## 1 Introduction
Introducing radio frequency (RF) wireless energy harvesting (EH) technology into cognitive relay networks could potentially solve both the energy and spectrum problems, which has attracted significant attention in the academic communities [19]. In [20], [PERSON] et al. derive and compare the outage probabilities of the primary network and the EH cognitive network under direct transmission, single-user cooperation and multi-user cooperation scenarios. In [21], [PERSON] et al. investigate the error probability of an energy harvesting co-operative cognitive radio network with several relay selection criteria. [PERSON] et al. [22] study an energy harvesting-based secure transmission scheme for cognitive multi-relay networks and analyze the average secrecy rate, the secondary secrecy outage probability and the ergodic secrecy rate. More recently, some researchers have begun to study the SWIPT protocols and resource allocation for cognitive AF two-way relay networks [23; 24]. The optimization model of [23] aims to maximize the total transmission throughput of the system, and the authors propose an algorithm by optimizing the transmit power of sensor nodes. In [24], the approximate closed-form expression of minimizing the outage probability and throughput is taken as the optimization objective, and the closed-form solution of the optimal power control parameters and power partition ratio are obtained. [PERSON] et al. [25] evaluate the performance of the proposed SWIPT-enabled NOMA system by considering both the perfect and imperfect successive interference cancellation for the legitimate users over Nakagami-m fading in terms of outage probability, system throughput and energy efficiency. However, to the best of our knowledge, much of the previous references that emphasize performance optimization for an energy harvesting cognitive two-way relay network focus on the AF transmission protocol. On the other hand, the fairness issue and the inter ference effects of the main network on the secondary network are seldom studied. In our previous studies [26], we have investigated the power allocation under power control for a simultaneous wireless information and power transfer (SWIPT)-based cognitive two-way relay network with rate fairness consideration. However, the time allocation and power splitting issue have not been considered yet. In this paper, we consider the two-way DF cognitive relay network and investigate the jointly-optimum design based on the PS energy harvesting protocol, which aims to maximize the minimum cognitive user transmission rate with rate fairness and power control consideration. We achieve this by jointly optimizing the power allocation at source nodes, the time allocation of frames and the power splitting ratio at the relay. The main contributions are summarized as follows. 1. We develop a joint optimization scheme to maximize the minimum cognitive user transmission rate under rate fairness and power control consideration. The goal is to maximize the minimum cognitive user transmission performance through the joint optimization of time, power and power component ratio. 2. A stepped alternating optimization algorithm is proposed to solve the complex non-convex optimization problem. Through decoupling, the original problem is transformed into convex optimization problems and an alternating optimization problem. This avoids solving the complex non-convex optimization problem. 3. The results show that the proposed scheme improves the unfairness of inter-user transmission caused by channel asymmetry, and its superiority over the traditional scheme in terms of outage probability is depicted. The rest of this paper is organized as follows: Section 2 presents the system model and problem formulation. Section 3 proposes the joint power control and resource allocation scheme. Section 4 studies and compares the performance of the proposed scheme under a simulation system setup. Finally, Section 5 concludes the paper.