Identification of Terahertz Link Modulation in Atmospheric Weather Conditions

Abstract

With the rapid increase of wireless connectivity, current spectrum resources are not enough for significant requirements for large data capacity. Research interests are moving towards the high-frequency band in the terahertz range for wider bandwidth. However, multipath scattering and induced time delay, suffered by terahertz links propagating in outdoor weather, lead inevitably to increasing expenses in baseband signal processing. This trades away the advantage of low time latency and high stability, which are commonly considered as important merits of terahertz wireless communication techniques. To reduce the burden in signal processing and explore the feasibility of modulation identification in the terahertz band, a method of wireless link modulation identification is considered as a potential solution. In this work, it is investigated theoretically by employing two kinds of neural networks: the convolutional neural network (CNN) and the long short-term memory network (LSTM). Link deterioration caused by different atmospheric weather is introduced into the theoretical model, and the performance of this method is evaluated. Results show that the identification accuracy of the constructed neural networks can be up to 99%, which means such a method is efficient for identification of the modulation format of terahertz wireless links under different weather conditions. This work demonstrates the feasibility of modulation identification in outdoor terahertz communication scenarios and provides specific references.

1. Introduction

The number of global fifth-generation (5G) mobile subscriptions is predicted to exceed 4.39 billion by 2027 [1], which means there will be a significant increase in wireless connections. This brings the existing sub-6 GHz band to near-saturation point and a larger bandwidth is required urgently [2]. The current spectrum resources are mainly divided into aviation, commerce, military and other fields. The surge in the number of users accessing the internet has further led to congestion in the existing frequency band and reduced link stability. In terms of transmission capacity, the transmission rate of existing frequency bands is gradually becoming unable to meet the high-capacity data transmission needs of emerging industries such as cloud computing and artificial intelligence. A higher frequency band up to terahertz (THz) frequency has been envisioned as a promising candidate to offer ultra-broad bandwidth and support higher-speed data transmission [3]. However, wireless links at terahertz frequencies are more susceptible to absorption and to scattering effects by atmospheric weather and suffer more serious deterioration in link performance [4,5]. In order to offset this influence, methods based on high-power antennae [6], signal repeaters [7], and adaptive signal processing [8] have been proposed and proved to be effective. Modulation identification, as an important signal processing method [9], can recognize different link modulation formats based on the weight matrix of signal features and help to decrease the response time of the entire system finally. It has been considered as a potential solution to reduce the time consumed by the additional processing burden caused by the link deterioration.

Recent years have witnessed rapid growth in the development of methods to enable link modulation identification. This technology can alleviate the impact of waveform changes caused by interference and address the inability in demodulation due to data interference. Examples of classifiers and neural networks have been discussed for many years [10,11], with rapid improvements continuing to be reported. The research scenario in reference [11] is different from that of terrestrial communication, as the authors investigated signal modulation identification in underwater acoustic environments. Mathad et al. [12] presented a signal modulation identification technique using block repetition, which achieved an accuracy of around 99% in a filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) at a sampling frequency of 10 kHz. An accuracy of up to 100% has been achieved in a 150 kHz wireless link by using a decision tree classifier [12]. For wireless links operating at several hundred MHz, an accuracy of over 90% can also be achieved by exploring their autocorrelation or constellation features in a neural network [13,14]. However, the works done by predecessors are mainly based on the low communication frequency band, and there is very little research on modulation identification in the terahertz frequency band. In addition, the modulation identification of terahertz signals, which takes the atmospheric environment into account as an important factor, has never been carried out. These research gaps are not conducive to the infrastructure construction of 6G or 7G networks. Considering the problems caused by resource congestion and the prospects for expanding communication frequency bands, it is necessary to study the modulation identification technique of terahertz signals in atmospheric environments. Therefore, this paper carries out this original work for the first time, focusing on the feasibility and effect of modulation identification in outdoor terahertz wireless scenarios.

In this work, we report an attempt to bridge this research gap, with the investigation of a modulation identification method in a terahertz wireless link propagating under rain, fog, haze and wind weather conditions. This work aims to research the feasibility and effect of modulation identification in terahertz wireless communication, which is conducive to alleviating the burden of terahertz signal processing under severe weather conditions. Similar work has never been conducted before, but we think such comprehensive research is really necessary for the outdoor applications of terahertz wireless communication techniques. The method proposed in this work and the relevant conclusions obtained provide valuable references for the future construction of terahertz base stations. This method can be extended to other application scenarios, such as indoor or space–ground terahertz transmission.

