# Throughput Enhancement in Downlink MU-MIMO Using Multiple Dimensions
## 3 Proposed Scheme
### Data Transmission Model  
To exploit both the power and space domain, BD and SC scheme are used. The overall transmission model is shown in Figure 5. First, SC is used for exploiting power domain. The transmit symbols are superposed with different powers in one signal. Therefore, the transmitter can transmit more data stream at the same time. In the existing NOMA scheme, SC and SIC are used to suppress the MUI by allocating the different powers to different users. However, the proposed scheme uses SC for separating the symbols in one superposed signal on the same user which BS transmits. In the proposed scheme, the transmit signals for the \(i\)-th receiving antenna can be written as follows,  
\[s_{i}=\sqrt{P_{1}}s_{i,1}+\sqrt{P_{2}}s_{i,2}+\cdots+\sqrt{P_{N}}s_{i,N}, \tag{3}\]  
where \(i\) is a receiving antenna index, \(N\) is the number of symbols in one superposed signal. \(\tilde{s}\) are the symbols in one superposed signal. The proposed scheme allocates optional power to symbols to detect each symbol, leading \(P_{1}<P_{2}<\cdots<P_{N}\). Then, transmit signals for the \(k\)-th user are defined as follows,  
\[\textbf{s}_{k}=\left[ \begin{array}{c}s_{1}\left(k\right)\\ s_{2}\left(k\right)\\ \vdots\\ s_{N_{r}}\left(k\right)\end{array} \right]=\left[ \begin{array}{c}\sqrt{P_{1 }}\tilde{s}_{1,1}\left(k\right)+\sqrt{P_{2}}\tilde{s}_{1,2}\left(k\right)+ \cdots+\sqrt{P_{N}}\tilde{s}_{1,N}\left(k\right)\\ \sqrt{P_{1}}\tilde{s}_{2,1}\left(k\right)+\sqrt{P_{2}}\tilde{s}_{2,2}\left(k \right)+\cdots+\sqrt{P_{N}}\tilde{s}_{2,N}\left(k\right)\\ \vdots\\ \sqrt{P_{1}}\tilde{s}_{N_{r},1}\left(k\right)+\sqrt{P_{2}}\tilde{s}_{N_{r},2} \left(k\right)+\cdots+\sqrt{P_{N}}\tilde{s}_{N_{r},N}\left(k\right)\end{array}  \right]. \tag{4}\]  
Figure 4: The downlink MU-MIMO broadcasting model. Figure 5: The proposed signal transmission model. For exploiting space domain, the precoding matrix \(\mathbf{W}\) should be designed in SDMA. In the scheme, BD beamforming is adopted to suppress the MUI since BD method shows a strong performance in terms of capacity and has a good flexibility. The objective of the BD method is to completely eliminate the MUI by employing the precoding matrix \(\mathbf{W}\). Then, the precoding matrix design for MUI elimination can be defined as follows,  
\[\mathbf{\tilde{H}}_{k}\mathbf{W}_{k}=0,k=1,\cdots,K. \tag{5}\]  
where \(\mathbf{\tilde{H}}_{k}\) is represented as the channel matrix for all users except for user \(k\),  
\[\mathbf{\tilde{H}}_{k}=[\mathbf{H}_{1}^{T}\cdots\mathbf{H}_{k-1}^{T}\ \mathbf{H}_{k+1}^{T}\cdots\mathbf{H}_{K}^{T}]^{T}. \tag{6}\]  
With the help of singular value decomposition (SVD), the precoding matrix for eliminating the MUI is designed. SVD is used to decompose a matrix into matrices representing rotation and scaling. By applying the SVD, the \(\mathbf{\tilde{H}}_{k}\) is defined as follows  
\[\mathbf{\tilde{H}}_{k}=\mathbf{U}_{k}\mathbf{\Lambda}_{k}[\mathbf{V}_{k}^{(1) }\ \mathbf{V}_{k}^{(0)}]^{H}, \tag{7}\]  
where \(\mathbf{\Lambda}_{k}\) is the diagonal matrix of which the diagonal elements are singular value of \(\mathbf{\tilde{H}}_{k}\). \(\mathbf{V}_{k}^{(0)}\) contains vectors of the zero singular values, \(\mathbf{V}_{k}^{(1)}\) and contains vectors of the non-zero singular values. \(\mathbf{V}_{k}^{(0)}\) is an orthogonal basis for the null space of \(\mathbf{\tilde{H}}_{k}\) and the required precoding matrix. As a result, intended user's channel is projected on the null space in order to have the transmission under the constraint of zero-interference (i.e.,\(\mathbf{\tilde{H}}_{k}\mathbf{\tilde{V}}_{k}^{(0)}=0\), \(k=1,\cdots,K\).) The received signal of the \(k\)-th user after eliminating MUI is defined as follows,  
\[