# In-Band Full-Duplex Relaying for SWIPT-Enabled Cognitive Radio Networks
## 4 Numerical Results  
We consider that an FDR (denoted by R) equipped with \(N\) receive antennas and \(M\) transmit antennas is located 20 m away from PT, i.e., \(d_{\mathtt{PT}}=20\) m, where \(d_{\mathtt{x},\mathtt{y}}\) is the distance from x to y. An ST is located between PT and FDR such that \(d_{\mathtt{PT},\mathtt{ST}}=2\) m. PR and SR are located at two points, which are symmetric with respect to the line from PT to FDR, such that \(d_{\mathtt{R},\mathtt{PR}}=d_{\mathtt{R},\mathtt{SR}}=5\) m, \(d_{\mathtt{PT},\mathtt{PR}}=\sqrt{d_{\mathtt{PT},\mathtt{R}}^{2}+d_{\mathtt{R},\mathtt{PR}}^{2}}\) m, and \(d_{\mathtt{ST},\mathtt{SR}}=\sqrt{d_{\mathtt{ST},\mathtt{R}}^{2}+d_{\mathtt{SR }}^{2}}\) m. The channel responses are determined by \(\mathbf{\hat{h}}=d_{z}^{-\gamma}\mathbf{\hat{h}}\), where \(\mathbf{\hat{h}}\in\{\mathbf{h}_{p},\mathbf{h}_{s},\mathbf{g}_{p},\mathbf{g}_ {s},f_{ps},f_{pp}\}\) corresponds to the link \(z\in\{(\mathtt{PT},\mathtt{R}),(\mathtt{ST},\mathtt{R}),(\mathtt{R},\mathtt{PR} ),(\mathtt{R},\mathtt{SR}),(\mathtt{PT},\mathtt{ST}),(\mathtt{PT},\mathtt{PR} )\}\), respectively; the path-loss exponent is assumed to be \(\varphi=3\), while the elements of \(\mathbf{\hat{h}}\) follow \(\mathcal{CN}(0,1)\). Unless otherwise specified, the transmit power at PT, background noise power, and energy conversion parameter are respectively set as \(P_{\mathbf{p}}=26\) dBm, \(\sigma^{2}=-104\) dBm, and \(\eta=0.5\)[26; 27; 28], while the suppression level of the residual SI is set as \(\rho=-90\) dB following the worst-case design in [29]. Figure 3 depicts the sum rate of SR and PR versus the maximum power budget at PT. The range of the examined power budget is from 18 to 43 dBm, which is usually used for the maximum power at BS in small-cell to macro-cell scenarios [30]. To evaluate the proposed algorithm (Algorithm 1), we consider three other schemes: (i) SR and PR directly receive the signals from ST and PT, respectively, in which the harvesting time \(\alpha\) for ST is optimized (Opt.\(\alpha\) w/oFDR); (ii) data transmission using the same beamforming and detection as the proposed method is performed with \(\alpha\) fixed to 0.5 (fixed \(\alpha\) w/FDR); (iii) we plot the performance of a baseline scheme using a half-duplex relay (HDR) (named as \"Alg. 1 w/HDR\"), in which the proposed algorithm is utilized to find the optimal value of \(\alpha\), and the later phase with time fraction \((1-\alpha)\) is split into two sub-phases: one sub-phase for transferring signals from ST and PT to HDR and the other sub-phase for forwarding the messages from HDR to SR and PR. We can observe that the proposed method provides the best performance, due to the fact that the power is efficiently utilized by a cooperation between the harvesting time and beamforming at the FDR. In particular, for all the considered values of \(P_{\mathbf{p}}\), the proposed scheme gives about 2 bps/Hz higher than the one using \"fixed \(\alpha\) w/FDR\", due to only the linear difference in time fraction optimization. Meanwhile, the gain of the proposed scheme over \"Opt. \(\alpha\) w/o FDR\" decreases as \(P_{\mathbf{p}}\) increases. Clearly, \"Opt. \(\alpha\) w/o FDR\" suffers from high attenuation, due to the long-distance propagation from PT (ST) to PR (SR), which is merely compensated by the increase in power budget at the PT. It can be observed that with a low transmit power at PT, \"Alg. 1 w/HDR\" slightly outperforms \"Opt. \(\alpha\) w/o FDR\", which confirms the benefit of the use of relaying. However, the performance gap is seen to diminish as \(P_{\mathbf{p}}\) increases. Figure 4 further investigates the system performance with various numbers of receive/transmit antennas at FDR. Obviously, the performance of the scheme without FDR is independent of the number of antennas, while the rate gain obtained by the proposed method is verified. Indeed, the performance of FDR-assisted schemes is improved more quickly when both \(N\) and \(M\) increase than when only one of them increases.