Deep-Learning-Based Carrier Frequency Offset Estimation and Its Cross-Evaluation in Multiple-Channel Models

Abstract

The most widely used Wi-Fi wireless communication system, which is based on OFDM, is currently developing quickly. The receiver must, however, accurately estimate the carrier frequency offset between the transmitter and the receiver due to the characteristics of the OFDM system that make it sensitive to carrier frequency offset. The autocorrelation of training symbols is typically used by the conventional algorithm to estimate the carrier frequency offset. Although this method is simple to use and low in complexity, it has poor estimation performance at low signal-to-noise ratios, which has a significant negative impact on the performance of the wireless communication system. Meanwhile, the design of the communication physical layer using deep-learning-based (DL-based) methods is receiving more and more attention but is rarely used in carrier frequency offset estimation. In this paper, we propose a DL-based carrier frequency offset (CFO) model architecture for 802.11n standard OFDM systems. With regard to multipath channel models with varied degrees of multipath fadding, the estimation error of the proposed model is 70.54% lower on average than that of the conventional method under 802.11n standard channel models, and the DL-based method can outperform the estimation range of conventional methods. Besides, the model trained in one channel environment and tested in another was cross-evaluated to determine which models could be used for deployment in the real world. The cross-evaluation demonstrates that the DL-based model can perform well over a large class of channels without extra training when trained under the worst-case (most severe) multipath channel model.

1. Introduction

The Deep Learning (DL) algorithm has recently altered traditional wireless communication methods. Signal detection, channel estimation, demodulation, error correction coding, and end-to-end communication have all been evaluated using DL-based methods at the physical layer. Deep learning techniques based on massive volumes of data have the potential to reduce the complexity caused by advanced mathematical models in wireless communication.It outperforms standard approaches in some areas, but it also has drawbacks, such as difficulties assuring generalization and gathering datasets [1,2,3].

1.1. Deep Learning for Wireless Physical Layer

Deep learning network efforts on communication receivers fall into two categories: optimizing a specific module and directly carrying out end-to-end network design. Recently, several DL-based methods for estimating channel state information (CSI) in OFDM systems have been proposed. Some of these models rely on pilots [4], while others may function without pilot [5]. Some of the datasets they utilize are simulated [6], while others are collected over the air. They all performed admirably in their separate tests.

Ref. [7] exploited deep learning to handle wireless OFDM channels in an end-to-end manner. The DL-based methodology, which is more robust than conventional methods, can mitigate channel distortion and detect transmitted symbols with performance comparable to the minimum mean-square error estimator. The cycle prefix is eliminated when fewer training pilots are used and nonlinear clipping noise exists. Ref. [8] also examined the deep neural network (DNN) layers made of long-short term memory (LSTM) for signal detection and proposed that the signal bit error (SER) is equivalent to or better than that of the minimum mean squared error (MMSE) and least square (LS) methods. In the data-driven, pilot-aided method applied to IEEE 802.11p, a channel estimation technique based on a gated recurrent unit (GRU)-based deep learning scheme is suggested for extracting time and frequency domain features to suppress error propagation. Ref. [9] investigates the channel estimation problem for the MIMO system with received SNR feedback using a DL-based method. Ref. [10] implements a novel non-coherent binary phase shift keying demodulator based on a deep neural network on software-defined radio that provides significantly better performance in terms of bit error rate compared with conventional demodulators. Ref. [11] proposes to construct the long short term memory (LSTM) unit-aided intelligent DNN-based deep learning (DL) demodulator for OFDM-aided differential chaos shift keying (OFDM-DCSK) systems. Ref. [12] presents a novel, DL-based frame format detection method for IEEE 802.11 WLANs to replace conventional detection procedures. The deep learning architectures for estimating the carrier frequency of a complex sinusoid in noise from the 1-bit samples of the in-phase and quadrature components were developed and analyzed in [13],which is able to accurately estimate carrier frequencies from 1 to bit quantized data with fewer pilots and lower signal-to-noise ratios (SNRs) than traditional signal processing methods. Under similar constraints, Deep Learning (DL) methods outperform FFT-based methods. All of these studies performed well in their individual data sets; However, the research on robustness in unknown channel environments was limited.

