## 1 Introduction  
The concept of simultaneous wireless information and power transfer (SWIPT) has emerged as a potential scheme to realize the Internet-of-Things, consisting of many small devices. In SWIPT, the radio frequency (RF) source is used to carry both information and power [1]. However, a realistic SWIPT system is often restricted by the limited received power [2]. Previous research has shown that the RF to direct current (DC) power conversion efficiency (PCE) can be improved by using high peak-to-average power ratio (PAPR) waveforms such as multisine signals, which highlights the potential of using multisine signals in SWIPT systems. [3; 4; 5; 6]. A considerable amount of studies have been published on the topic of transmission strategies for the MISO (Multiple Input Single Output) SWIPT system [7; 8; 9; 10]. The authors of [7] designed optimal and sub-optimal joint beam-forming and power ratio splitting strategies for a multi-user MISO system with a quasi-static flat-fading channel. The work of [8] considered a more practical MISO SWIPT system where the channel state information is not perfect at the base station. [PERSON] et al. [9] proposed a strategy to maximize energy efficiency of data transmission by jointly applying zero-forcing beam-forming and power splitting. Similarly, the researchers of [10] balanced the system fairness and throughput by optimization of the beam-former and power splitter. However, all the aforementioned studies considered a linear wireless power transfer model. As the rectifier, which is the key component to transfer RF power to DC, is not linear, a more complex model is needed. To design reliably a transmission strategy for a realistic SWIPT system, a non-linear energy harvesting model is necessary. While there exists several nonlinear energy harvesting models in literature [11; 12; 13; 14; 15], these models solely reveal the influence from the signal power or PAPR. Three such general energy harvesting models were compared in [16], showing that only the complete rectifier circuit model shows the complete influence of the received RF signal. To evaluate the PCE corresponding to different multi-tone signal excitations, we adopt the complete circuit model in [17] to calculate the harvested DC power, thereby using the exact Shockley equation and other RF circuit parameters. This model is valid for a wide range of rectifiers and for different input power levels. While the complete circuit model makes the analytical derivation of the optimal transmission strategy not possible, it gives results that match the measurements well [17]. Several attempts have discussed the optimal input symbol distribution for information transfer for a given wireless power transfer constraint [18; 19]. Moreover, several works have studied potential modulation schemes to improve the PCE in SWIPT systems [20; 21; 22]. These approaches adopt a simple nonlinear model for the rectifier and/or are based on amplitude modulation based techniques. In this work, we investigate the multisine phase-shift keying (PSK) modulation since this scheme would not distort the signal envelope and thus the PAPR, and this is combined with a realistic nonlinear rectifier model. To evaluate the information rate of the signals, we rely on the capacity bound of PSK modulation as a function of obtained symbol energy to noise ratio. As a benchmark, we also consider quadrature amplitude modulation (QAM) which allows both amplitude and phase modulation. It is shown by simulations that the proposed multisine PSK scheme significantly improves the normalized PCE (defined as the harvested DC power divided by the transmitted power), however it decreases the information rate due to the loss of a degree of freedom in the modulation, as will be discussed next.