# Throughput Enhancement in Downlink MU-MIMO Using Multiple Dimensions
## 3 Proposed Scheme
### Signal Detection Model  
The MUI is perfectly eliminated by using the precoding matrix. Since the \(k\)-th user receives its own data without MUI, the appropriate receiver structure for each user is similar to the point-to-point MIMO. In Equation (8), MIMO detection is performed. In MIMO detection algorithm, there exist linear and non-linear algorithms. In the proposed scheme, linear detection algorithms such as zero-forcing(ZF) and minimum mean squared error (MMSE) can be applied simply. If the ZF detection scheme is used, the filter matrix for the \(k\)-th user is as follows,  
\[\mathbf{G}_{k}=\mathbf{H}_{eff,k}^{H}(\mathbf{H}_{eff,k}\mathbf{H}_{eff,k}^{H})^ {-1}. \tag{9}\]  
The detected superposed signals of the \(k\)-th user using ZF MIMO detection can be represented as follows,  
\[\mathbf{\hat{s}}_{k}=\mathbf{G}_{k}\mathbf{y}_{k}=\mathbf{H}_{ eff,k}^{H}(\mathbf{H}_{eff,k}\mathbf{H}_{eff,k}^{H})^{-1}(\mathbf{H}_{eff,k} \mathbf{s}_{k}+\mathbf{n}_{k}) \tag{10}\] \[=\mathbf{H}_{eff,k}^{H}\Big{(}\mathbf{H}_{eff,k}^{H}\Big{)}^{-1} \Big{(}\mathbf{H}_{eff,k}\Big{)}^{-1}\mathbf{H}_{eff,k}\mathbf{s}_{k}+\mathbf{ H}_{eff,k}^{H}(\mathbf{H}_{eff,k}\mathbf{H}_{eff,k}^{H})^{-1}\mathbf{n}_{k}= \mathbf{s}_{k}+\mathbf{G}_{k}\mathbf{n}_{k}.\]  
In the Equation (10), \(\mathbf{s}_{k}\) can be detected since it satisfies \(\mathbf{G}_{k}\mathbf{H}_{eff,k}=\mathbf{I}\). However, if the linear detection algorithms are used, the bit error rate (BER) performance is too poor since the power of symbols in one superposed signal is low. Low performance detection techniques in terms of BER can cause a negative effect on performing SIC. Therefore, the non-linear detection algorithms can be applied such as maximum likelihood (ML), ordered successive interference cancellation (OSIC), decision feedback equalizer (DFE), QRD-M.  
From Equation (10), the estimated superposed signals of the \(k\)-th user after performing MIMO detection can be reconstructed as follows,  
\[\mathbf{\hat{s}}_{k}=\left[\begin{array}{c}\hat{s}_{1}\left(k\right)\\ \hat{s}_{2}\left(k\right)\\ \vdots\\ \hat{s}_{N_{r}}\left(k\right)\end{array}\right]=\left[\begin{array}{c}\sqrt{ P_{1}}\hat{s}_{1,1}\left(k\right)+\sqrt{P_{2}}\hat{s}_{1,2}\left(k\right)+ \cdots+\sqrt{P_{N}}\hat{s}_{1,N}\left(k\right)\\ \sqrt{P_{1}}\hat{s}_{2,1}\left(k\right)+\sqrt{P_{2}}\hat{s}_{2,2}\left(k \right)+\cdots+\sqrt{P_{N}}\hat{s}_{2,N}\left(k\right)\\ \vdots\\ \sqrt{P_{1}}\hat{s}_{N_{r},1}\left(k\right)+\sqrt{P_{2}}\hat{s}_{N_{r},2} \left(k\right)+\cdots+\sqrt{P_{N}}\hat{s}_{N_{r},N}\left(k\right)\end{array} \right], \tag{11}\]  
where\(\hat{s}\) are the symbols at each estimated superposed signal. In Equation (11), the superposed signal can be decoded by conducting SIC. Therefore, SIC is performed at each receiving antenna. In estimated superposed signal, the strong symbol, i.e., \(\sqrt{p_{N}}\hat{s}_{Nr,N}\) is first decoded. The first decoded symbol can be represented as follows,  
\[\mathbf{\hat{s}}_{k}^{d}=\left[\begin{array}{c}\hat{s}_{1,N}^{d}\left(k \right)\\ \hat{s}_{2,N}^{d}\left(k\right)\\ \vdots\\ \hat{s}_{N_{r},N}^{d}\left(k\right)\end{array}\right]. \tag{12}\]  
The decoded symbol is then subtracted from the superposed signal.  
\[\mathbf{\hat{s}}_{k}-\mathbf{\hat{s}}_{k}^{d}=\left[\begin{array}{c}\sqrt{ P_{1}}\hat{s}_{1,1}\left(k\right)+\sqrt{P_{2}}\hat{s}_{1,2}\left(k\right)+ \cdots+\sqrt{P_{N}}\hat{s}_{1,N}\left(k\right)\\ \sqrt{P_{2}}\hat{s}_{2,1}\left(k\right)+\sqrt{P_{2}}\hat{s}_{2,2}\left(k \right)+\cdots+\sqrt{P_{N}}\hat{s}_{2,N}\left(k\right)\\ \vdots\\ \hat{s}_{N_{r},N}^{d}\left(k\right)\end{array}\right]-\left[\begin{array}{c} \hat{s}_{1,N}^{d}\left(k\right)\\ \hat{s}_{2,N}^{d}\left(k\right)\\ \hat{s}_{N_{r},N}^{d}\left(k\right)\end{array}\right]=\left[\begin{array}{c} \hat{s}_{1,N-1}^{d}\left(k\right)\\ \hat{s}_{2,N-1}^{d}\left(k\right)\\ \vdots\\ \hat{s}_{N_{r},N-1}^{d}\left(k\right)\end{array}\right]. \tag{13}\]  
Finally, all the symbols in the superposed signal can be decoded by performing SIC. The receiver model is described in Figure 6.