Throughput Analysis of Buffer-Aided Decode-and-Forward Wireless Relaying with RF Energy Harvesting

In this paper, we investigated a buffer-aided decode-and-forward (DF) wireless relaying system over fading channels, where the source and relay harvest radio-frequency (RF) energy from a power station for data transmissions. We derived exact expressions for end-to-end throughput considering half-duplex (HD) and full-duplex (FD) relaying schemes. The numerical results illustrate the throughput and energy efficiencies of the relaying schemes under different self-interference (SI) cancellation levels and relay deployment locations. It was demonstrated that throughput-optimal relaying is not necessarily energy efficiency-optimal. The results provide guidance on optimal relaying network deployment and operation under different performance criteria.


Introduction
Internet of things (IoT) is a major technology of the incoming industrial revolution 4.0 [1]. An IoT network consist of a large number of connected devices, each of which requires a reliable energy supply for efficient operation [2]. This requirement can be satisfied by embedding batteries into the IoT devices, possibly incurring high-cost and safety-related issues to replace [3]. Harvesting energy from the ambient environment, such as solar, wind, thermal and radio frequency (RF) signals to empower electronic devices is becoming the future of IoT [4]. In particular, energy harvesting (EH) from RF signals has attracted significant interest because it can offer simultaneous wireless information and power transfer (SWIPT) while other natural energy sources are usually reliant on the climate of deployment locations [5][6][7]. Such SWIPT-based systems are inherently useful in applications with hard-to-access devices such as inside bodies, building structures, vehicles, or remote areas [8]. In particular, EH-based communications systems are suitable for intelligent transportation systems (ITS) [9][10][11], where vehicles form a vehicle-to-vehicle (V2V) wireless communication network. This V2V communication can take place in transit with moving transmitters and receivers, as well as in slow-changing environments such as car parks, where the devices are more static. Moreover, full-duplex communication is a mature field in wireless communication. There have been numerous works in the literature on the combination of energy harvesting and full-duplex for more advanced and self-sustain communication [12,13].
In this paper, we studied a buffer-aided dual-hop wireless relaying communication model, where the source and relay harvest RF energy from a dedicated power station for data transmission to the destination. respectively equalize the throughput on the SR and RD channels. The process to determine optimal α 2 and α 3 is illustrated in Figure 3. Energy harvest at S & R Transmission from S to R   The energy harvested at S and R is given by: where 0 < η < 1 is the energy conversion efficiency of energy harvesting circuitry at S and R, P is the RF signal power broadcast by the power source. The channel power gains are computed using the standard path loss model: where F c 4π f c 2 , c is the speed of light, f c is the carrier frequency, m is the path loss exponent. Rayleigh fading channels are assumed because we consider a general deployment in reality where the channels between the power station and the devices are multi-paths. As a result, e p is a complex exponential random variable with unit mean.

Half-Duplex (HD) Relaying
We first consider HD relaying. The transmission powers P s,HD of S and P r,HD of R are given by: The signal-to-noise ratios (SNR) at the relay, γ r,HD , and at the destination, γ d,HD are given by: where σ 2 sr and σ 2 rd are variances of the AWGN noise at the relay and destination, respectively. With a buffer-aided relay system, the (end-to-end) throughput τ HD is given by [17]: where C r,HD and C d,HD are the ergodic capacities of the SR and the RD channels, respectively. E[.] denotes the statistical expectation over fading channels. We also assumed the timescales of energy harvesting and channel fading block duration is sufficiently long so that long codeword transmissions are possible to achieve the capacity. In the case of short packets (or finite blocklength code) [18], only smaller rates than the capacity log(1 + SNR) are achieved and hence, the throughput obtained in our work will serve as the upper bounds. If the system were using non-buffer relaying mode, the throughput would be given by: Mathematically, we can see that the throughput of a buffer-aid system is always higher than a non-buffer one [17]. In order to find the analytical expression for C r,HD , we firstly evaluate the cummulative distribution function (CDF) of γ r,HD , F γ r,HD (γ) and then evaluate the probability distribution function (PDF) of γ r,HD , f γ r,HD (γ). The CDF F γ r,HD (γ) is given by: where Pr(.) denotes probability operator, K 1 (.) is the first-order of the second kind modified Bessel and λ 1 and λ 3 are the mean values of the exponential random variables |h 1 | 2 and |h 3 | 2 , respectively.

