Automatic Modulation Classification for Underwater Acoustic Communication Signals Based on Deep Complex Networks

Automatic modulation classification (AMC) is an important method for monitoring and identifying any underwater communication interference. Since the underwater acoustic communication scenario is full of multi-path fading and ocean ambient noise (OAN), coupled with the application of modern communication technology, which is usually susceptible to environmental influences, automatic modulation classification (AMC) becomes particularly difficult when it comes to an underwater scenario. Motivated by the deep complex networks (DCN), which have an innate ability to process complex data, we explore DCN for AMC of underwater acoustic communication signals. To integrate the signal processing method with deep learning and overcome the influences of underwater acoustic channels, we propose two complex physical signal processing layers based on DCN. The proposed layers include a deep complex matched filter (DCMF) and deep complex channel equalizer (DCCE), which are designed to remove noise and reduce the influence of multi-path fading for the received signals, respectively. Hierarchical DCN is constructed using the proposed method to achieve better performance of AMC. The influence of the real-world underwater acoustic communication scenario is taken into account; two underwater acoustic multi-path fading channels are conducted using the real-world ocean observation dataset, white Gaussian noise, and real-world OAN are used as the additive noise, respectively. Contrastive experiments show that the AMC based on DCN can achieve better performance than the traditional deep neural network based on real value (the average accuracy of the DCN is 5.3% higher than real-valued DNN). The proposed method based on DCN can effectively reduce the influence of underwater acoustic channels and improve the AMC performance in different underwater acoustic channels. The performance of the proposed method was verified on the real-world dataset. In the underwater acoustic channels, the proposed method outperforms a series of advanced AMC method.


Introduction
Automatic modulation classification (AMC) plays an important role in underwater acoustic communication, especially in non-cooperative communication. AMC can be used in monitoring and identification of communication interference, such as spectrum surveillance and electronic countermeasure [1]. Modern underwater platforms (such as submarines, autonomous underwater vehicles (AUV), and underwater unmanned vehicles (UUV)) are in urgent need of advanced AMC technology.
AMC is the intermediate process of signal detection and demodulation [2], occupying a very important position in signal processing technologies. Currently, most of the research on AMC focuses on radio signals (e.g., radar, cellular, satellite), and there is relatively little research on the classification of underwater communication signals. However, the demand for AMC in underwater acoustic communication is increasingly urgent with the development of modern communication technology. AMC of underwater acoustic communication signals is an important approach to the acquisition and analysis of target 1.
We adopted DCN to AMC of underwater acoustic communication signals to adequately learn features from the raw complex baseband signals.

2.
Two physical signal processing layers were constructed based on DCN to improve the AMC performance, including a deep complex matched filter (DCMF) and deep complex channel equalizer (DCCE). The DCMF can help to remove noise from the signals, and the DCCE can reduce the influence of multi-path fading effectively. DCMF and DCCE were embedded in DCN to improve the AMC performance. 3.
The influence of underwater acoustic channels on the signals was fully considered, and different underwater acoustic channels were simulated by using the real-world ocean observation dataset and ambient noise. The effectiveness of the proposed method was verified in different underwater acoustic channels and real-world dataset.
This paper is organized as follows. Section 2 presents a review of underwater acoustic communication signals and channels. Then it introduces the proposed AMC method of underwater acoustic communication signals based on DCN. In Section 3, we evaluate the performance of the proposed method with simulation experiments. Finally, the conclusion of the paper is given in Section 4.

Underwater Acoustic Communication Signals and Channel
where A is the amplitude of the signal, f c is the carrier frequency offset, φ is the phase offset of carrier frequency, n is the symbol index, N is the total number of symbols, p[t] is the baseband pulse shaping filter, T s is the symbol period, e jθ n and s(n)e jθ n map the transmitted symbols of PSK and QAM, respectively.

