# Resource Allocation for Relay-Based OFDMA Power Line Communication System
## 1 Introduction
However, the PLC networks have not been designed for communication purposes; the existing resource allocation strategies for wireless networks are not suitable [18; 19; 20; 21; 22; 23]. The PLC systems usually use the phase line to neutral line to transmit informations. The imbalance of the two wire to ground results in common mode current which greatly enhances the electromagnetic radiation. Meanwhile, the impedance mismatch between the power line and the load causes the signal reflection and form standing wave, which also generates strong electromagnetic radiation. Therefore, the power line is not a good medium for communication. The power line channel also has defects, such as frequency selective multipath fading with time-varying characteristics and color background noise, etc., which are the main difference between PLC systems and wireless communication systems. In order to  
Figure 1: Diagram of the relay-aided power line communication (PLC) system. deal with the poor channel conditions, the PLC system must apply an efficient resource allocation technique. In [24], a sub-carrier and power allocation algorithm is proposed for power spectrum limitation of indoor power line communication OFDM systems and the performance of the algorithm under various variable channel conditions is simulated. For the Homeplug AV standard in power line communication, two bit allocation algorithms with the largest system capacity under the condition of guaranteed bit error rate (BER) and target average BER are proposed [25; 26]. In [5], the power allocation problem of a hybrid system composed of a cascaded power-line communications (PLC)/visible light communications (VLC) link in parallel to an radio frequency (RF) wireless link is investigated. This formulated and analyzed the problem of minimizing the total transmission power consumption under a defined quality of service constraint. [27] proposed a dynamic load-based PLC system model for energy efficiency maximization. By optimizing the paremeters including the load impedance, transmission power and subchannel allocation, they investigated power allocation of the multi-receiver PLC OFDM downlink network with non-white Gaussian noise channel. The simulation results showed that compared with the baseline scheme, the proposed system is more energy-efficient, and can greatly improve the energy efficiency by optimizing the impedance and adopting the subchannel allocation strategy. The resource allocation problem in a relay-aided OFDMA PLC system usually involves a mixed integer nonlinear programming (MINLP) problem [28; 29], which leads to an algorithmic complexity of an order of magnitude. The subcarriers and power are jointly optimized, which makes it difficult to obtain an optimal resource allocation strategy. Based on the single-user system model, this paper discusses the optimal resource allocation scheme in multi-user environment, and proves that the system can maximize the system throughput by using the optimal resource allocation strategy proposed in the paper. The specific contents of this paper are as follows: Firstly, for the case of power constraints of the transmission source or relay, the problem description of maximizing the throughput of the system under the constraints of average power is given; secondly, for the case of multi-user OFDMA, The method of separating subcarrier and power allocation is used to give the optimal resource allocation strategy under the average power constraint and the interference power constraint. The remainder of this paper is organized as follows. Section 2 presents a mathematical description of the relay-based multi-user OFDMA downlink system model. Section 3 discusses the optimal subcarrier allocation and power control schemes in a PLC environment; Section 4 gives the numerical simulations and analysis; Conclusions are given in Section 5. _Notations:_\(\mathbb{E}\left\{\cdot\right\}\) denotes the expectation w.r.t. all fading channels.