Ref. [14] shows that deep learning methods can be used to improve a standard belief propagation decoder, despite the large example space. Furthermore, those works do not take the effect of CFO and its equalization into account. Those papers aimed to optimize single or multiple specific modules and achieved positive results without considering the problem of the CFO. Ref. [15] developes a DL-based architecture of IEEE 802.11ax-based OFDM receivers that achieves comparable performance to or outperforms the conventional WLAN receivers. Ref. [16] demonstrates that over-the-air transmissions using DL-based methods are possible. End-to-end network design focuses on overall optimization, and there is no large-scale, mature deployment at present. In addition, hybrid methods between metaheuristics and machine learning successfully combine machine learning and swarm intelligence approaches and have proven to be able to obtain outstanding results in different areas, which can be used for better model deployment and utility [17,18].

1.2. Related Works

Wi-Fi in our everyday consumer communications items has piqued their interest. The majority of wifi communication products employ OFDM modulation technology, which performs well for LAN connection, and is compliant with the 802.11 series standards. The CFO of the transmitter and receiver has a negative impact on the OFDM system’s performance. The performance of the OFDM system will be significantly impacted if the estimated error of the CFO is too significant. Many conventional algorithms have been proposed for frequency offset estimation in OFDM systems [19,20]. In recent years, the DL-based method has been proposed to solve the problem of CFO estimation.

A CNN-aided channel and CFO estimation for high altitude platform station low earth satelite link was proposed in [21].The suggested convolutional neural network-based estimator is used to reduce residual Doppler effects, channel equalization, and carrier frequency offset. The data rate is then increased by employing a non-orthogonal multiple access approach to increase spectral efficiency. It was observed that the proposed AI-powered HAPS-LEO network not only has a high data throughput per second but also a higher service quality due to the agile signal reconstruction process.

Kumari et al. [22] proposed a deep-learning-based channel and CFO equalization technique for OFDM systems without any preamble or pilot sequences, which performs better and works for various propagation environments, and they considered the change in Doppler frequency across an OFDM symbol. However, the benefits of performance come at the expense of increased complexity, as NN processing involves numerous complex computations.

Ref. [23] presents a performance and complexity analysis of packet detection and CFO estimation using both the conventional and the DL-based approaches. The goal of the study is to investigate under which conditions the performance of the DL-based methods approaches or even surpasses that of the conventional methods, but also, under which conditions their performance is inferior. Focusing on the emerging IEEE 802.11ah standard, the investigation uses both the standard-based simulated environment, and a real-world testbed based on software-defined radios.Especially for the case of CFO estimation, RNNs are identified as the best-performing architecture that is able to match the accuracy of the conventional method (at low-to-medium SNRs) in this paper.

Few papers discuss the generalization of neural network models in communication systems, but reliability is the most important requirement of communication systems.

Rather than focusing solely on the design of the neurel network architecture, this paper discusses the generalized capability of DL-based model tranning in various channel models. The main contribution of this paper is

• We propose a DL-based method for CFO estimation in 802.11n OFDM systems, which has higher estimation accuracy than the conventional method.The proposed model is expected to replace the CFO estimation module in wireless communication to achieve better performance.
• We evaluated the estimation ability of DL-based models trained in different channels to adapt to new channel states experimentally and discussed the reasons for the cross-evaluation phenomenon.The study helps to explore which model is suitable for reliable wireless communication.
• We find that the proposed deep learning method can outperform traditional methods in terms of estimation range without degrading performance.It proves that the DL-based model will have better adaptability to the environment with worse carrier frequency offset than traditional methods.

2. Background and System Model

2.1. 802.11 Frame Structure and Channel Model

In this paper, we focus on preamble-based IEEE 802.11n OFDM technology, whose physical layer (PHY) packet structure, pilot placement and channel type definitions are defined by the 802.11n standard [24]. The sequence of data symbols in preamble-based systems is preceded by a preamble of known data required to estimate the channel state information, carrier frequency offset, and time synchronization [25]. The preamble structure is determined by the 802.11n standard and is based on a certificate repeated pattern, which represents sequences with good correlation properties, allowing for good time and carrier frequency synchronization.The preamble structure remains the same as in conventional 802.11 series standards, which have the same or similar preamble structure. This paper’s preamble is made up of the following parts.

• Short training field (STF). The short training field, which lasts 8 μs, consists of 10 same sequences (each containing 16 identical data samples) in the time domain. The correlation properties of STF are excellent, so STF is used for coarse timing synchronization, coarse frequency offset estimation and (coarse) channel estimation.
• Long trainning field (LTF). The long training field, which also lasts 8 μs, consists of 2 same sequences (each containing 64 identical data samples and 32 cyclic prefixes) in the time domain. Thanks to the longer duration of each sequence, LTF can be used for fine timing synchronization, fine frequency offset estimation and (fine) channel estimation.