Proof. Appendix A
The PDF f γ r,HD (γ) is then given by (using [19], 8.486.18): The capacity of the SR channel, C r,HD is: Similarly, the capacity of the RD channel, C d,HD can be implied as: where and λ 2 and λ 4 are the mean values of the exponential random variables |h 2 | 2 and |h 4 | 2 , respectively.

Full-Duplex (FD) Relaying
We now consider FD relaying. The transmission powers P s,FD and P r,FD in FD communication, are given by: Under FD relaying, data reception at the relay suffers SI generated by the its own transmission signal, in addition to the AWGN noise. The capacity of the RD channel, C d,FD is analogous to the case of HD relaying: where . On the other hand, the SNR of the SR link, γ r,FD , is given by: where β is the residual SI noise factor. The CDF of γ r,FD , F γ r,FD (γ) is given by: where

Proof. Appendix B
The PDF of γ r,FD , f γ r,FD (γ) is then given by: The capacity of the RD channel is then given by: Finally, the throughput τ FD is given by: Table 1 below summarizes the analytical expressions of ergodic capacities and end-to-end throughput in HD and FD transmission modes. Table 1. Summarized analytical expressions of ergodic capacities and end-to-end throughput.

Simulation Parameters
In our experiments, Matlab was used as the simulation tool because it contains efficient built-in functions to simplify the coding and accelerate the simulation speed. The geometrical settings of the model simulates a wireless V2V communication system in constrained environments such as car parks where transmitters and receivers are more static or slowly moving. We assume that the dedicated power station has an effective range of 10 m, or d 3 = 10 m. The distance between the power station and the destination is 30 m. The angle θ = 135 • , using geometry we can compute the SD distance (i.e., d 1 + d 2 ) and maximum d 1 as 37.74 m and 16 m respectively. In the simulations, the distance d 1 is varied from 1 to the maximum d 1 with an increment of 1 m. We compute the d 2 and d 4 adaptively with each value of d 1 using geometry.
In the simulations, we compute the channel gains using the standard path loss model with carrier frequency f c = 2.4 GHz and path loss exponent m = 2.7. Moreover, we assume that the noise power per Hertz is -160 dBm, or -190 dB, giving the total noise power is 10 −19 × 100 kHz (transmitted bandwidth) = 10 −14 .
We assume that the energy harvesting circuitry at S and R ideally has maximum efficiency, η = 1. The transmitted power at the power station, P is set at 10 Watts and the SINR varies in a range [-∞ -10dB]. The mean values, λ 1 , λ 2 , λ 3 and λ 4 are all set to 1.
Our model considers imperfect SI cancellation in FD communication with the residual SI is proportional to the relay transmission power. The calculation of SINR is given by: The energy efficiency η EE is defined as the number of bits transmitted by one Joules: where E CC is the circuitry energy consumption and it is set at 1.5 WT.

