Abstract-This paper investigates the application of simultaneous wireless information and power transfer (SWIPT) to cooperative non-orthogonal multiple access (NOMA). A new cooperative multiple-input single-output (MISO) SWIPT NOMA protocol is proposed, where a user with a strong channel condition acts as an energy-harvesting (EH) relay to help a user with a poor channel condition. The power splitting (PS) scheme is adopted at the EH relay. By jointly optimizing the PS ratio and the beamforming vectors, the design objective is to maximize the data rate of the "strong user" while satisfying the QoS requirement of the "weak user". It boils down to a challenging nonconvex problem. To resolve this issue, the semidefinite relaxation (SDR) technique is applied to relax the quadratic terms related with the beamformers, and then it is solved to its global optimality by two-dimensional exhaustive search. We prove the rank-one optimality, i.e., the SDR tightness, which establishes the equivalence between the relaxed problem and the original one. To further reduce the high complexity due to the exhaustive search, an iterative algorithm based on successive convex approximation (SCA) is proposed, which can at least attain its stationary point efficiently. In view of the potential application scenarios, e.g., Internet of Things (IoT), the single-input single-output (SISO) case of the cooperative SWIPT NOMA system is also studied. The formulated problem is proved to be strictly unimodal with respect to the PS ratio. Hence, a golden section search (GSS) based algorithm with closed-form solution at each step is proposed to find the unique global optimal solution. It is worth pointing out that the SCA method can also converge to the optimal solution in SISO cases. In the numerical simulation, the proposed algorithm is numerically shown to converge within a few iterations, and the SWIPT-aided NOMA protocol outperforms the existing transmission protocols. Index Terms-Non-orthogonal multiple access (NOMA), simultaneous wireless information and power transfer (SWIPT), semidefinite relaxation, successive convex approximation, semiclosed-form solution. Recently, great interests have been drawn in non-orthogonal multiple access (NOMA), which is envisioned as an enabling technique to improve the spectral efficiency (SE) of the upcoming fifth generation (5G) network [2] , especially in order to satisfy the requirement of the Internet of Things (IoT) to support massive connectivity [3] . The key idea of NOMA is to realize multiple access in the power domain, which allows multiple users to be concurrently severed at the same resource elements, e.g., time slots, frequency bands and spreading codes. By applying power-domain multiplexing at the transmitter and successive interference cancellation (SIC) at the receivers, the NOMA scheme can achieve a better system performance compared with the conventional orthogonal multiple access (OMA) scheme [4]- [6] . Due to the advances in multiple-input multiple-output (MIMO) techniques, the combination of NOMA and MIMO has been investigated to improve the system SE further [7]-[9]. A multiple-input single-output (MISO) NOMA scheme was considered in [10] , in which the downlink sum rate is maximized by applying the minorization-maximization (MM) method. A relay-aided cooperative NOMA scheme [11] was proposed to improve the communication reliability of the cell-edge users, wherein, the cell-center users act as relays to help the cell-edge users. In addition to the requirement of high SE, the energy efficiency (EE) is also a key performance indicator in 5G. As a promising solution to improve EE, scavenging energy from the environment to power the communication system has been studied intensively in the past several years [12] , [13] . Since radio-frequency (RF) signals can carry both information and energy, simultaneous wireless information and power transfer (SWIPT) was introduced initially in [14] and attracted increasing attention in the communication research community [15] , [16] . Specifically, to handle the limitation of the stateof-the-art circuit design, two practical receiver architectures, namely, the time switching (TS) receiver and power splitting (PS) receiver, were investigated in [15] . The transmitter design for SWIPT in a MISO interference channel is considered in [16] , and therein the sum rate maximization problem was studied under four practical receiver architectures. In order to exploit the diversity gain of the cooperative transmission, many
Xu et al. REF proposed a joint design of the transmit beamforming and receive power splitting in a similar NOMA aided cooperative network, which aims for maximising the achievable throughput of the so-called 'strong users', while ensuring the minimum throughput requirements of other 'weak users'.
Joint Beamforming and Power Splitting Control in Downlink Cooperative SWIPT NOMA Systems
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Mathematics Computer Science