802.11n standard refer to multipath severity as being proportional to the number of clusters and taps per cluster, with different channel models listed in

Table 1. 802.11n standard channel models.

Model	Delay Spread (ns)	Number of Clusters	Numbe of Taps	Environment
Model A	0	1	1	N/A
Model B	15	2	9	Residential
Model C	30	2	14	Residential small office
Model D	50	3	18	Typical office
Model E	100	4	18	Large office
Model F	150	6	18	Large space (indoors/outdoors)

. Channel A is a single delay tap that can be regarded as an awgn channel.Channels B-F each have more than one delay tap, with F having the most severe multipath and B having the least severe multipath.

2.2. Carrier Frequency Offset Influence

802.11 standard OFDM system have N subcarriers separated by $F_0$ in the frequency domain. Transmitter map the binary information onto the sequences of complex modulation sysmbols X allocated to different subcarriers and coverted into time-domain signal x via Inverted Discrete Fouie. The resulting discrete-time complex baseband signal is obtained as Equations (1) and (2).

$$x_n=\frac{1}{N}\sum _{k=0}^{N-1}{X}_k{e}^{\frac{j\left(2\pi kn\right)}{N}}$$

(1)

$$t_n=x_n{e}^{j2\pi f_{tx}n{T}_s}$$

(2)

where $f_{tx}$ is transmitter carrier frequency, $T_s$ is sample time. If awgn noise is ignored, the complex baseband signal in the receiver can be used by Equation (3).

$$\begin{array}{cc}\hfill r_n& =x_n{e}^{j2\pi f_{tx}n{T}_s}{e}^{-j2\pi f_{rx}n{T}_s}\hfill \\ \hfill & =x_n{e}^{j2\pi (f_{tx}-f_{rx})n{T}_s}\hfill \\ \hfill & =x_n{e}^{j2\pi f_{\mathsf{\Delta }}n{T}_s}\hfill \end{array}$$

(3)

where $f_{\mathsf{\Delta }}=f_{tx}-f_{rx}$ is the CFO between transmitter and receiver, and

$$T_s=\frac{1}{F_s}$$

(4)

$$F_s=N{F}_0$$

(5)

$$\epsilon =\frac{F_s}{F_0}$$

(6)

where $F_0$ is the subcarriers interval frequency. Equation (3) can be denoted as Equation (7)

$$r_n=x_n{e}^{j2\pi \epsilon \frac{n}{N}}$$

(7)

It can be seen in Equation (7) that $r_n$ is distorted due to the $\epsilon$. $\epsilon$ is usually subdivided into integer and decimal parts. The integer part can move the modulation symbols to the position of nearby subcarriers. The modulation symbols are still orthogonal at this point, but the phase has been rotated to other constellations, which can cause demodulation errors. The decimal part will destory the orthogonal of the modulation symbols.

2.3. The Conventional Method of Estimating the CFO

In 802.11n standard, the sampling delay between two consecutive repeated symbols in STF is D (D = 16), so the sum of the complex correlation denoted as Equation (8)

$$\begin{array}{cc}\hfill R& =\sum _{n=0}^{L-1}{r}_n{r}_{n+D}^{\ast }\hfill \\ \hfill & =\sum _{n=0}^{L-1}{x}_n{e}^{j2\pi f_{\mathsf{\Delta }}n{T}_s}{\left(x_{n+D}{e}^{j2\pi f_{\mathsf{\Delta }}(n+D)T_s}\right)}^{\ast }\hfill \\ \hfill & =e^{-j2\pi f_{\mathsf{\Delta }}D{T}_s}\sum _{n=0}^{L-1}{\left|x_n\right|}^2\hfill \end{array}$$

(8)

R should be a constant if $f_{\mathsf{\Delta }}=0$. To estimate CFO,

$$\widehat{f_{\mathsf{\Delta }}}=-\frac{1}{2\pi D{T}_s}\angle R$$

(9)

where $\angle R$ is angle measured operation, strictly defined in $[-\pi ,\pi ]$. The smaller N, the shorter the training symbol, the larger the range of frequency offset that can be estimated. For 802.11n STF, $N=16$, $T_s=0.05$ μs, so the range of CFO by LTF estimated is ($-625,625$) KHz. For LTF, $N=64$, $T_s=0.05$ μs, the range of CFO by LTF estimated is $(-156.2,156.2)$ KHz. STF is first used to estimate the coarse frequency offset and subsequently LTF is used to estimate the fine frequency offset in the conventional CFO approach. Because a CFO more than 625 KHz will cause the phase of the coarse CFO estimate to exceed $\pi$, the range of CFO using the conventional method is not equal to the sum of coarse and fine CFO. As a result, the inaccurate coarse CFO estimate cannot be utilized to add.

