## Appendix A Transmitters
### Proposed Identification Algorithm
This process is an improved form of the repetitive expectation-maximization mechanism, which results in a significant increase in the rate at which the algorithm converges, while maintaining the merits of efficiency and reliability [50; 51]. Instead of predicting all parameters simultaneously, SAGE utilizes a set of cycles during each round. Updates to the parameter subset associated with a cycle are made by optimizing the log-likelihood of the received signal that belongs to this cycle. Thus, the multidimensional search challenge needed to optimize the likelihood function is simplified into a set of one-dimensional, computationally easy search tasks. The following provides the theoretical specifications of the SAGE process that has been developed for computing the parameters that are taken into account. We create \(U\) distinct subsets out of the unknown parameters, none of which overlap: \(\Big{\{}\alpha(0),\Omega(0),\overline{\mathbf{h}}^{(0)}\Big{\}}\), \(\cdots,\Big{\{}\alpha(U-1),\Omega(U-1),\overline{\mathbf{h}}^{(U-1)}\Big{\}}\). Parameter changes are applied to one user at a time. Each round consists of \(U\) cycles, during which a user's subset is adjusted. The following procedures constitute the \((\zeta+1)\)th round, provided the starting estimates. * The \(u\)th cycle includes updating the subset of user \(u\), but nothing is changed in the subgroups of the other users. * When the multiple access interference of each other user is deducted from the total signal received. The result is \[\mathbf{y}_{u}=\mathbf{r}-\sum_{u^{\prime}=0,\,u\
eq u^{\prime}}^{U-1}\mathbf{ Q}^{(u^{\prime})}_{\widetilde{\alpha}(u^{\prime},\zeta),\widehat{\Omega}(u^{ \prime},\zeta)}\widehat{\mathbf{h}}^{(u^{\prime})}(\zeta),\] (9) where \(\mathbf{y}_{u}\) is the user-\(u\)-collected signal portion, \(\mathbf{Q}^{(u^{\prime})}_{\widetilde{\alpha}(u^{\prime},\zeta),\widehat{ \Omega}(u^{\prime},\zeta)}\) represents the a posteriori expectation of matrix \(\widetilde{\mathbf{C}}^{(u^{\prime})}\) at the estimated values \(\widehat{\alpha}(u^{\prime},\zeta)\) and \(\widehat{\Omega}(u^{\prime},\zeta)\), which were computed in the previous round \(\zeta\), and \(\widehat{\mathbf{h}}^{(u^{\prime})}(\zeta)\) is the \(\zeta\)th estimate of \(\overline{\mathbf{h}}^{(u^{\prime})}\). Notably, since the BS does not know what the information symbols are, it is unable to access matrix \(\overline{\widetilde{\mathbf{C}}}^{(u^{\prime})}_{\widetilde{\alpha}(u^{\prime},\zeta),\widehat{\Omega}(u^{\prime},\zeta)}\). Therefore, \(\mathbf{Q}^{(u^{\prime})}_{\widetilde{\alpha}(u^{\prime},\zeta),\widehat{ \Omega}(u^{\prime},\zeta)}\) is utilized in (9) rather than \(\overline{\mathbf{C}}^{(u^{\prime})}_{\widetilde{\alpha}(u^{\prime},\zeta), \widehat{\Omega}(u^{\prime},\zeta)}\). We can write \(\mathbf{Q}^{(u^{\prime})}_{\widetilde{\alpha}(u^{\prime},\zeta),\widehat{ \Omega}(u^{\prime},\zeta)}\) as \[\mathbf{Q}^{(u^{\prime})}_{\widetilde{\alpha}(u^{\prime},\zeta),\widehat{ \Omega}(u^{\prime},\zeta)}=\mathrm{E}\Big{[}\overline{\widetilde{\mathbf{C}} }^{(u^{\prime})}_{\widetilde{\alpha}(u^{\prime},\zeta),\widehat{\Omega}(u^{ \prime},\zeta)}\Big{|}\mathbf{y}_{u^{\prime}},\widehat{\mathbf{h}}^{(u^{ \prime})}(\zeta)\Big{]},\] (10)where \(\mathrm{E}[\circ]\) is the average operator over the possible information symbols of user \(u\).