# DeepGOMIMO: Deep Learning-Aided Generalized Optical MIMO with CSI-Free Detection
## 4 Simulation Results
### BER Performance  
We further evaluate and compare the BER performance of the proposed CSI-free DNN detector with the other three benchmark detectors in the 4 \(\times\) 4 GOMIMO system. Figure 4a,b compare the BER performance of four detectors for GOSM with the receiver located at the center and the corner of the receiving plane, respectively. When the receiver is located at the center of the receiving plane, as shown in Figure 4a, the ZF-ML detector requires a high transmitted SNR of 163.4 dB to achieve the target BER of \(10^{-3}\). However, the required SNR to reach BER = \(10^{-3}\) is reduced to 138.9 dB for the joint ML detector. As a result, a substantial 24.5-dB SNR gain can be obtained by the joint ML detector in comparison to the ZF-ML detector, which is mainly because the ZF-ML detector suffers from severe noise amplification and error propagation. Moreover, it can be further seen that the ZF-DNN detector with an optimal 140-dB training SNR can achieve comparable BER performance as the joint ML detector in the high SNR region, suggesting the excellent error performance of the ZF-DNN detector under the condition of accurate CSI for ZF  
Figure 3: MSE training loss of the proposed CSI-free DNN detector with receiver located at the center of the receiving plane for **(a)** GOSM and **(b)** GOSMP. equalization. Finally, for our proposed CSI-free DNN detector, we investigate the impact of training SNR on its error performance and three different training SNRs of 130, 140, and 150 dB are considered. It is clearly shown that the CSI-free DNN detector with 140-dB training SNR achieves nearly the same BER performance as the joint ML detector across the whole SNR region, which slightly outperforms the ZF-DNN detector in the low SNR region. However, the joint ML detector outperforms the CSI-free DNN detector when a lower training SNR of 130 dB or a higher training SNR of 150 dB is adopted, and the reasons can be explained as follows. The DNN module can better learn the statistics of the noise with a relatively small training SNR, whereas the statistics of the data symbols can be more accurately learned when the training SNR is relatively large. As a result, there exists an optimal training SNR which can make a tradeoff for the DNN module to learn the statistics of both the noise and the data symbols and hence lead to a minimum overall BER. When the receiver is moved to the corner of the receiving plane, as shown in Figure 4b, we can observe that the joint ML detector outperforms the ZF-ML detector by an SNR gain of more than 40 dB at BER = \(10^{-3}\), whereas the ZF-DNN detector with an optimal training SNR of 160 dB obtains near-optimal BER performance as the joint ML detector only for relatively low BERs. Furthermore, the CSI-free DNN detector achieves comparable BER performance as the joint ML detector in the high SNR region, which outperforms the ZF-DNN detector in the low SNR region. It should be noted that an error floor occurs for the CSI-free DNN detector with a lower training SNR of 140 dB, which is mainly due to the insufficient learning of the statistics of the data symbols in a very noisy environment. Figure 4: BER comparison of the proposed CSI-free DNN detector and three benchmark detectors for GOSM at (**a**) the center and (**b**) the corner. The BER versus transmitted SNR for GOSMP is plotted in Figure 5. As we can see, the ZF-DNN detector with an optimal training SNR can achieve very close performance as the joint ML detector when the receiver is located at the center of the receiving plane, but it performs worse than the joint ML detector when the receiver is moved to the corner, especially in the low SNR region. In contrast, the proposed CSI-free DNN detector can achieve comparable BER performance as the joint ML detector for both center and corner receiver locations. Moreover, error floors occur for the CSI-free DNN detector when the adopted training SNR is too small or too large.