## 6 Results and Discussion  
This part presents the numerical results for the proposed Bi-PA and SAS approaches. Three cases are employed for the Pre-PA: \(IL(\text{dB})=6\), 9.54, and 12.8 for Case 1, Case 2, and Case 3. In comparison, the proposed Bi-PA changes the power ratios adaptively. Classic SM-LDM without SAS is abbreviated as SM-LDM, whereas the proposed SAS-based SM-LDM is abbreviated as SAS-SM-LDM. Figure 3 shows the power ratios versus the SNR generated using Pre-PA and Bi-PA for \(LL\) and \(UL\) in SM-LDM systems where \(N_{t}=N_{r}=4\), and select QPSK for \(UL\) and 16-QAM for \(LL\). The UL information bits select an antenna to convey its QPSK symbol. Similarly, the \(LL\) bits transmitted are mapped to the active antenna and 16-QAM symbols. In Pre-PA, the power ratios assigned to each symbol are fixed to \(\rho_{U}=0.8\) and \(\rho_{L}=0.2\). Alternatively, as shown in the results of Figure 3, the ratios are adaptively changed with the SNR. Referred to Equation (5), \(\rho_{L}\) decreases along with the increase of SNR while \(\rho_{U}\) increased. Furthermore, the results show that the power ratio thresholds for both layers are satisfied where \(0<\rho_{L}\leq 1/2\) and \(\frac{1}{2}<\rho_{U}<1\). The BER of two layers of the SM-LDM system is depicted in Figure 4 when the Pre-PA and proposed Bi-PA methods are used. We set \(N_{t}=N_{r}=4\), and select QPSK for _UL_ and 16-QAM for _LL_. Given this configuration, the IL ratios for the Bi-PA are adaptively changing with the SINR and given as follows: [4.0850 4.5149 5.0474 5.6769 6.3909 7.1742 8.0116 8.8901 9.7993 10.7310 11.6795 ] dB. The results show that the Pre-PA cases suffer from BER floor problems at high SNR. Additionally, increasing the IL ratio decreases the _UL_ BER at low and medium SNR, but it increases the _LL_ BER. On the other hand, the results demonstrate that the proposed Bi-PA solves the error floor problem and provides better fairness between the layers. It is worth noting here that the Bi-PA adaptively allocates the power ratios based on equalizing the SINRs for both layers. Hence, the ratios are continuously specified such that the BER of _UL_ and _LL_ is nearly identical. This enhances fairness and simultaneously finds the appropriate ratios even though the SNR and interference are varying. In Figure 5, the SE results are shown for the case of two layers and the configuration is identical to Figure 4. For clarity, only two cases are shown for the Pre-PA. Note that the transmission rate of the layers is \(UL^{TR}=4\) bits/s/Hz, \(LL^{TR}=6\) bits/s/Hz. Firstly, by investigating the Pre-PA cases, it can be noticed that the _UL_ rate is relatively improved particularly at low and medium SNR values via increasing the IL ratio as in Case 2 compared to Case 1. However, this could affect the capability of the _LL_ receiver to correctly estimate its information which negatively affects the achievable _LL_ rate and consequently the Sum-rate. On the other hand, the adaptive and dynamic change of the power ratios in the Bi-PA enhances the achievable _LL_ rate and the Sum-rate, especially at the low and intermediate SNR regions. Figure 3: Power ratios allocated for _UL_ and _LL_ in SM-LDM system under the Pre-PA and proposed Bi-PA. _UL:_ QPSK, and _LL:_ 16-QAM, and \(N_{t}=N_{r}=4\). Figure 4: BER of SM-LDM system under different power allocation techniques (Pre-PA and proposed Bi-PA). Two layers, _UL:_ QPSK, and _LL:_ 16-QAM, and \(N_{t}=N_{r}=4\). Pre-PA, Case 1: \(IL\approx 6.02\) dB, \([\rho_{U}=0.8,\rho_{\rm L}=0.2]\). Pre-PA, Case 2: \(\rm IL\approx 9.54\) dB, \(\rho_{U}=0.9,\rho_{L}=0.1]\), Pre-PA, Case 3: \(IL\approx 12.8\) dB, \([\rho_{U}=0.95,\rho_{\rm L}=0.05]\). Dashed lines for _UL_ and solid lines for _LL_. The following Figures 6-8 evaluate the proposed SAS technique in terms of SE and BER. Note that the Bi-PA is applied in all cases. The layers rates and the sum-rate are shown, respectively, in Figures 6 and 7.