in the NOMA heterogeneous networks. If the interference is not effectively managed, it will decrease the service quality of the edge users and increase the outage probability of the whole system [28], [29]. Furthermore, due to the need to use SIC in downlink transmission of signal in NOMA network, through power control, different levels of power are allocated to users sharing the same frequency, which is very important for decoding and removing interference signals. Therefore, it is necessary to use the power control method to effectively manage the interference. Benjebbovu et al. [30] used fractional transmit power control (FTPC) to allocate the powers based on the different channel gains; also a joint optimization of users is addressed. Parida and Das [31] proposed an approach to allocate power to each user based on the Difference-of-Two-Concave-Functions. Mili et al. [32] proposed a power control algorithm to maximize the transmission rate of users and to minimize the transmission power. Senel and Akar [33] proposed a new distributed power adaptive algorithm where the transmission power adjustment of user is associate to the signal quality of adjacent users.

However, the aforementioned methods are based on perfect channel state information. In the real communication environment, the channel gain is disturbed by other factors. Hence, the assumption of perfect channel state information is not practical. To tackle the real environment, the statistical channel state information is taken into account of the NOMA network. Lu et al. [34] proposed a simple NOMA system which is engaged with a single base station and two users. The Nakagami-m fading channel is taken into account in the system, and the outage probability of NOMA network is formulated with the statistical channel state information. Tai et al. [35] proposed a resource optimization scheme for NOMA networks based on statistical channel state information. Although the proposed model is relatively simple, it provides a solution for the imperfect channel state information network in NOMA.

In [36], Qian et at. proposed a global optimization algorithm in wireless networks, which is suitable for small-scale topology only. The centralized algorithms are also developed in references [37] and [38], however they may not be applicable in 5G network, because it is difficult to exchange the global network information in such settings, including the random network deployment and the limited backhaul capacity available for control and signaling. The distributed algorithm has great advantage in the research of wireless heterogeneous network. In [39], the authors studied the problem of supporting real-time and non real-time distributed power distribution. In [40], the authors proposed a distributed solution for energy-saving resource allocation and inter cell interference management in wireless networks, which realizes the flexible dynamic partitioning of resources between macro cells and small cells. In [41], the author uses game theory to solve the resource allocation of wireless communication network, and proposes a simple distributed algorithm to solve the optimization problem.

In this paper, the approach of robust resource optimization is studied in the two-tier heterogeneous NOMA network. A distributed joint optimization algorithm for user association and power control is proposed to tackle the uncertainty of channel state information (CSI). The user association algorithm attempts to determine the optimal solution of user association in the NOMA network. In the power control scheme, the successive convex approximation (SCA) method is used to transform the non-convex problem into the convex one, and the power control problem is solved by the iteration method. The simulation results show that the resource optimization strategy is able to improve the energy efficiency of the system and reduce the intra-cell and inter-cell interference. The main contributions of this paper are summarized as follows:

• In two-tier NOMA heterogeneous network, a practical interference management problem through power control is formulated, including inter-cell interference between base stations, intra-cell interference between different users performing SIC in the same base station, and cross-tier interference between macro base station and small base station.

• The probability constraint method is used to describe the uncertainty of channel state information. While guaranteeing the minimum user rate requirement and the maximum transmission power limit of the base station, the energy efficiency of the whole system is maximized.

• The joint user association and power control algorithm is proposed to solve the robust resource optimization problem. Under the complex interference environment, the energy efficiency of system is improved and the robustness of users is guaranteed.

The rest of the paper is organized as follows. In Section II, we describe the system model and problem formulation. In Section III, we analyze user association problem with the fixed transmit power of base station. In Section IV, we give the resource allocation scheme which attempts to optimize the energy efficiency of system by power control. In Section V, we propose an algorithm to determine the solutions of user association and power allocation. In Section VI, simulation results and performance analysis are provided to demonstrate the effectiveness of the proposed algorithm. Finally, conclusions are drawn in Section VII.