## 2 Conventional Spatial Modulation-Layer Division Multiplexing (SM-LDM) System Model  
In a single-cell broadcasting network, consider a two-layer LDM downlink system. The _UL_ and _LL_ layers provide low and high data rate services to mobile and fixed receivers, respectively as portrayed in Figure 1. Each one of these receivers is equipped with \(N_{r}\) receive antennas (RAs) whereas the base station (BS) employs \(N_{t}\) transmit antennas (TAs). In conventional SM-LDM systems [12; 13; 14; 15; 16], at every transmission time, the data of each layer are split into antenna selection (AS) and symbol selection (SS) bits. The AS bits of the _UL_ (\(b_{AS}^{\textit{L}}=\log_{2}(N_{t})\)) specify the _i_th active antenna to convey the _m_th modulation symbol \(s_{m}\left(E\left[|s_{m}|^{2}\right]=1\right)\) that is chosen by the SS bits (\(b_{SS}^{\textit{UL}}=\log_{2}(M_{\textit{UL}})\)). Similarly, the _j_th active antenna is determined through the AS bits of the _LL_ (\(b_{AS}^{\textit{L}}=\log_{2}(N_{t})\)) to transmit the _n_th symbol \(s_{n}\) that is identified via the SS bits (\(b_{SS}^{\textit{L}}=\log_{2}(M_{\textit{L}})\)). Accordingly, the received signal at _UL_ and _LL_ receivers are given as follows:  
\[ \begin{split}&\mathbf{y}_{\textit{L}}=\sqrt{\rho_{\textit{L}}}\mathbf{h}_{i} ^{\textit{L}}s_{m}+\sqrt{\rho_{\textit{L}}}\mathbf{h}_{j}^{\textit{L}}s_{n}+\mathbf{w }_{\textit{L}}\\ &\mathbf{y}_{\textit{L}}=\sqrt{\beta_{\textit{L}}}\Big{(}\sqrt{\rho_ {\textit{L}}}\mathbf{h}_{i}^{\textit{L}}s_{m}+\sqrt{\rho_{\textit{L}}}\mathbf{h}_{j}^{ \textit{L}}s_{n}\Big{)}+\mathbf{w}_{\textit{L}}.\end{split}  \tag{1}\]  
where \(\mathbf{h}_{i}^{\textit{L}}\) and \(\mathbf{h}_{j}^{\textit{L}}\) denote the (\(N_{r}\times 1\)) column channel vectors from the (\(N_{r}\times N_{t}\)) channel matrices of the _UL_ and _LL_, respectively. Each component of the channel vectors can be viewed as an independently and identically distributed (i.i.d.) complex Gaussian random variable with a zero mean and unit variance. The additive white Gaussian noise (AWGN) at _UL_th and _LL_th receivers are, respectively, represented by \(\mathbf{w}_{\textit{U}}\) and \(\mathbf{w}_{\textit{L}}\); their components are i.i.d. complex Gaussian random variables with mean zero and variance \(\sigma_{0}^{2}=1/\gamma\), where \(\gamma\) is the total signal-to-noise ratio (SNR) per receive antenna at the _UL_th receiver. Additionally, \(\rho_{\textit{U}}\) and \(\rho_{\textit{L}}\) represent the ratio of the transmit power allocated for _UL_ and _LL_, respectively, such that \(\rho_{\textit{U}}+\rho_{\textit{L}}=1\) and the injection level is given by \(\textit{IL}=\rho_{\textit{U}}/\rho_{\textit{L}}\). Low SNR thresholds of 0 dB are typical values for the _UL_th receiver, where it is considered to face more challenging reception conditions than the _LL_th receiver. Hence, \(\beta_{\textit{L}}\) is defined here as the SNR threshold difference ratio between _UL_ and _LL_ receivers. Accordingly, the total SNR at the _UL_th receiver is equal to \(\rho_{\textit{U}}\gamma\) whereas the SNR at the _LL_th receiver is \(\rho_{\textit{L}}\beta_{\textit{L}}\gamma\). Assuming perfect channel state information (CSI) at the receivers, the _UL_ estimates its _i_th and _m_th indices to detect the transmitted AS and SS bits by applying the maximum likelihood (ML) detector as  
\[\hat{i},\hat{m}=\underbrace{arg\ min}_{1\leq i\leq N_{t},1\leq m\leq M_{ \textit{UL}}}\Big{\|}\mathbf{y}_{\textit{U}}-\sqrt{\rho_{\textit{U}}}\mathbf{h}_{i}^{ \textit{L}}s_{m}\Big{\|}^{2}. \tag{2}\]  
On the other hand, the _LL_th receiver applies SIC to remove the interference of the _UL_th signal.