2. Channel Model

2.1. Atmospheric Model

The theoretical model constructed in this work compromises link propagation under four kinds of weather conditions—clear, rainfall, fog and haze, and wind. In clear weather, gaseous absorption plays a main role, apart from the free space path loss (FSPL) due to diffraction. There is no multipath or misalignment caused by weather particles and wind-induced turbulence bubbles. The gaseous absorption is often caused by water vapor and oxygen in the air and can lead to serious link interference when the operating frequency is close to absorption peaks. It can be modeled by the international telecommunications union (ITU) model [15] and can be expressed by equation γ = 0.1820 f(N″_Oxygen(f) + N″_WaterVapor(f)) [15] with parameter f as the operating frequency [GHz], and N″_Oxygen, N″_WaterVapor as the imaginary part of the associated negative refractive index of oxygen and water vapor, respectively. Values of these parameters depend on atmospheric pressure, water vapor density and temperature. In this work, this model is considered under all the weather conditions with the proposed water vapor density set to 12.3, 12.3, 7.7 and 7.7 g/m³ for rain, fog and haze, clear weather and wind, respectively. The corresponding atmospheric pressure and temperature are chosen to be 1.0037 × 10⁵ Pa and 287.63 K, respectively. Environmental parameters such as link distance are shown in

Table 1. Weather model parameters.

	Weather	Clear	Rain	Fog and Haze	Wind	Remark
Parameter
Distance (km)		1	1	1	1	/
Atmospheric pressure (Pa)		1.0037 × 105	1.0037 × 105	1.0037 × 105	1.0037 × 105
Temperature (K)		287.63	287.63	287.63	287.63
Water vapor density (g/m3)		7.7	12.3	12.3	7.7
Rainfall rate (mm/h)		/	25	/	/	heavy rain
Fog concentration (g/m3)		/	/	0.5	/	dense fog and heavy haze
Haze particle density (1/cm3)		/	/	7000	/
Wind speed (m/s)		/	/	/	15	strong wind

. The attenuation caused by these parameters is considered to be static, due to the spatial- and temporal-average algorithms on the receiver side in typical wireless communication and sensing systems.

2.1.1. Rainfall Weather

Mie scattering theory and the ITU-R model are both commonly used approaches to calculate terahertz link degradation in falling rain [16,17]. The former can provide a better agreement with measurements when an exact distribution of raindrop particles is offered. The latter is proposed based on a wide range of measurements and regarded as an empirical model, which is employed in our calculation due to its wider applicability. In the standard defined by the ITU-R, attenuation by falling rain can be expressed as γ_R = kR^α [dB/km], with the parameter R as the rainfall intensity [mm/h]. Coefficients k and α are frequency-dependent and polarization-dependent, respectively, with their values can be obtained in the ITU-R P.838-3 protocol [17]. In the following calculation, we set a link distance of 1 km in falling rain and a rainfall rate of 25 mm/h corresponding to heavy rain. In the simulation, we consider it as a static parameter.

2.1.2. Fog and Haze

As a type of aerosol particle, fog droplets suspend in air and can have serious absorption effects on terahertz frequencies [18]. The attenuation caused by fog can be calculated by equation γ_c (f, T) = K_l (f, T)M [19], with parameter f as the frequency [GHz], T as the temperature [K], and M as the density of liquid water in fog [g/m³]. Parameter K_l is the specific attenuation coefficient of liquid water with its dielectric constant predicted by the double Debye model. A situation of dense fog with a fog concentration of 0.5 g/m³ is considered in the model, which leads to a visibility of 50 m [19].

