# DMCNet-Pro: A Model-Driven Multi-Pilot Convolution Neural Network for MIMO-OFDM Receivers
## 5 Experimental Design and Results
### Performance and Parameter Count of Fully Connected Networks  
In [6], the authors employed a fully connected network (DNN) as the receiver for single-antenna OFDM signals. For the MIMO-OFDM system studied in this paper, the experiments were also conducted using a fully connected network. The number of fully connected layers used in the experiments was 3, with a gradually increasing number of neurons in each layer. The output data were fixed as the 16 bits from the 128 th to the 143 rd positions. The last layer of the fully connected network utilized a sigmoid activation function to ensure the output fell within the [0, 1] range. Finally, a bit decision function was employed to convert the neural network output into binary (0 or 1) bits:  
\[output=\begin{cases}0&x<=0.5\\ 1&\text{else}\end{cases}. \tag{8}\]  
The bit error ratio (BER) performance of the fully connected network under 8 pilot tones and 32 pilot tones is shown in Figures 8 and 9.  
Figure 8: BER of MIMO-OFDM fully connected receiver under eight pilot tones.  
Figure 9: BER of MIMO-OFDM fully connected receiver under 32 pilot tones.  
It can be observed that in the MIMO-OFDM scenario, the receiver performance of the fully connected network is significantly worse compared to the single-antenna OFDM scenario. By increasing the number of neurons in the fully connected layers, the BER performance can be gradually improved. However, once the number of neurons in the fully connected layers reaches a certain value, the network's bit error rate reaches a bottleneck, and further increasing the network size does not yield significant benefits.  
In [6], the authors employed a scheme where each fully connected network estimates only 16 input bits, resulting in a total of 512 input bits. Therefore, 32 parallel fully connected networks are required for estimation, and their output results are subsequently concatenated. However, for the MIMO-OFDM receiver, the number of input bits is higher, necessitating a larger number of sub-networks. To investigate the impact of the output bit number on the receiver's BER performance, we conducted experiments with output lengths of 8 bits, 16 bits, 32 bits, 64 bits, and 128 bits under eight pilot symbols. The predicted data corresponded to the input starting from the 128 th data point, which, respectively, covered the ranges of 128-135 bits, 128-142 bits, 128-159 bits, 128-171 bits, and 128-255 bits. The results are shown in Figure 10:  
Based on the experimental results, it can be concluded that the performance of a single fully connected network deteriorates as the number of predicted bits increases. As the prediction length decreases, the BER gradually decreases, but at a slower rate. When the output length is 16 bits, further reducing the output length has little impact on performance as it reaches saturation. Additionally, a smaller number of predicted bits per network requires a larger number of sub-networks. In this study, a prediction length of 16 bits was used, which means a total of 64 sub-networks are needed to concatenate the final output.  
Furthermore, the parameter count is a significant concern in the fully connected solution. In the case of MIMO-OFDM receivers with a large number of input bits, using a  
Figure 10: Relationship between prediction length and BER of an MIMO-OFDM fully connected receiver.  
fully connected approach requires multiple large sub-networks to combine the outputs. The parameter count for each parameter configuration in the graph is already substantial, and employing a fully connected approach with a high parameter count yields a mediocre performance. Therefore, the fully connected signal reception solution suitable for single-antenna scenarios is not applicable to MIMO-OFDM scenarios. The following fully connected experiments employ a 2048-2048-512 network configuration.