## 4 Results and Discussion  
In this section, the estimation accuracy of the active LED indexes is evaluated with the index error rate (IER), and the BER characteristics of the proposed methods (LFC-DNN, SFC-DNN, and CNN) are compared with those of the conventional index estimation algorithms (the best method is MAP detection). Besides, the complexity costs are also compared in terms of the run time measurement. More specifically, a MIMO VLC system's performance composed of 4 LEDs and 4 PDs are shown. For convenience, the system configurations of the simulation are similar to those in [18]: a \(5\,\mathrm{m}\times 5\,\mathrm{m}\times 3\,\mathrm{m}\) room, positions of LEDs, PDs, and the channel gain matrix are similar to the physical channel C in [18] is used for the simulation. At the transmitter, OFDM is employed with two cases. Case 1 and 2 have \(N=8\) and \(N=32\) subcarriers, respectively. In both cases, 4-QAM symbols are mapped onto the subcarrier before the IFFT. A CP length of six is chosen for the computer simulation to ensure that it covers the maximal delay spread of the channel. Subsequently, the IE-DNNs are trained over 200 iterations with a batch size of 400 samples. Moreover, the networks are trained with 200 epochs during each iteration. When the validation loss value stops improving, the iteration can be terminated early. When the validation loss does not improve after 50 epochs, the learning rate is reduced by 1/3 until it reaches the minimum (0.0002). Figure 3 compares the index error rates (IER) of the different algorithms. Nevertheless, the MAP estimator only achieves an IER below 0.1 while the proposed SFC-DNN and CNN are better in estimating the active LED index. More specifically, an accuracy of 0.001 can be obtained in the high SNR regime. In addition, the higher the number of subcarriers is, the better the index accuracy is. Because the LFC-DNN and MAP detection have similar results, the simultaneous extraction of all received signals at the PDs and the additional signal features remarkably improve the index estimation accuracy. Figure 4 presents the BERs of Case 1. As the IER values of the MAP detection and LFC-DNN are similar, their BERs are the worst among those of all compared estimators. The CNN-based estimator exhibits significantly better BERs than the others. More specifically, at the SNR value of 10 dB, the proposed CNN, FCN, and the conventional MAP detector achieve a BER value of \(10^{-4}\), \(10^{-3}\), and \(10^{-2}\), respectively. Nevertheless, the SNR gain in the BER is only 4 dB when a CNN instead of MAP detection is used. This is because the total number of correctly estimated active LED indexes is not the sole dominant factor that affects the BERs of the demodulator. Because the estimator only estimates the active LED index, after the CNN-based and other estimators, the signal magnitude of the active LEDs is also an essential factor that impacts the BER. With its lower IER, MAP detection can estimate a good number of active LEDs with large signal magnitudes, which leads to an acceptable BER. Moreover, owing to the remarkably high accuracy of SFC-DNN and CNN regarding the IER, the additional correct LED index estimation usually lower in signal magnitude and not as important as the higher ones. Therefore, only an SNR gain of 4 dB