Underwater Acoustic Channel
In the real-world underwater acoustic communication scenario, the influence of underwater acoustic channels on communication signals mainly includes two aspects: multi-path fading and OAN, as is shown in Figure 1. (1) Multi-path fading Multi-path propagation often exists in underwater acoustic communication. In a multi-path environment, the received signal can be represented as the superposition of a number of time-delayed and amplitude-attenuated versions of the transmitted signal. A typical underwater acoustic channel with multi-path fading can be seen as a filter whose impulse response function is h(t, τ), in which τ is the delay time. The impulse response reflects the properties of the multi-path fading channel and can be expressed as where K is the total number of paths, δ(·) is the delta function, a k and τ k are the attenuation, and the delay of the k-th path.
Since the source and receiver are usually not stationary and underwater acoustic reflection boundaries are unstable in most cases, multi-path fading is often accompanied by Doppler shift. We consider Doppler shift caused by relative motion in multi-path propagation. In a multi-path fading channel, each path has an independent Doppler shift factor f dk , which can be expressed as where f c is the carrier frequency of the transmitted signal, and v k is the radial velocity of the source relative to the receiver of the k-th path.
Assume the transmitted signal is s(t), then the received signal x(t) propagates through underwater acoustic channel can be expressed as where n(t) is the additive noise of the channel.
(2) Ocean ambient noise Ocean ambient noise (OAN) is an additive interference in underwater acoustic channels. The composition of the OAN is very complicated and full of impulsive interference due to numerous noise sources, such as ship-radiated noise, industrial noise, wind noise, biological noise, etc. The reasons mentioned above make the OAN cannot be simulated accurately using white Gaussian noise. AMC method based on Gaussianity assumptions will suffer degradation in their performance to a low level. We use real-world OAN as the additive noise of underwater acoustic channels to enhance the robustness of the proposed AMC method in real-world underwater acoustic communication scenarios.

DCN-Based AMC Method
In this section, we presented the proposed AMC method for underwater acoustic communication signals based on DCN. DCMF and DCCE were proposed to improve the performance of DCN for AMC. We used the raw I/Q signals as the input of the DCN without any feature extraction, by which the DCN was forced to learn features from highdimension complex time sequences. The framework of the proposed AMC method is illustrated in Figure 2.

Clean signals
Noise Received signals

Clean signals
Noise

Complex kernels
Received signals

Deep Complex Matched Filter
The matched filter is often used to improve the signal-to-noise ratio (SNR) of the received signal and optimize the quality of communication, which is an important module in communication. We proposed a deep complex matched filter (DCMF) to improve the SNR of the signals and optimize the classification performance. The DCMF in Figure 2 is made up of a modified CConv layer, which is optimized by an objective function.
The proposed DCMF has three input channels and three output channels. The first input channel of DCMF accepts received signals (x(t)) which are affected by an underwater acoustic channel (multi-path fading and OAN), x(t) propagates through the network, eventually producing categories. The second input is the clean received signals without noise (x c (t)), which is only affected by the multi-path fading. The last input channel accepts additive noise (n(t)). Clean received signals without noise (x c (t)) and the additive noise n(t) are used to optimize the DCMF. The outputs x 1 (t), x c1 (t), and n 1 (t) are the filtered signals corresponding to the three inputs, respectively. The forward propagation of DCMF can be formulated as where the f (·) is a linear complex activation function. * represents the CConv operation, W 1 and b 1 are the complex weight and complex bias of the DCMF. The CConv kernels of the DCMF can be seen as a matched filter bank. In the forward propagation of the DCN, the three inputs of the DCMF are filtered by the filter bank, and the three inputs share the same filters. In the backpropagation, the parameters are updated by the gradient of the objective function, as is shown in Figure 2. The objective function is the SNR increment from input signals to output signals. The DCMF is trained to maximize the objective function. The training process can be formulated as a minimization process: arg min where θ dcm f is the trainable parameters of DCMF, F dcm f is the objective function, γ in and γ out are the SNR of input and output signals, respectively. Note that each output of DCMF is made up of a group of one-dimensional filtered signals and each of them corresponds to one CConv kernel of DCMF, so the γ out is calculated at all dimensions. On the other hand, Equation (7) can be converted to a more computationally appropriate format: arg min

Deep Complex Channel Equalizer
The multi-path fading in the underwater acoustic channels will cause ISI, which will degrade the performance of AMC. We propose DCCE to overcome the influence of multipath fading by reconstructing the transmitted signal s(t) from the signals distorted by the multi-path fading. The DCCE is designed to accept the outputs of DCMF, and there are two input and output channels of DCCE. The first input channel accepts x 1 (t), while the second accepts the sum of x c1 (t) and n 1 (t). The outputs x 2 (t) and x n2 (t) are the equalized signals corresponding to the inputs, respectively. There are several kernel boxes in DCCE, which are independent of each other. Each box accepts one feature map of the input data, which means that the number of boxes are equal to the number of kernels in DCMF. Two CConv layers were designed in one box, and each of them has one complex kernel. The difference between DCCE from ordinary CConv layer is that the kernels of the DCCE are individual, we only perform convolution operations in the time direction of the input signal. Each kernel connects to one output channel of DCMF, as is shown in Figure 2. The processing of DCCE can be formulated as where M is the number of boxes in DCCE, the superscript i means the i-th feature map of input data or the i-th box in DCCE, W i 2a , W i 2b , b i 2a , and b i 2b are the complex weight, and complex bias of DCCE in the i-th box, f (·) is a linear complex activation function.
The transmitted signals s(t) are processed by an individual CConv layer. The number of kernels of this CConv layer is M, and the width of each kernel is 1. This CConv layer was designed to map s(t) several feature maps to match the dimension of x n2 (t), and the randomly initialized complex kernels can ensure that each feature map is not equal to another, including amplitude and phase. The output of this CConv layer is s 1 (t). The objective function is the mean square error (MSE) of x n2 (t) and s 1 (t): where θ dcce is the trainable parameters of DCCE, F dcce is the objective function, the objective function is optimized to minimize the MSE of x n2 (t) and s 1 (t).

