## 3 Simulation Results
### DNN Simulation Results  
Numerous experiments have been conducted to evaluate the efficacy of deep learning techniques in simultaneously estimating channels and detecting symbols within OFDM wireless communication systems. These experiments involved training a DNN model using simulated data and comparing its performance against conventional methods by assessing the BERs across various SNRs. In these experiments, the OFDM system parameters were set to 64 sub-carriers and a cyclic prefix length of 16. Two types of wireless channel models were utilized: Rayleigh fading and realistic scenarios. The choice of these channel models allows for a comprehensive evaluation, considering both idealized and real-world conditions, thus providing a robust assessment of the DNN model's performance across different environments. Additionally, the consistent carrier frequency of 2.6 GHz and the use of QPSK modulation ensure uniformity and comparability across experiments, eliminating potential confounding factors and allowing for a focused analysis of the DNN model's effectiveness. Figure 12 illustrates the training progress of the DNN regression model using a dataset consisting of 100,000 generated frames. The SNR spans from 0 to 30 dB, with 75% of the dataset allocated for training. Validation was conducted using a separate dataset from the training set, while testing was performed at a fixed SNR of 5 dB, with the channel modeled as a Rayleigh fading channel. This experimental setup ensures rigorous evaluation of the DNN model's performance under varying SNR conditions, facilitating insights into its robustness and generalization capabilities. Figure 13 shows the BER of DNN regression when comparing with the traditional MMSE approach. As illustrated in Figure 13, the superiority of the DNN model over the traditional minimum mean square error (MMSE) estimates is evident, particularly as the number of simulation frames increases, especially in the context of Rayleigh fading channels. This enhanced performance can be attributed to several key factors inherent to DNNs. Firstly, DNNs excel at handling the complex and nonlinear relationships present in wireless communication channels. Unlike the traditional MMSE methods, which rely on linear assumptions, DNNs have the capacity to capture intricate channel patterns and variations, allowing them to more accurately model the underlying channel characteristics. Moreover, DNNs possess the ability to adapt to specific channel conditions by automatically extracting relevant features from the data. This adaptability enables DNNs to discern subtle differences between different channel conditions, thereby improving their performance in distinguishing between signal and noise components. Furthermore, DNNs exhibit robustness across a wide range of scenarios and generalize well to unseen data. This robustness is particularly advantageous in practical deployment scenarios where the channel conditions may vary unpredictably. By leveraging a diverse dataset encompassing varied channel conditions, DNNs are able to learn and generalize effectively, ensuring reliable performance in real-world applications. Additionally, with an increasing number of simulation frames, DNNs undergo iterative parameter refinement, thereby enhancing their adaptability and performance. This iterative learning process enables DNNs to continually optimize their parameters to better align with the underlying channel characteristics, resulting in improved performance over time. Figure 12: Training progress of DNN regression for 100,000 frames. Figure 13: BERs of DNN regression and MMSE approach for 100,000 frames. Overall, the superior performance of DNNs in channel estimation and symbol detection tasks can be attributed to their ability to handle complex relationships, adapt to specific channel conditions, demonstrate robustness across varied scenarios, and undergo iterative parameter refinement. These qualities make DNNs a promising approach for enhancing the efficiency and reliability of wireless communication systems.