## 1 Introduction  
Rate-splitting multiple access (RSMA) has become a promising multiple-access framework that is being considered for implementation in future 6G networks and beyond [1]. Recent studies have shown that RSMA outperforms traditional multiple-access techniques, such as non-orthogonal multiple access (NOMA) and space-division multiple access (SDMA), in terms of energy and spectral efficiency for multi-antenna systems [1, 2, 3, 4]. The concept behind RSMA involves dividing user messages into multiple parts, which are transmitted using superposition coding at the transmitter and decoded using successive interference cancellation (SIC) at the receivers. The most common approach is based on single-layer rate splitting (RS), involving two parts: a common part and a private part. The common parts from all users are transmitted simultaneously using a shared codebook and must be decoded by all users, whereas the private parts are transmitted using private codebooks. This approach allows RSMA to transmit all the messages simultaneously and in the same frequency band using the power and spatial domains. Consequently, RSMA offers flexibility, where interference can be treated as noise or fully decoded, making it a versatile framework encompassing SDMA and power-division NOMA as special cases [3, 5]. Modern wireless systems consider communication trends, such as the Internet of Things (IoT) and machine-type communications (MTC). The key priorities in wireless communications involve advancing green technology and reducing device power consumption [6]. Various studies have been undertaken to establish self-sustainable communication systems using energy-harvesting (EH) techniques. One of the EH technologies contributing to these objectives is simultaneous wireless information and power transfer (SWIPT) [7]. SWIPT is an effective technology that enables the base station (BS) to transmit energy and information simultaneously to wireless users. Within SWIPT, the most well-known architectures are the power-splitting (PS) architecture and time-switching (TS) architecture, where both schemes consider an EH module and an information decoding (ID) module at the receiver. In the TS architecture, the receiver periodically alternates between the ID and EH modules based on a TS sequence. In the PS architecture, the incoming radio frequency (RF) signal is divided into two streams based on a PS ratio, which are sent to the ID and EH modules. The authors of [7] focused on the PS architecture because it has been established in the literature as achieving the best balance between energy harvesting and information decoding. A cost-effective solution was proposed in [8] using low-cost stations called power beacons (PBs) for wirelessly recharging devices using RF energy. PBs primarily serve as a source of wireless energy, extending the operational lifespan of battery-powered devices through wireless recharging. PBs do not necessitate complex computations and have low backhaul link requirements, enabling cost-effective and adaptable placement, making them a valuable addition to the system. SWIPT has been widely studied, ranging from single-antenna systems [9] to multiple-antenna systems [10; 11]. [PERSON] et al. [10] optimized the precoding vectors and PS ratios in a multiuser multiple-input single-output (MU MISO) system to minimize the transmission power while considering both the minimum signal-to-interference-plus-noise ratio (SINR) and minimum EH at the user side. An extension to a multiuser multi-input multi-output (MIMO) system was explored in [11], considering the EH constraints and a maximum tolerable mean square error (MSE) for received information. SWIPT has also been implemented along with the NOMA method in multi-antenna systems to maximize data rates [12], minimize transmit power [13], and enhance energy efficiency [14]. On the other hand, there is limited research on the performance of networks implementing SWIPT in conjunction with the RSMA method. In the context of RSMA, a pioneering study introduced the concept of RS [2].