The diameter of haze droplets is two orders of magnitude smaller than that of fog particles. Its number density lies between 10 and 1000/cm³ [18]. When foggy weather occurs, haze particles (such as PM 2.5) in the air can be adsorbed onto the surface of fog particles, and fog and haze weather finally forms. Attenuation caused by haze can be conducted from equation A_s(f) = exp(∑_j k_s^j (f)r) [18]. Parameter k_s^j is the scattering coefficient of particles of different sizes, and r refers to the radius of haze particles. In the case of heavy haze, r is approximately 0.2 μm. k_s^j = N^j_s σ^j_s is particle density- and refractive index-dependent. Here, parameter N^j_s is the particle density of haze, and can be 7000/cm³ for heavy haze [18]. Parameter σ^j_s is the Rayleigh scattering cross-section by the haze particle, which can be obtained when the refractive index of haze particles is ready [20]. These parameters will remain unchanged to form a static attenuation.

2.1.3. Wind

Tall towers for communication base stations have been increasing with the requirement for reliable data transmission and wide coverage. They are generally sensitive to wind loads. Wind excitation induces fluctuating stresses on the tower leading to antenna tilting. This results in a beam deviation between transmitter and receiver, and then problems such as beam jitter will occur [21]. Therefore, wind-induced attenuation is also introduced into the loss assessment as one of the atmosphere-induced factors. The wind speed in the natural environment is generally between 1.6 m/s and 13.6 m/s. By calculating the attenuation caused by the wind-induced inclination angle, the path loss in the wind environment can be obtained by equation g(θ) = 20log[u′/(2J₁(u′))]. Parameter u′ is a variable related to signal wavelength, antenna diameter, and tilt angle [21]. For terahertz antennas, their diameters are set to be a common value of 0.16 m. Parameter J₁ refers to solving the first kind of Bessel function for the variable. As shown in Table 1, the simulated link distance is set to be 1 km, as with other weather conditions. In the introduction of wind-induced attenuation, wind speed is set to be 15 m/s in this model as strong wind. This wind speed will be considered as a constant to obtain static (averaged) performance.

2.2. Neural Network Model

A neural network, as a tool with self-adaptive processing capability, forms internal rules by training a large amount of data. It can achieve goals of classification, identification, and prediction of new data with the signal processing time shortened. Then, the overall time latency of the system is reduced. As the most commonly used network, the convolutional neural network (CNN) plays an important role in image processing, object recognition, emotion recognition, and so on [22,23]. It also serves as an auxiliary tool to assist research in other fields, such as the metamaterial [24].

The CNN network used in this work contains one input layer, seven convolution kernels, one discarding layer, two fully connected layers, one activation layer, and one output layer as in Figure 1a. Each convolution kernel consists of one convolutional layer, one normalization layer, one nonlinear activation layer, and one pooling layer. There are 64 filters used in each convolutional layer. The input and pooling layers are designed with size matrices of 2 × 1024 × 1 and 1 × 2, respectively. A NVIDIA Geforce RTX 2060 GPU is used to train the CNN network with an Adam optimizer employed. The regularization parameter and the initial learning rate are both set to be 0.0001. To weaken the overfitting phenomenon, the fading period and fading factor are set and listed in

Table 2. Training parameters of CNN and LSTM networks.

Parameter	CNN	LSTM
Optimizer	Adam	Adam
Initial learning rate	0.0001	0.0001
Regularization parameter	0.0001	0.00001
Number of rounds	65	30
Fading period	40	/
Fading factor	0.1	/
Training environment	GPU	GPU
Multi-GPU parallel processing	No	No

.

The long short-term memory network (LSTM) network is a new type of network based on the evolution of time series models. It has a better memory mechanism and can make a better usage of past and future data. It is more suitable for object recognition based on time series data instead of image data by CNN. The LSTM architecture consists of one sequence input layer, six bidirectional LSTM layers, six normalization layers, six nonlinear activation layers, one discarding layer, one fully connected layer, one activation layer, and one output layer as shown in Figure 1b. Since the input of the LSTM network is a data sequence, the multidimensional array should be transformed to be 3-dimensional before inputting. The construction and training of neural networks are carried out on MATLAB R2021b.

For the network training of LSTM, the same GPU environment and optimizer are used. Due to the different allocation strategies of CNN and LSTM to data weights, different parameter settings are adopted to weaken overfitting as shown in Table 2. In terms of learning parameter settings, the initial learning rate of LSTM is 0.0001. In particular, due to their difference in network construction and total number of parameters, the overfitting cannot be mitigated with an identical regularization parameter. It is set to be 0.00001 in LSTM network with one order of reduction compared to CNN, which helps to avoid overfitting. In addition, since the LSTM does not need such a large number of training rounds as CNN, no fading factor is set in the training process.

