# A Scheduling Scheme for Improving the Performance and Security of MU-MIMO Systems
## 2 System Model
### Channel Model and Received Signals  
Consider the uplink of a single-cell MU-MIMO system that employs \(A\) antennas at the BS to serve \(U\) user terminals (UTs), each of them equipped with a single antenna, such that \(A\geq U\). The \(U\)UTs transmit simultaneously over the same frequency channel (subcarrier), which has a bandwidth less than the channel coherence bandwidth, \(B_{c}\). Therefore, the transmitted signals are affected by flat fading (This scenario appears in multicarrier systems that employ orthogonal-frequency-division-multiplexing (OFDM), where the total \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**MIMO Research Area** & \multicolumn{10}{c}{**Previous Works**} & \multicolumn{1}{c}{**[P]**} \\ \cline{2-11}  & **[7,10]** & **[8]** & **[14]** & **[16,17]** & **[19]** & **[20, 21, 22, 23, 24, 25, 26]** & **[27]** & **[31]** & **[32, 33, 34]** & \\ \hline Performance evaluation & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} \\ in Rayleigh fading & & & & & & & & & & & & \\ \hline Performance evaluation & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} \\ in generalized fading & & & & & & & & & & & \\ \hline Imperfect channel & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{X} & \multirow{2}{*}{} & \multirow{2}{*}{} & \multirow{2}{*}{} & \multirow{2}{*}{X} \\ estimation & & & & & & & & & & & \\ \hline Multiuser detection & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} \\ \cline Scheduling algorithms & & & & & & & & & & & \\ \hline Physical layer security & \multicolumn{10}{c}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} & \multirow{4}{*}{X} \\ \hline \multicolumn{10}{c}{[P] = Proposal presented in this work.} & & & & & & & & \\ \end{tabular}
\end{table} 
Table 1: Related work summary. bandwidth used by the system is greater than \(B_{c}\), but the bandwidth of each subcarrier is much less than \(B_{c}\). This, along with the use of a cyclic prefix allows removal of inter-symbol interference (ISI) and inter-carrier interference (ICI), and guarantees that each subcarrier is affected by flat fading [36]) [5]. Under these premises, the vector of samples received in the BS during a symbol interval \(\mathbf{y}\) of dimensions \(A\times 1\), can be written as  
\[\mathbf{y}=\mathbf{Hs}+\mathbf{n}=\sum_{k=1}^{U}\mathbf{h}_{k}s_{k}+\mathbf{n}, \tag{1}\]  
where \(\mathbf{s}\) is a \(U\times 1\) vector containing the transmitted symbols. Thus, \(s_{k}\) is the symbol transmitted by the \(k\)-th user and \(\mathbf{H}=[\mathbf{h}_{1}\ \mathbf{h}_{2}\ \cdots\ \mathbf{h}_{U}]\) is an \(A\times U\) matrix containing the wireless channel gains. Therefore, the column vector \(\mathbf{h}_{k}\) contains \(A\) channel gains affecting the \(k\)-th user transmission. The elements of \(\mathbf{h}_{k}\) are complex Gaussian random variables, i.e., \(h_{a,k}=g_{1}+\mathrm{j}g_{2}\), such that \(g_{1}\) and \(g_{2}\) are real Gaussian random variables with mean \(\mu/\sqrt{2}\) and variance \(\sigma^{2}\).