# Achievable Rate Maximization for Multi-Relay AF Cooperative SWIPT Systems with a Nonlinear EH Model
###### Abstract  
In this paper, the maximization of the achievable information rate is proposed for the multi-relay amplify-and-forward cooperative simultaneous wireless information and power transfer communication systems, where the nonlinear characteristic of the energy harvesting (EH) circuits is taken into account for the receivers of the relay nodes. The time switching (TS) and power splitting (PS) schemes are considered for the EH receivers and the achievable rate maximization problems are formulated as convex and non-convex optimization problems, respectively. The optimal TS and PS ratios for the relay nodes along with the maximum achievable rates for the system are obtained, respectively, by solving the optimal problems with efficient algorithms. The asymptotic maximum achievable rates at low and high input signal-to-noise ratios (SNRs) for both the PS and TS schemes are also analyzed. It is demonstrated that the PS scheme is more susceptible to the variation of the relays' location and the channel parameters than TS scheme, whereas the TS scheme is more susceptible to the mismatch of the resource allocation than PS scheme. Specifically, compared to the linear EH model, the nonlinear EH model achieves significant performance gain for the TS scheme, whereas inconspicuous performance improvement is achieved for the PS scheme. m 222222304113 April 20222222304113 April 202  
for the performance analysis in [11; 12], where the bit-error-rate (BER) performance was studied for the systems with differential modulation in [11] and the outage probability and BER performance was studied for the systems with both coherent and non-coherent modulations in [12]. In [13; 14; 15], the decode-and-forward (DF) protocol was applied to the relaying systems, where the long-term throughput was investigated in [13] for buff-aided hybrid relay, while the outage probability was analyzed in [14; 15], respectively, for a single source-destination pair with spatially random relays and the non-orthogonal multiple access (NOMA). In [16], the AF relay systems with an adaptive receiving architecture for information processing and energy harvesting (EH) were considered, where the ergodic capacity and the outage performance were derived. Besides a performance study for the SWIPT cooperative system with different relay protocols, various resource allocation schemes were proposed to enhance the system performance. In particular, to maximize the system throughput, the authors in [17] considered AF relay networks and proposed the joint relay selection and power allocation schemes, and in [18], the authors proposed the beamforming design for full-duplex multiple-input single-output relay systems. In [19], a joint optimization scheme of relay placement, power splitting (PS), and power allocation was proposed to improve the outage performance for the DF relay systems. The joint EH scheduling and beamforming was proposed in [20] for the SWIPT systems with multiple relays working in a time switching (TS) mode. In [21], the power splitting ratios at multiple relays were optimized for maximizing the information rate for the relaying systems with DF and AF protocols. In [22; 23], the outage and throughput performance, and the joint user paring and resource allocation were, respectively, presented for the SWIPT-enabled cooperative NOMA systems. The aforementioned papers considered the simple and ideal linear EH model, where linear input-output characteristic was assumed for the energy harvester at the receiver. However, practical measurement and observation has shown the nonlinearity of the input-output characteristic of practical energy harvester [3; 24]. Recently, the nonlinear EH model has attracted increasing interest in the SWIPT system design and performance analysis. In [25], a parametric and circuit-specific nonlinear EH model was presented based on the curve fitting method.