3. Simulation and Discussion

In this work, a baseband signal of 10 GHz is simulated and upconverted to 120 GHz, which has been confirmed for data transmission over a long distance up to several km [25]. Five modulation schemes, namely binary-phase shift keying (BPSK), quad-phase shift keying (QPSK), eight-phase shift keying (8PSK), 16-quadrature amplitude modulation (16QAM), 64-quadrature amplitude modulation (64QAM) are selected and have been reported to achieve large data capacity [26,27]. In order to reflect the influence of signal-to-noise (SNR) level, different values are considered and changed by adjusting the transmitter output power, antenna gain and/or receiver sensitivity [28,29]. Specific parameter settings for path losses due to atmospheric weather are given in Section 2. The simulation and signal processing of terahertz links are carried out on MATLAB R2021b.

To demonstrate the impact caused by harsh weather, a clear weather condition is considered and used for comparison. Usually, the humidity in clear weather is much lower than that in rain, fog and haze, where it is measured to be around 60% (96% in rain and fog and haze weather, 60% in wind weather) [4]. The attenuation suffered by the 120 GHz link in clear weather is around 1.62 dB, which is much smaller than that due to other atmospheric environments. Attenuation caused by different weather conditions will be introduced into the THz simulation link as additive Gaussian white noise (AWGN). Other losses caused by internal hardware are not considered, as they are difficult to measure. These channel attenuations are calculated using models in Section 2.1 and incorporated into the experiment to directly attenuate the simulated terahertz signal, ultimately resulting in different path gains. We will use identification accuracy as an evaluation indicator for the proposed method.

In terms of experiments, we assume that the overall process is as follows. The CNN and LSTM models used operate at the receiving end. The transmitted signal is attenuated through the atmospheric channel model and reaches the neural network at the receiving end. The neural network recognizes the modulation type of the signal and assigns type labels, which will ultimately assist in subsequent data processing. The specific object processed by these neural network models is the IQ constellation of the signal. The neural network utilizes known constellation data for training to obtain constellation laws of various modulation formats, ultimately achieving the goal of using constellation information to complete modulation identification. Due to the lack of terahertz signal datasets in open-source datasets related to constellation maps, the relevant constellation data is generated by MATLAB software. The main modulation types used are M-PSK and M-QAM, mentioned above. In each modulation scheme, there are 5000 frames generated, each containing 1024 samples. Each transmission frame contains 128 symbols (i.e., 128 spf), and we set the symbol rate not to change with the modulation format. Finally, there should be a total number of 25,000 data frames and a four-dimensional data matrix of [2, 1024, 1, 25,000]. We choose 80% of them for network training, 10% for validation, and 10% for testing, which is a common setting in data training. The accuracy of identification is calculated by comparing the matching degree between the real label and the predicted label, which presents the real modulation formats and identified modulation formats, respectively.

3.1. Performance under Different Weather Conditions

Comparing to microwaves, terahertz with large capacity is more sensitive to the impact of low SNR (such as 13 dB) under the massive amount of information. Therefore, this is an additional challenge for terahertz wireless communication. The simulation results in Figure 2 illustrate the performance of the identification method with CNN and LSTM networks employed, for a single-frequency (120 GHz) link propagating under different weather conditions and an SNR value of 13 dB. The value in each grid represents the number of one real label identified to be itself or other labels. If we take the first line of grids as an example, the first grid from the left side refers to the number of 16QAM labels which are identified to be 16QAM, and the second grid is that identified to be 64QAM.

We first explore the performance of this method by using the CNN network and observe the highest accuracy in identification of the BPSK modulation format under all the weather conditions (about 90%), which proves that this method is more efficient for lower-order modulation schemes. This is consistent with previous work results [26]. We also note that the accuracy is lowest in rainy weather, regardless of the modulation format. This is not surprising, as the terahertz link suffers a higher deterioration due to rain [5]. In the recognition process of all modulation formats, 16QAM and 64QAM are the most easily confused with each other, and QPSK is the most easily recognized as 8PSK. We believe this is related to the distribution of points in the constellation diagram.

