## 4 Numerical Results and Discussions
### Spectral Efficiency
#### 4.2.3 Sum Spectral Efficiency  
Figure 18 portraits sum SE of the users in S\({}_{1}\) against SNR for different antenna combinations and order of modulations. The inset term represents the following parameters: (i) the number of antennas at BS (A\({}_{\text{BS}}\)), NU (A\({}_{\text{NU}}\)), D\({}_{1}\) (A\({}_{\text{D}_{1}}\)), D\({}_{2}\) (A\({}_{\text{D}_{2}}\)), and FU (A\({}_{\text{FU}}\)), respectively, and (ii) the modulation order used by BS and D\({}_{1}\) to transmit FU symbol. We considered same number of antennas at all users for each instance to make consistent transmission. Please note that both BS and D\({}_{1}\) should use same modulation order for efficient transmission of information from BS to FU via D\({}_{1}\), according to our system model; otherwise, inconsistency in data transmission will arise between \(P_{1}\) and \(P_{2}\). We noted that in each instance sum SE curves approach to theoretical number of data bits which is anticipated because of the same reason as mentioned before. We recall that in S\({}_{1}\), FU data bits depend on the modulation order employed by BS and D\({}_{1}\). We observed that a higher order of modulation can be used to transmit FU information at a higher rate. This correspondingly effects the total SE of S\({}_{1}\). As QAM is more spectral efficient than PSK modulation, we noticed that sum SE with QAM is better than that with PSK for the same order of modulation with identical antenna combination.  
Figure 19 depicts sum SE of the users in S\({}_{2}\) against SNR for different antenna combinations and order of modulations. The inset term represents the following parameters: (i) BS uses M-PSK/QAM modulation to transmit NU information, (ii) the number of antennas at BS (A\({}_{\text{BS}}\)), NU (A\({}_{\text{NU}}\)), D\({}_{1}\) (A\({}_{\text{D}_{1}}\)), D\({}_{2}\) (A\({}_{\text{D}_{2}}\)), and FU (A\({}_{\text{FU}}\)), respectively, and (iii) the modulation order used by D\({}_{1}\) to transmit FU data  
Figure 16: SE of FU in S\({}_{2}\).  
Figure 17: SE comparison among the users in S\({}_{2}\).  
symbol. We considered same number of antennas at all users for each instance to make consistent transmission. We noted that in each instance sum SE curves approach to theoretical number of data bits which is obvious. Recall that in S\({}_{2}\), NU data bits depend on the modulation order used by BS, whereas FU data bits depend on the number of antennas at BS. We observed that a higher order of modulation can be used by BS to transmit NU information at a higher rate, whereas D\({}_{1}\) is limited to use a modulation order that corresponds to the number of antennas available at BS to forward FU information. Different modulation orders and antenna combinations effect the total SE correspondingly.  
Finally, we show a comparison of sum SE between our proposed scenarios S\({}_{1}\) and S\({}_{2}\) in Figure 20. We observed that sum of SE in S\({}_{1}\) and S\({}_{2}\) are quite identical to each other for the same combinations of antenna and modulation order. However, it needs to be mentioned that FU has the privilege of higher data rate through adoption of higher order of modulation in S\({}_{1}\), whereas in S\({}_{2}\), NU avail  
Figure 19: Sum SE in S\({}_{2}\) for different combinations of antenna number and modulation order.  
Figure 18: Sum SE in S\({}_{1}\) for different combinations of antenna number and modulation order.