# DeepGOMIMO: Deep Learning-Aided Generalized Optical MIMO with CSI-Free Detection
## 3 Detection Schemes for GOMIMO Systems
### Proposed CSI-Free DNN Detection  
Considering the many disadvantages of CSI-based ZF-DNN detection due to the requirement of instantaneous CSI for ZF equalization, in this work, we for the first time propose a novel CSI-free DNN detection scheme for GOMIMO systems. Figure 2 depicts the schematic diagram of the proposed CSI-free DNN detector, which consists of a preprocessing module and a feedforward DNN module. It can be seen that a preprocessing module is placed in front of the feedforward DNN module in the proposed CSI-free DNN detector, which is the key to dealing with the impact of MIMO transmission through free-space channels and hence realize detection without the need of CSI. Specifically, as can be found from (1), the impact of MIMO transmission on the transmitted signal vector \(\mathbf{x}\) can be characterized from the following two aspects. First, because the channel coefficients in typical MIMO-OWC systems are within the region from \(10^{-6}\) to \(10^{-4}\)[8; 33], the electrical path loss caused by MIMO transmission is about 80 to 120 dB. Secondly, MIMO transmission also inevitably leads to channel crosstalk, which might cause severe ICI, especially for GOSMP systems. As a result, the designed preprocessing module should be able to address both the path loss issue and the channel crosstalk issue caused by MIMO transmission. As shown in Figure 2, our specially designed preprocessing module mainly contains two parts: one is the amplitude scaling part and the other is the feature-extraction part. Specifically, the amplitude scaling part is adopted to address the path loss issue by multiplying the received signal vector \(\mathbf{y}\) with a scaling factor \(\alpha\). Note that a proper \(\alpha\) value is determined in advance for each receiver location in the GOMIMO system, and hence no instantaneous CSI is needed to achieve amplitude scaling. Moreover, the feature-extraction part is used to address the channel crosstalk issue, which multiplies the scaled received signal vector \(\alpha\mathbf{y}\) by a feature matrix \(\mathbf{F}\). Hence, the output signal vector of the preprocessing module in the CSI-free DNN detector, i.e., \(\hat{\mathbf{y}}=[\hat{y}_{1},\hat{y}_{2},\cdots,\hat{y}_{N_{t}}]^{T}\), can be obtained by  
\[\hat{\mathbf{y}}=\alpha\mathbf{F}\mathbf{y}. \tag{9}\]  
In order to provide enough information for the following feedforward DNN module to efficiently learn and remove the impact of channel crosstalk caused by MIMO transmission, the feature matrix \(\mathbf{F}\) should be able to reflect all the potential signal superposition cases at the receiver side. Consequently, according to the mapping tables of both GOSM and GOSMP in Figure 1, we adopt the corresponding unified mapping matrix as the feature matrix, i.e.,  
Figure 2: Schematic diagram of the proposed CSI-free DNN detector consisting of a preprocessing module and a feedforward DNN module. \[\mathbf{F}=\left[ \begin{array}{cccc}1&1&0&0\\ 1&0&1&0\\ 0&1&0&1\\ 0&0&1&1\end{array} \right]. \tag{10}\]  
Subsequently, the preprocessed signal vector \(\mathbf{\hat{y}}\) is fed into a feedforward DNN module, which mainly consists of an input layer, multiple hidden layers, an output layer, and a decision layer. Because \(\mathbf{\hat{y}}\) is a vector with \(N_{r}\) elements, the input layer contains \(N_{r}\) neurons accordingly. Moreover, we set totally four fully connected hidden layers in the feedforward DNN module, which are used to learn the statistical characteristics of both the input signal and the additive noise. The number of neurons in the \(i\)-th (\(1\leq i\leq 4\)) hidden layer is denoted by \(L_{i}\), and the rectified linear unit (ReLU) function, i.e., \(f_{\text{ReLU}}(\alpha)=\max(0,\alpha)\), is adopted as the activation function of the hidden layers. For the output layer, it adopts the Sigmoid function, i.e., \(f_{\text{Sigmoid}}\left(\alpha\right)=1/\left(1+\exp^{-\alpha}\right)\), as the activation function to generate a fuzzy bit information, so as to map the output of each neuron within the range [0, 1].