In the Conventional CFO estimate method, LTF is first used to estimate coarse replacedCFOfrequency offset and then LTF is used to estimate fine CFO. Significantly, the range of CFO by the conventional method is not equal to the sum of coarse and fine CFO because a CFO larger than 625 KHz will cause the phase of the coarse CFO estimate to exceed $\pi$, and the incorrect coarse CFO estimate can no longer be used to add.

Generally, the carrier frequency synchronization error is required to be less than 4% of the subcarrier interval in AWGN channels and 2% of the subcarrier interval in multipath channels.

3. System Model

3.1. Model Architecture

The effect of CFO estimated by conventional methods under low SNR is limited, which often affects the performance of the whole communication system, especially for OFDM system. We try to use the DL-based method to replace the CFO estimation module of the standard communication system. As shown in Figure 1, we no longer pay attention to the mathematical relationship contained in the preamble, and directly input the preamble sequence into the network. The network training process will independently learn the relationship between the CFO and the input sequence, and finally output the carrier frequency offset estimate.

In this paper, we use Gate Recurrent Unit (GRU) architecture to estimate the CFO from the received preamble of 802.11n. The estimation output can be expressed as Equation (10).

$$\widehat{f_{\mathsf{\Delta }}}=f\left(rx\right)$$

(10)

where $rx$ is the IQ sample received preamble. To input the model, we use both the STF and LTF fields as a sequence. By learning the relationship between preamble and CFO, the model directly output CFO value. In this paper, we estimate the CFO using GRU and dense layers. GRU is an improved Recurrent Neural Network (RNN) that is capable of establishing temporal correlation between previous and current circumstances [26]. GRU is an abbreviation for LSTM. its cells contain special units known as memory blocks in the recurrent hidden layer, which improves its ability to model long-term dependencies [27]. In comparison to LSTM, GRU only has two gates: an update gate and a reset gate [28].

It’s worth noting that instead of using the GRU’s output as the next layer’s input, we use the GRU’s hidden state h. h contains all of the previous node’s information, so it also contains the frequency offset information to be predicted. Using h as the next layer’s input can significantly reduce network size while maintaining good performance. Finally, our network structure is illustrated in

Table 2. Network layer of DL-base CFO estimator.

Layer	Output Dimensions	Activation Function
Input	320 × 2	None
Rearrange	$2\times 320$	None
GRU	$2\times 1024\times 3$	None
Dense	256	None
Dense	16	None
Dense	1	Tanh

.

3.2. Data Set Generation

We construct the 802.11n standard Non-HT format physical layer (PHY) protocol data unit (PPDU) given in

Table 3. Dataset paramets.

Dateset	Channel Model	CFO Range (Hz)
A	AWGN channel	(−625,000, 625,000)
B	802.11n channel model B	(−625,000, 625,000)
C	802.11n channel model C	(−625,000, 625,000)
D	802.11n channel model D	(−625,000, 625,000)
E	802.11n channel model E	(−625,000, 625,000)
F	802.11n channel model F	(−625,000, 625,000)
G	802.11n channel model A–F	(−625,000, 625,000)
H	802.11n channel model F	(−1,000,000, 1,000,000)

using the simulated environment and channel models A–F. Because we only use the PPDU preamble, the PHY service data unit (PSDU) length is set to 1 byte. After the PPDU is generated, a random CFO effect in a certain range will be applied, and then it will be sent to the Awgn channel to get the received signal. The data set will be composed of the received signal. Different datasets are generated under different channel models, and all the work is completed in matlab. We created a number of datasets, including independent datasets from models A to F with CFO ranging from (−625, 625) KHz, datasets that exceed the CFO estimate range by convention, and datasets that include all six channel models. We utilized these datasets to train the eight model weights and assess a model’s ability to estimate another channel after training on one. At the same time, we may investigate if the CFO estimate range of the DL-based technique can outperform the conventional way.

The simulation SNR range is set to 0–30 dB, with a step of 1 dB. Each SNR generates 10,000 received packets. As a result, each dataset produced has 310,000 samples.