The most surprising aspect of Figure 2 is the higher accuracy from using a LSTM network under all the weather conditions and for all the modulation formats, which is also confirmed by the performance comparison based on average accuracy in the last table for each situation. It can also be seen intuitively from the confusion matrix that the confusion degree of modulation formats in LSTM is weaker than that of CNN. In addition, the situation where QPSK was mistakenly identified as 8PSK has been greatly corrected, and the degree to which M-QAM was mistakenly identified as M-PSK has also been weakened. This suggests that the LSTM network can be more a potent algorithm in assisting the method of terahertz modulation identification. This can be understood from the design of the networks, as the LSTM can discard invalid data automatically by using a bidirectional memory algorithm, which is unavailable in the CNN network algorithm.

To improve the accuracy of the CNN network, there have been several methods using external algorithms (such as dynamic threshold updating) proposed and demonstrated [27]. They are based on signal preprocessing with a sacrifice of system complexity, which leads to additional computation. We use a voting algorithm to avoid such a drawback with its vote number determined by the amount of data [30,31]. There are 25,000 data frames in our simulation, which means that at least a five-vote enhancement algorithm should be required to get enough voting efficiency. In this work, we choose a seven-vote algorithm in the simulation.

Using the CNN network with the voting enhancement algorithm (CNN enhancement), an obvious improvement in the identification accuracy can be observed when comparing Figure 3 and Figure 2a–d. From the last table, the average accuracy is increased to 64.32% in clear weather and to around 58% under the other three weather conditions. This means the voting algorithm is effective at improving the performance of the network. With the assistance of voting algorithms, the confusion of modulation formats in CNN is significantly reduced, and its ability to distinguish different modulation formats is stronger than that of a single CNN network. However, the CNN enhancement algorithm is still not enough when compared with the results from the LSTM network (Figure 2e–h), which can be more than 70% always. These research results provide valuable references for the construction of future base stations. For example, if the construction cost only allows for the use of one neural network, LSTM is the more feasible one.

To see the difference between the real and predicted values, we calculated the mean square error (MSE), root mean square error (RMSE) and mean absolute percentage error (MAPE) of LSTM and CNN (using voting algorithms) under various weather conditions, as shown in

Table 3. MSE, RMSE and MAPE of models.

Variable	Model	Clear Weather	Rain	Fog and Haze	Wind
MSE	CNN (Voting)	0.3568	0.4332	0.4104	0.4144
	LSTM	0.2084	0.248	0.28	0.2524
RMSE	CNN (Voting)	0.5973	0.6582	0.6406	0.6437
	LSTM	0.4565	0.4979	0.5291	0.5024
MAPE	CNN (Voting)	35.68%	43.32%	41.04%	41.44%
	LSTM	20.84%	24.80%	28.00%	25.24%

. These variables can indirectly reflect the performance of the model, where MSE = (∑(y_p − y_r)²)/n, RMSE = ((∑(y_p − y_r)²)/n)^1/2, MAPE = 100% × (∑(|y_p − y_r|/y_r))/n; n is the total quantity, y_p is the predicted value, and y_r is the real value (y_p, y_r ∈ [1, n]).

In Table 3, the value of each variable of LSTM is better than that of CNN. The MSE and RMSE of LSTM are, on average, 38.8% and 21.82% lower than those of CNN, and the MAPE is on average 38.8% lower than that of CNN. These results indicate that the difference between the real values and the predicted values provided by LSTM is smaller and that the LSTM model has a more precise identification ability and can be assessed as a better model.

A big problem for the neural-network-based identification method is its weak generality capability. This is because the networks are mostly trained with a fixed SNR, and they can only be applied to recognize the modulation formats with the corresponding SNRs [32]. However, due to the serious degradation suffered by terahertz wireless links in outdoor scenarios, the SNR of the identification stage is always varying, resulting in a different SNR level in the training stage. Besides, a degraded performance of neural networks at low SNR levels has been reported [33]. Thus, the efficiency of the identification method with neural works should be evaluated under different SNR levels.

Table 4. Results from CNN and LSTM networks.

