## Appendix A Transmitters
\begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Meaning** \\ \hline \(U\) & Total number of users \\ \(u\) & User index \\ \(\mathcal{N}\) & Total available number of subcarriers \\ \(\Phi(u)\) & The subcarrier set allocated to user \(u\) \\ \(\langle\Phi(u)\rangle\) & The cardinality of \(\Phi(u)\) \\ \(\phi\) & The empty set \\ \(\Omega(u)\) & The modulation type of user \(u\) \\ \(\alpha(u)\) & The STBC format of user \(u\) \\ \(\mathbf{d}_{z}^{(u)}\) & The \(z\)th data sequence of user \(u\) \\ \(\mathbf{F}_{z}^{(u)}\) & The \(z\)th frequency-domain SC-FDMA sequence of user \(u\) \\ \(\mathbf{s}_{z}^{(u)}\) & The \(z\)th time-domain SC-FDMA sequence of user \(u\) \\ \(\mathbf{\bar{s}}^{(u)}\) & The input to the encoder of the selected STBC format \\ \(P^{(u)}\) & The number of transmit antennas of user \(u\) \\ \(Z_{2}^{(u)}\) & The number of STBC time intervals of user \(u\) \\ \(Z_{1}^{(u)}\) & The number of symbols fed into the STBC encoder of user \(u\) \\ \(\mathbf{h}^{(u,p)}\) & The CIR between \(p\) transmit antenna of user \(u\) and the base-station \\ \(\mathbf{r}\) & The received signal at the base-station \\ \(\odot\) & The linear convolution between two vectors \\ \(\mathbf{w}\) & The noise vector at the base-station \\ \(\mathbf{C}_{\alpha(u),\Omega(u)}^{(u,p)}(v_{1},v_{2})\) & The component situated at row \(v_{1}\) and column \(v_{2}\) of matrix \(\mathbf{C}_{\alpha(u),\Omega(u)}^{(u,p)}\) \\ \(\mathbf{\bar{s}}_{\alpha(u),\Omega(u)}^{(u,p)}(v_{1}-v_{2})\) & The \((v_{1}-v_{2})\)th component of vector \(\mathbf{\bar{s}}_{\alpha(u),\Omega(u)}^{(u,p)}(v_{1}-v_{2})\) \\ \(\mathrm{Pr}(\mathbf{\sigma}|\triangledown)\) & The probability density function of \(\mathbf{\sigma}\) given \(\triangledown\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notation. in \(Z_{2}^{(n)}\) time intervals. For illustration, the STBC of parameters \(Z_{1}^{(u)}=2\), \(Z_{2}^{(n)}=2\), and \(P^{(n)}=2\), named Alamouti code [49], sends two symbols \(\mathbf{s}_{z}^{(u)}\) and \(\mathbf{s}_{z+1}^{(u)}\) via two antennas in two successive time intervals. The first antenna delivers \(\mathbf{s}_{z}^{(u)}\) and \(-\mathbf{s}_{z+1}^{(u)*}\) in two time intervals, whereas the second one sends \(\mathbf{s}_{z+1}^{(u)}\) and \(\mathbf{s}_{z}^{(u)*}\) during the same periods. Each user \(u\) picks a STBC type, represented by \(\alpha^{(u)}\), from a set of possibilities. The time-domain vectors broadcast throughout the various time intervals, \(\mathbf{\tilde{\kappa}}_{\alpha(u),\Omega(u)}^{(u,p)}=[\mathbf{c}_{0}^{(u,p)}, \ldots,\)\(\mathbf{c}_{N^{(u)}-1}^{(u,p)}]\), are combined to produce the signal that is sent from antenna \(p\). Here \(N^{(u)}=Z^{(n)}Z_{1}^{(n)}/Z_{2}^{(n)}\) and \(\mathbf{\tilde{\epsilon}}_{\alpha^{(u)}}^{(u,p)}\) is linked to \(\mathbf{s}^{(u)}\) via the special architecture of \(\alpha^{(u)}\). We add \(\alpha(u)\) and \(\Omega(u)\) as subscripts to underline that the construction of vector \(\mathbf{\tilde{\epsilon}}_{\alpha(u),\Omega(u)}^{(u,p)}\) relies on STBC \(\alpha(u)\) and modulation pattern \(\Omega(u)\). Lastly, each user's broadcast antenna interacts with the BS over a frequency-selective channel, \(\mathbf{h}^{(u,p)}=\left[h^{(u,p)}(0),\cdots,h^{(u,p)}(L-1)\right]\), where \(L\) is the channel length. Figure 1: The block-diagram of the SC-FDMA system under consideration.