In addition to the training datasets, we utilized the same procedure to construct testing datasets. The SNR range is also set to 0–30 dB, with a step of 1 dB. Each SNR generates 1000 received packets, so each testing datasets generates 31,000 PPDU packets in total. We produced a total of 8 testing datasets, one for each channel model.

3.3. Training Experiments

To train a DL-based model, we defined the loss function as illustrated in Equation (11). We utilized the same model parameters to train eight model weights for datasets (A–H), and we performed cross validation on the A–F test dataset. Furthermore, we trained the model on the H dataset and compared its prediction range to that of older approaches. The loss function of mean squared error (MSE) is utilized by Equation (11).

$$L_{MSE}=\sum _i{(\widehat{f_{\mathsf{\Delta }}}-f_{\mathsf{\Delta }})}^2$$

(11)

The training phase is realized in Python based on Pytorch and powerful GPU (RTX3090), using Adam optimizer.

4. Summary of Results

4.1. Comparison of Conventional and DL-Based Models

In different channels, we compared the estimated performance of DL-based models with the conenvtional mothod. We calculate the estimated MSE of CFO in each channel using the method outlined in Section 2.3 and compare it to the DL-based models. The final results are depicted in Figure 2. The figure shows that the performance of the DL-based estimating CFO is considerably superior to the conventional approach under any channel model. When the SNR is lower than 10 dB, the estimation mean absolute error of the DL-based models is at least one time lower than that of the conventional method. In particular, the lower the SNR, the better the performance of the DL-based models. Under all test SNRs, the performance of the DL-based models is better than the conventional method.The conventional method performs badly, especially at low SNR, whereas the DL-based models maintain sufficient precision and meet the standard criterion of 2%. It can be observed that the DL-based models have the potential to outperform the conventional method while being available at low SNR.

It can be seen from Figure 2 that the performance of the DL-based model is much better than that of the traditional method, whether it is the average, variance or median of absolute error (In Figure 3, CM refers to conventional method, GRU refers to GRU model, and A–F refers to channel model A–F). When the testing and training datasets are in the same channel model, the mean absolute error of the DL-based models estimation will be reduced by 70.54% on average compared with the traditional method.

At the same time, both the conventional method and the DL-based models performance gradually declines as SNR decreases, but the DL-based models declines slowly, indicating that neural networks are more insensitive to noise. All models show performance degradation from channel A to channel F, indicating that estimation performance will gradually decline with increasing channel complexity, which is consistent with the conclusion of conventional communication theory.

4.2. Cross-Evaluation in Different Channel Model

We cross-evaluated the models trained under different channels to further discuss the model’s ability in unknown channel models. We let “X cross-evaluated on Y” denote a model trained on the training set for channel model X and then evaluated on the testing set for channel model Y. In the case where X = Y, this corresponds to conventional training and evaluation. Figure 4 shows the cross-evaluation results. Each subfig represents the estimation performance of seven models under one test channel, while the echo curve corresponds to the model that was trained on one dataset described in Table 3.

Starting with Figure 4a, only models trained with channels A and A–F perform well, with channel A having a slight advantage in the low SNR regime. Despite the fact that channel A is the least severe multipath model, with only one tap, other models that have not been trained on channel A cannot perform well. This is an intriguing phenomenon that will be discussed further below. Moving to Figure 4b, it can be seen that all models, with the exception of the model trained under channel A, can have good accuracy. The model trained under channel B has the best performance, while the model trained under channel F has minor drawbacks. Figure 4c illustrates a similar outcome to Figure 4b, except the model trained in channel B performs worse. Figure 4d indicates that models trained in channels B or C do not perform well in channel D. Figure 4e,f indicate that models trained using the better-case multipath channel model do not perform well when used with the poor-case multipath channel model. The discussion section has a more in-depth exploration of this phenomenon.

Additionally, the model trained under dataset G perform well in each subfigure of Figure 4, demonstrating that DL-based models are capable of making accurate CFO predictions when given enough training data.

4.3. CFO Estimate Range of DL-Based Model and Conventional Method

To estimate the CFO outside the estimation range of the conventional approach, we trained a DL-based model on dataset G. Figure 5a illustrates that when the estimation range of 625 KHz is exceeded, the DL-based model can maintain the same performance as the prior model training. In general, when the frequency offset reaches 625 KHz, the classical method loses estimation capability due to frequency offset estimation inaccuracy induced by phase ambiguity (shown in Figure 5b). At this time, the conventional method of calculating MSE performance will yield very poor results, whereas the DL-based models will still yield good performance. It demonstrates that the DL-based models do not estimate the frequency offset by computing the correlation value as in the traditional method, allowing them to exceed the conventional method’s estimation range and be applied to more application scenarios.