Effects of Energy Harvesting Time
To investigate the effects of the energy harvesting time factor α 1 on the throughput performance of HD and FD communications, we fix the relay location at d 1 = 9 m. Figure 4 shows that the throughput increases when α 1 increases from 0 to an optimal value and starts decreasing beyond the optimal value of α 1 . This can be explained as smaller α 1 values give less time for energy harvesting, causing less energy for transmission and a lower end-to-end throughput as a result. On the other hand, when α 1 is beyond the optimal value, more time is spent for energy harvesting, but time for data transmission is constrained. Hence, it also leads to a lower throughput value. Figure 4 also demonstrates that the optimal harvesting time increases when SINR decreases in FD mode. This is because lower SINR values impose slower increase of SI when the relay is harvesting more energy.
For a given α 1 value, FD communication always has higher effective transmission time compared to HD. However, the transmission time advantage is not sufficient to compensate for the throughput loss caused by the SI trade-off. Therefore, in our simulations, HD mode only produces lower throughput than the no-SI FD communication as shown in Figure 4. Figure 5 reveals that energy efficiency increases when α 1 increases from 0 to an optimal value and starts decreasing beyond the optimal α 1 value. At smaller α 1 values, the harvested energy is insignificant compared to the E CC , causing lower energy efficiencies. Although larger α 1 (i.e., beyond the optimal value) generate more harvested energy, it constrains the data transmission capacity and reduces the energy efficiency as a result.

Effects of Relay Location
In general, the maximum throughput improves when the relay moves from the source toward an optimal location and starts decreasing beyond that point. It can be observed that HD communication and FD communication with perfect SI cancellation outperform the others, particularly when d 1 is further from S (i.e > 50% SR length).
Additionally, HD and no-SI FD communication have optimal relay locations within the range of 6-10 m (±10% from the middle point of SR). The distance from the relay to the power station is shortest when the relay is at the middle of SR. Around this point, more harvested energy favors HD and no-SI FD communication.
In contrast, higher SINR FD communication (i.e., ≥−20 dB) has optimal relay locations closer to the source. After the end-to-end throughput achieves the peak, it plunges rapidly before it marginally decreases to a stable value. When d 1 increases from 1 to an optimal value, the relay harvests more energy for transmission, improving the end-to-end throughput. In this stage, the end-to-end throughput increase is driven by the capacity increase on the RD channel.
When SINR level is high, SI is quickly amplified as d 1 moves from the optimal locations to the middle point of SR due to the larger energy harvested by the relay, hence rapidly reduces the throughput on the SR channel. Beyond the middle point of SR, larger source-relay distance reduces the channel gain due to higher path loss, resulting in lower channel capacity on the SR link. Beyond the optimal relay location, the declination of the end-to-end throughput is dictated by the capacity reduction on the SR link. Figure 6 suggests that in applications where energy efficiency is important (i.e., green communication), HD and no-SI FD communication offer highest achievable energy efficiencies in the range 6-10 m of d 1 . This is consistent with results achieved in Figure 7. It leads to a result that highest end-to-end throughput with highest energy efficiency can be achieved within ±10% range from the middle point of the SR distance, using HD communication or FD with perfect SI cancellation. Nevertheless, HD communication can be more suitable in particular applications that tolerate certain throughput and efficiency performance, because it requires less implementation complexity than FD communication.

Conclusions
In this paper, a buffer-aided DF relaying model for V2V communication was investigated, which consists of energy-constrained source and relay harvest RF energy from a dedicated power station for data processing and transmission. The numerical results compare the throughput performance and the energy efficiency between HD and FD communications under the effects of the energy harvesting time and the relay deployment locations. To compute the throughput, we derived ergodic capacity expressions which are summarized in Table 1. The work in this paper can be extended by applying resource allocation techniques [17] and investigating a constrained delay at the relay [20]. In the future, we will also investigate the combination of energy harvesting with more complicated non-orthogonal multiple access (NOMA) or multi-point NOMA cooperative relay with various relaying protocols, as an extension of this work [21].

Appendix A
This appendix presents the working details to derive the CDF F γ r,HD (γ) of γ r,HD in HD communication.

Appendix B
This appendix presents the working details to derive the CDF, F γ r,FD , of γ r,FD in FD communication. where ω = γ(b 4 z+c 4 ) a 4 x (using the product distribution rule). Because e 1 , e 3 and e 4 are exponential random variables, F γ r,FD is then given by: where t 4 = 4γ(b 4 z+c 4 ) a 4 λ 1 λ 3 , using (3.324.1, 518) [19].