# Optical Interference Suppression Based on LCD-Filtering
## 4 MIMO Communication  
The numerical results reported so far are valid for the previously given application examples but are not directly applicable to MIMO and multi-user scenarios where the detection of multiple data streams is intended and receiver-side decorrelation methods are used. In order to compare our novel filter approach to a conventional MIMO receiver, we use the indoor scenario from [13] as reference. This is a \(N_{t}\times N_{r}\) MIMO set-up with \(N_{t}=4\) LED transmitters mounted at the ceiling at a height of 2.5 m pointing downwards to the receivers located on a desk of 0.75 m height. The four transmitters with a FOV of 15\({}^{\circ}\) each are arranged in square configuration with a variable distance \(d_{t}\) of 0.2 m, 0.4 m, and 0.6 m. The \(N_{r}\) receivers are also arranged rectangularly and \(d_{r}=0.1\) m apart, enabling a reasonably small sized receiver ensemble. Given this scenario, we extend the receivers by the novel LCD filter. Instead of four times replicating the receiver structure shown in Figure 1, a single LCD is used for simultaneously decorrelating all four PDs. Hereby, the number of required filter elements is reduced to one. This promising alternative is depicted in Figure 7. Both possible receiver structures will show equal  
Figure 6: Reduction of modulated interference, according to the analytical method described in Section 3.2.  
performance as long as the previously established requirements on the geometry are considered. One benefit of LCD-based filtering is a reduced receiver size since the required distance \(d_{\text{PD}}\) of the PDs is considerably smaller compared to the conventional MIMO system that relies on a sufficient large PD distance \(d_{r}\). In accordance with the conventions in [13], we have calculated the following channel matrices by applying the Lambertian law to the LOS paths:  
\[\mathbf{H}_{d_{t}=0.2\,\text{m}}\approx 10^{-4}\cdot\left[ \begin{array}{ c c c c}0.317843&0.000120&0.000126\\ 0.000120&0.317843&0.000126&0.000120\\ 0.000120&0.000126&0.317843&0.000120\\ 0.000126&0.000120&0.000120&0.317843\end{array} \right],\]  
\[\mathbf{H}_{d_{t}=0.4\,\text{m}}\approx 10^{-4}\cdot\left[ \begin{array}{ c c c c}0.272697&0.000134&0.000134&0.000138\\ 0.000134&0.272697&0.000138&0.000134\\ 0.000134&0.000138&0.272697&0.000134\\ 0.000138&0.000134&0.000134&0.272697\end{array} \right],\]  
\[\mathbf{H}_{d_{t}=0.6\,\text{m}}\approx 10^{-4}\cdot\left[ \begin{array}{ c c c c}0.201909&0.000137&0.000137&0.00000\\ 0.000137&0.201909&0.00000&0.00137\\ 0.000137&0.000000&0.201909&0.000137\\ 0.000000&0.000137&0.000137&0.201909\end{array} \right].\]  
Since no analytical solution for calculating the MIMO intensity modulation with direct detection (IM/DD) capacity is known, modulation constrained MIMO performance figures are derived in [13]. Perfect channel knowledge, perfect time synchronisation and receiver-side maximum likelihood (ML) detection  
\[\hat{\mathbf{u}}=\arg\max_{\mathbf{u}}\mathbf{p}_{\text{y}}\left(\mathbf{y}| \mathbf{u},\mathbf{H}\right)=\arg\min_{\mathbf{u}}\|\mathbf{y}-\mathbf{H} \mathbf{u}\|_{\text{F}}^{2} \tag{17}\]  
are assumed for estimating the transmit vector \(\mathbf{u}\). Lower bounds for the BER of spatial multiplexing (SMP) and spatial modulation (SM) are given in [13], closely approximating the ML decoding results for BERs \(\leq 10^{-2}\). In the case of SMP, independent data streams are simultaneously transmitted. Each one is modulated using unipolar \(M\)-ary pulse amplitude modulation (\(M\)-PAM). SMP is a parallel scheme offering a constrained capacity of \(N_{t}\cdot\log_{2}(M)\,\text{bits/s/Hz}\) with the transmit power equally distributed on all \(N_{t}\) transmitters. The use of \(M\)-PAM is reasonable owing to its good optical power  
Figure 7: MIMO set-up using a single LCD for decorrelating two links. efficiency, e.g., shown in [14]. SM additionally exploits the spatial domain by assigning individual bit patterns to the transmitters.