5. Discussion

In Section 4.2, we discuss two interesting phenomena. To starters, the model trained using the worst-case (most severe) multipath channel model can perform well across a wide range of channels for channels B–F. Second, the model trained on channel A appears to be incompatible with channels B–F. It is demonstrated that the model trained in channel A performs poorly in channels B–F, and that the model trained in channel B–F likewise performs poorly in channel A. These findings appear perplexing, so we will propose a hypothesis.

Like all channel models, the channel impulse responses of IEEE802.11n channel models are characterized by the number of delay taps express as Equation (12).

$$h\left[n\right]={\Sigma }_{i=0}^{N-1}{a}_i\delta (n-{\tau }_i)$$

(12)

where N and $a_i$ are the number and the coefficients of the taps and ${\tau }_i$ is the delay time of ith tap. Among the six channel models, A has one delay tap, B has nine, and F has eighteen, etc. From A through F, there are successively more taps. At first glance, each model appears to be a subset of the models that follow.For channel B and C, if $a_i=0$ when $i>=9$, the impulse response expression of channel C is the same as that of channel B. It seems that $A\subset B\subset C\subset D\subset E\subset F$ (this is similar to the description in [29]).Thus, the data from the best-case scenario can be contained in the worst-case (most severe) multipath model, while the first phenomenon can be explained by this idea, the second cannot. Let us then talk about if there is an instance where $a_i=0$ when $i>9$. Channel B and C have a 15 ns and 30 ns rms delay spread, respectively.The rms delay spread expressed as Equation (13).

$${\tau }_{rms}={\left(\frac{{\sum }_{i=0}^{N-1}{\left|a_i\right|}^2{({\tau }_i-\tilde{\tau })}^2}{{\sum }_{i=0}^{N-1}{\left|a_i\right|}^2}\right)}^{1/2}$$

(13)

where $\tilde{\tau }$ is the weighted means of taps delay. ${\tau }_{rms}$ of model B and C can be equal to 15 ns and 30 ns, respectively, if $a_i=0$ when $i>=9$. Because the ${\tau }_{rms}$ of models B and C do not equal each other, the coefficients $a_i$ of these two models cannot be identical. we can draw the conclusion that the hypothesis of $B\subset C$ is incorrect. However, channel C may have the same expression as channel B, resulting in identical distributions, and it’s possible that channel B and channel C have an equal number of taps. When seen in this context, the model trained on channel C can function just as well on channel B. Channels C–F have a similar relationship, so a model developed for worst-case channels can also be used for best-case channels and perform well. When seen in this context, the model trained on channel C can function just as well on channel B. Channels B–F have a similar relationship, so a model developed for worst-case channels can also be used for best-case channels and perform well.

To explain the second phenomena, consider the circumstance of channel A. Channel A has an rms delay spread of 0, which means it can only have one delay tap and its delay time is 0. However, according to Equation (13), because ${\tau }_{rms}>0$ if $N>1$ and $\tilde{\tau }\ne 0$, the number of taps on channel B–F cannot be equal to 1. As a result, there is no single tap option in channels B–F, the weights trained in channel B–F do not perform well in channel A. This explains why the model trained on channel A appears to be incompatible with channels B–F.

6. Conclusions

In this paper, we proposed DL-based models for estimating the CFO of the 802.11n standard, as well as evaluated the estimation performance of DL-based models trained in different channels to adapt to the new channel state and discussed the reasons for our results. Simulation results show that the DL-based models have advantages over the conventional method in both accuracy and range. In addition, we found that the number of taps in channel model B can be a special case of channel model F but not the other way around when the channel complexity grows gradually from channel model B to channel model F. As a result, the training model for the complicated channel can likewise perform well in the simple channel. However, the performance of the model in the actual communication system cannot be assessed since it is challenging to get the frequency offset for the real communication system. We use simulation data to validate the model’s effectiveness, and embedding it into the actual system to evaluate its gain for the entire communication system involves a number of projects, because it involves the problem of synchronization and cooperation between the neural network module and other modules, which limits the application of the method proposed in this paper to some extent.

Finally, for our future work, we plan to try to investigate the gain of the DL-based models to the complete communication system, assess their performance in a real wireless setting using software-defined radio, and explore a general network structure for CFO estimation of OFDM systems.