SNR	Network	Clear Weather	Rain	Fog and Haze	Wind
13 dB	CNN	61.56%	51.32%	54.32%	55.76%
	LSTM	79.16%	75.20%	72.00%	74.76%
	CNN (Voting)	64.32%	56.68%	58.96%	58.56%
80 dB	CNN	80.48%	78.60%	80.80%	79.84%
	LSTM	99.88%	99.92%	100%	99.64%
	CNN (Voting)	82.04%	80.96%	80.84%	80.36%

shows averaged identification accuracy values at a low and a high SNR level. Here, we set the high level as 80 dB, because the identification accuracy can be upgraded to 100%. This value is difficult to achieve in reality, but we think it is still available when large power output, high-gain antenna and ultra-low noise amplifier are realized in future.

With a high SNR level of 80 dB, the average identification accuracy of all three network algorithms increases, and it can be almost 100% for the LSTM network, which is much better than that of the CNN network. This means the LSTM can offer a better identification performance always, due to the advantages in its algorithm, as demonstrated above. By calculating the MSE, RMSE, and MAPE at 80 dB, it can be observed that the performance of both models has been improved at a high SNR. The LSTM model still has a stronger identified capability than CNN and can even be considered an excellent model. It should also be noted that the accuracy of LSTM in rain, fog and haze, and wind weather is close to that in clear weather with the high SNR level, which indicates that the LSTM network has a potential to overcome the degradation caused by adverse weather conditions.

Currently, we consider that various environments occur independently, but the actual weather environments may occur simultaneously—for example, strong winds may be accompanied by rainfall. We believe this can lead to more serious identification errors. Therefore, we will carry out more work in different scenarios in the future to better align with the actual situation.

3.2. Performance at Water Vapor Absorption Peaks

One of the key characteristics of terahertz wireless links is the atmospheric absorption they suffer. This is very strongly frequency-dependent, especially when links are at frequencies close to the absorption resonances of the water vapor molecule [4,5]. What about the efficiency of this method if the link operates at such frequencies? In this sub-section, a preliminary study is conducted on a wireless link at 183 GHz, which corresponds to an absorption resonance [4,34]. Simulation results based on both CNN and LSTM networks in clear weather and rain are shown in Figure 4, for a high SNR level of 80 dB.

The identification accuracy of the CNN enhancement algorithm in rain is close to that in clear weather, with an identical average of 79%. Moreover, a 100% accuracy in both weather conditions can always be achieved by using the LSTM network, no matter the modulation scheme. This means this modulation identification method can overcome the deterioration caused by water vapor absorption by increasing the SNR levels, which is consistent with our discussion in Table 4.

4. Conclusions

Time consumed in baseband signal processing is usually considered as an important factor in evaluating the performance of wireless communication systems, especially when they operate in the terahertz frequency band to achieve a low time latency in the range of milli-seconds and micro-seconds. However, in outdoor scenarios, terahertz links are more vulnerable to the absorption and scattering effects caused by atmospheric weather than micro- or millimeter-wave setups. This degrades the efficiency of baseband signal processing and increases the time consumed, which can be alleviated by a prior identification of link modulation formats.

In this work, a theoretical model, combining particle scattering theory and ITU models, is presented to investigate the efficiency of this method in different weather (rain, fog and haze, and wind). Two kinds of neural networks (CNN and LSTM) are employed, and the performance of this method is evaluated. We observe that introducing the LSTM network can offer a higher accuracy than the CNN network and can achieve an accuracy close to 100% in adverse weather. This is close to the situation in clear weather, which means that introducing LSTM can overcome the deterioration of outdoor weather. The voting enhancement algorithm is employed in the CNN network and can get an obvious improvement in accuracy, even though it is still lower than that of the single LSTM. We also find that this method still works when a terahertz link operates at critical frequencies (such as 183 GHz), corresponding to an absorption resonance by water vapor.

These research results will help expand the practical application scenarios of neural networks, and they also provide a valuable reference for the construction of terahertz base stations under outdoor conditions. This work is the first to demonstrate the effectiveness of neural network algorithms in modulation format identification of terahertz links propagating in atmospheric weather, indicating that the proposed approach is feasible for assisting terahertz communication in outdoor environments. Neural networks can adjust their structure according to actual needs and even achieve multi-network fusion, so we believe that this approach has great potential to more effectively improve terahertz communication performance. We hope our findings can prompt more efforts in terahertz communication system designs, such as signal processing and physical-layer security.