# Denoising Generalization Performance of Channel Estimation in Multipath Time-Varying OFDM Systems
## 1 Introduction  
As a multicarrier modulation technology, OFDM technology has the characteristics of high spectrum utilization and strong anti-multipath transmission ability. It has been widely used in terrestrial radio broadcasting systems such as ATSC3.0 and DVB-T2 and mobile communication systems such as 4G and 5G. In practical wireless environments, signals tend to experience frequency selective fading during transmission due to channel multipath effects. This causes amplitude, frequency and phase distortion of the received signal at the receiver, making it difficult for the receiver to demodulate the correct transmitted signal. Therefore, channel estimation at the receiver is required to obtain accurate channel characteristics. This allows the channel to be compensated accordingly at the receiver to improve the transmission quality and ensure the reliability of the communication. In OFDM systems, the conventional channel estimation method approximates a frequency-selective fading wideband channel as a flat-fading narrowband channel one by one, and channel estimation is performed for each flat-fading channel to obtain a more accurate channel frequency response. This method is suitable in wireless environments where the mobile rate is not high and the Doppler frequency shift is small. With the rapid development of social and economic, the application of high-speed transportation such as trains and high-speed railways is becoming more and more popular, which greatly shortens people's travel time. However, wireless channels in high-speedenvironments are highly time-varying, often accompanied by shifts in the channel model and rapid changes in the Doppler shift. At this point, the narrowband channels in each frequency domain can no longer be approximated as flat, and traditional channel estimation methods such as Least Square (LS) and Minimum Mean Square Error (MMSE) are no longer applicable. Therefore, more sophisticated and targeted measures are needed to estimate the channel. To overcome this problem, data-driven OFDM channel estimation based algorithms have attracted discussions among scholars. Preliminary results show that DL-based OFDM channel estimation algorithms outperform traditional model-driven algorithms in high-speed mobile scenarios. However, the performance of this algorithm depends on the richness of the channel information used. If the designed model deviates significantly from the channel environment, the performance of the algorithm will be much worse compared to the theoretical calculation. Then how to use the DL-based denoising technique in multipath time-varying systems to further improve the generalization of the algorithm under the environment mismatch while ensuring the accuracy of channel estimation is the focus of this paper. In this paper, we first design a feedforward network \(CNN_{\text{N}}\) to estimate the noise level of the current environment. Then cascade the DnCNN as a denoising network \(CNN_{D}\) to denoise the noisy channel estimation matrix. Finally, use the residual module to improve the convergence speed of the model. The experimental results indicate that the overall implementation complexity of the proposed algorithm is lower than that of the conventional channel estimation algorithm, which improves the engineering practicability of the algorithm. In general, the main contributions of this paper include:  
* This paper uses 5G standard channels and parameters to construct an OFDM communication system, which has excellent engineering practicability. * A DL-based OFDM channel estimation denoising network NDR-Net is proposed. The receiver first obtains the noisy channel matrix using the traditional channel estimation algorithm. Then it is modeled as a two-dimensional image and fed into a denoising network with \(CNN_{N}\) and \(CNN_{D}\) cascade. The \(CNN_{N}\) is an NLE subnet to extend the generalization noise interval, and the \(CNN_{D}\) is a DnCNN with residual layer, which mainly serves to denoise the channel images.