## 6 Results and Discussion
As described in the caption of the figures, the transmission rates (TRs) of the layers are \(UL^{TR}=4\) bits/s/Hz and \(LL^{TR}=6\) bits/s/Hz. The SM-LDM applies \(N_{t}=4\), QPSK, and 16-QAM, respectively, for _UL_ and _LL_. For SAS-SM-LDM, recall that _UL_ bits (i.e., \(\log_{2}N_{t}\)) select the active antenna among \(N_{t}\); hence, it applies an SSK signal, and no modulation symbol is transmitted. On the other hand, the _LL_ conveys a modulation symbol chosen from \(M_{L}\) constellation. Three configurations are examined here where the spatial and modulation constellation sizes are varied. Referring to the captions, the spatial bits (i.e., \(\log_{2}N_{t}\)) are shared between _UL_ and _LL_. Among the arrangements, the results reveal that increasing \(N_{t}\) provides higher rates and sum-rate than increasing \(M_{L}\). For example, 16-QAM for _LL_ and \(N_{t}=64\) in Config. 2 offer higher rates, particularly for _LL_ at medium and high SNR regions than 64-QAM for _LL_ and \(N_{t}=16\) in Config. 1. Similarly, 8-PSK for _LL_ and \(N_{t}=128\) in Config. 3 deliver further improvement compared to Config. 1 and Config. 2. Furthermore, it is worth noting here that all SAS-SM-LDM models provide a high rate for _UL_ and sum-rate than SM-LDM at low and medium SNR values. Moreover, conveying more spatial bits than the modulation bits in the SAS-SM-LDM systems allows for maximization of the gain at low and medium SNR and simultaneously minimizes the performance gap relative to the SM-LDM at high SNR values. These spatial bits mapped from the _LL_ user led to a higher achievable rate at the _LL_ receiver for low and intermediate SNR values. The increased likelihood of correct detection for spatial bits in noise-limited regions is consistent with this finding, as reported in the SM literature. In addition, at high SNR values, the impact of _LL_'s interference on the _UL_ interference-limited user has been mitigated thanks to the reduction of _LL_'s modulation order and the implicit conveyance of spatial bits. Figure 8: BER comparisons between SM-LDM and different configurations of the proposed SAS-SM-LDM. \(UL^{TR}=4\) bits/s/Hz, \(LL^{TR}=6\) bits/s/Hz. SM-LDM: \(N_{t}=4\), QPSK for _UL_ and 16-QAM for _LL_. SAS-SM-LDM, Config. 1: \(N_{t}=16\), 64-QAM for _LL_ (\(b^{U}_{AS}=4\), \(b^{U}_{SS}=0\), \(b^{L}_{AS}=0\), \(b^{L}_{AS}=6\)). SAS-SM-LDM, Config. 2: \(N_{t}=64\), 16-QAM for _LL_ (\(b^{U}_{AS}=4\), \(b^{U}_{SS}=0\), \(b^{L}_{AS}=2\), \(b^{L}_{AS}=4\)). SAS-SM-LDM, Config. 3: \(N_{t}=128\), 8-PSK for _LL_ (\(b^{U}_{AS}=4\), \(b^{U}_{SS}=0\), \(b^{L}_{AS}=3\), \(b^{L}_{AS}=3\)). Bi-PA is applied for SM-LDM. The BER comparison between the SM-LDM and SM-LDM-SAS is shown in Figure 8. The same configuration as in Figure 7 is used here. As can be seen, the SM-LDM layers have nearly identical BERs because of the Bi-PA. The results then confirm that the proposed SAS technique allows for greater flexibility and utilization of the spatial domain, resulting in an overall BER improvement for both _UL_ and _LL_. Increasing the number of antennas in the various SAS configurations also reduces the BER. Furthermore, after \(SNR>12\) dB, the results show that the SM-LDM-SAS with Config. 3 provides the best BER performance for both layers. It is caused by implicitly modulating all of _UL_'s information bits in the spatial domain. Furthermore, the sharing property allows for a reduction in the QAM/PSK constellation size of _LL_, which reduces ILI and allows for better detection of the _LL_ bits.