# Two-Way Multi-Antenna Relaying with Simultaneous Wireless Information and Power Transfer
## 5 Simulation Results  
In this section, we evaluate the performance of the proposed multiple-antenna relaying schemes (i.e., PS-DF, PS-DF-STC, PS-AF, TS-DF, TS-DF-STC, and TS-AF) in terms of average BER of the end nodes T\({}_{1}\) and T\({}_{2}\). Suppose that T\({}_{1}\) and T\({}_{2}\) are separated by a distance of 2 m, and the relay R is located halfway between them. Unless stated otherwise, we set the total signal power, \(P=1\) W; the power ratios of T\({}_{1}\) and T\({}_{2}\), \(\zeta_{1},\zeta_{2}=0.5\); the path loss exponent, \(\
u=2.7\); the power energy conversion efficiency, \(\eta=1\); the power splitting ratio in the PSR protocol, \(\rho=0.5\); and the time fraction used for energy harvesting in the TSR protocol, \(\alpha=0.5\). The simulated BERs of the PS-DF, PS-DF-STC, and PS-AF schemes are plotted versus antenna noise variance \(\sigma_{\mathrm{a}}^{2}\) for different numbers of relay antennas \(M\) (with fixed conversion noise variance \(\sigma_{\mathrm{c}}^{2}=0.01\)) in Figure 4 and versus conversion noise variance \(\sigma_{\mathrm{c}}^{2}\) for different values of \(M\) (with fixed antenna noise variance \(\sigma_{\mathrm{a}}^{2}=0.01\)) in Figure 5. The theoretical BER curves of the PS-DF scheme (computed with Equations (9), (16), and (17)) and the PS-DF-STC scheme (computed with Equations (9), (17), and (24)) are also included and labeled with \"(theor.)\". We can see that the theoretical results perfectly match their simulation counterparts, which verifies the BER formulae derived in Sections 3.1 and 3.2. Similarly, the results for the TS-DF, TS-DF-STC, and TS-AF cases are shown in Figures 6 and 7. As seen, the theoretical BER results (computed with Equations (17), (34), and (38) for the TS-DF case, and with Equations (17), (34), and (41) for the TS-DF-STC case) agree well with the simulated ones, which validates the BER analysis in Sections 4.1 and 4.2. It is clear that increasing the number of relay antennas generally improves the BER performance (the results at \(M=3\) are excluded to make the BER curves readable in all these figures). From Figures 4 and 5, we can see that the BERs of the PS-DF, PS-DF-STC, and PS-AF schemes are comparable when \(M=2\), and their difference becomes significant when \(M=4\). In the latter case, the PS-DF-STC scheme performs best while the PS-AF scheme does worst. Similar performance trends can be observed in the TS-DF, TS-DF-STC, and TS-AF schemes, as illustrated in Figures 6 and 7. Comparing Figures 4 and 6 (or Figures 5 and 7), one can find that, with the same number of relay antennas, the TS-DF and TS-AF schemes are generally superior to the PS-DF and PS-AF schemes, respectively. It would be interesting to study the effect of the power allocation parameters, i.e., power splitting ratio \(\rho\) and energy harvesting time \(\alpha\), on the BER performance. To this end, we show in Figure 8 the BER as a function of \(\rho\) for the PS-DF, PS-DF-STC, and PS-AF schemes, and in Figure 9 the BER as a function of \(\alpha\) for the TS-DF, TS-DF-STC, and TS-AF schemes. From these two figures, we observe that, in general, equal power allocation, i.e., \(\rho,\alpha=0.5\), is a good strategy for the PS-AF and TS-AF schemes. However, the optimal \(\rho\) and \(\alpha\) which minimize the BERs of the PS-DF and TS-DF schemes, respectively, depend mainly on the number of relay antennas \(M\). Specifically, these optimal \(\rho\) and \(\alpha\) increase (toward 1) as \(M\) increases. For example, the optimal \(\rho\) for the two-antenna PS-DF scheme is approximately 0.26 while that for the four-antenna PS-DF scheme is around 0.65 (See Figure 8). In addition, the optimal \(\rho\) for the two-antenna PS-DF-STC scheme (or the optimal \(\alpha\) for the two-antenna TS-DF-STC scheme) is nearly the same as that for the four-antenna PS-DF-STC scheme (or that for the four-antenna TS-DF-STC scheme). This result indicates that these optimal \(\rho\) and \(\alpha\) are not sensitive to the value of \(M\), unlike those for the PS-DF and TS-DF schemes, respectively.