Training Method
In the training process, x c (t), n(t), and s(t) are used to optimize the DCMF and DCCE. The received signals x(t) and the corresponding true labels y are used to optimize the rest trainable parameters, which are noted as θ r . The loss function used to optimize θ r is cross entropy: where N c is the number of classes, y p is the predicted label, i is the i-th element of the label. θ dcm f , θ dcce and θ r will be updated per epoch. Each of θ dcm f and θ dcce will be frozen when the corresponding loss stop decreases. The training will be stopped when the loss of θ r shows no improvement or the training step reaches the maximum iterations, as is shown in Algorithm 1.
In the predicting process, only the first input channel of DCMF is opened, and the received signals x(t) come from the testing dataset will be tested. Then the AMC accuracy will be obtained by the predicted labels and the true labels.

Experiments and Discussion
In this section, extensive simulations were conducted to verify the performance of the proposed AMC method based on DCN: (1) Experimental dataset under various conditions were built by simulations.
(2) We analyzed the influence of underwater acoustic channels on AMC performance.
(3) We compared the AMC performance between DCN and classical real-valued DNN.
(4) We analyzed the performance of DCMF by visualizing the kernels, then the performance gain of the proposed AMC method was verified by a series of contrastive experiments, including verifying real-world underwater acoustic communication signals.
(5) The AMC performance comparison between the proposed method and some other AMC methods were carried out. (6) Comparison experiments were carried out to analyze the limitations of the proposed method.
The results in this section were the average values over multiple runs.

Signals Generation
We considered six commonly used modulation types, including BPSK, QPSK, 8PSK, 16QAM, 32QAM, and 64QAM. The parameters for simulation are presented in Table 1. The SNR ranges from −9 dB to 21 dB with an interval of 3 dB. The received signals were expressed as the sampled complex baseband, the dimension of each signal sample is 6000 × 2, and the duration is 0.5 s. 10,000 signals are generated for each modulation type at each SNR, which contains 5000 training signals, 2000 validation signals, and 3000 test-ing signals, making a total of 330,000 training signals, 132,000 validation signals, and 198,000 testing signals.

Underwater Acoustic Channel
A real-world underwater acoustic communication scenario was considered in the following experiments. The ocean observation dataset of the chosen area came from the global gridded Argo dataset 2020 (BOA_Argo) [39]. We chose an area of the ocean near the geographic coordinate of 26.5 • N, 127.5 • E, as is shown in Figure 3. The dataset contains temperature, salinity, and static pressure for different months; we selected the data in January. The sound velocity profile can be calculated from temperature, salinity, and pressure by where T is the temperature, S is the salinity, and P are the static pressure, which is positively related to the depth. The depth of the chosen area is 460 m, and the sound velocity profile is shown in Figure 4. As we can see that the sound gradient in this area presents positive and negative at different depths. We put one transmitter (T x ) and two receivers (R x1 and R x2 ) in the underwater channel. The horizontal distance between the transmitter and the two receivers are 3 km and 5 km, respectively. The depths of the transmitter and receivers are 30 m and 80 m, respectively. The transmitter moves towards the receivers at a horizontal speed of 5 m/s, and the receivers keep stationary. Thus, we get two multi-path fading channels (Ch1 and Ch2) with different impulse responses. The time delays and amplitudes of the two channels are illustrated in Table 2, in which the modules of the amplitudes are normalized to [0,1]. We built several underwater acoustic channels based on Ch1 and Ch2 using realworld OAN and AWGN as the additive noise, respectively, in which AWGN is used as a benchmark. The total duration of the noise is 6 h. Figure 5 has shown the spectrogram of one OAN sample.

Experiment Results Analysis
In all classification experiments, we used classification accuracy to evaluate the classification performance. We just calculated the accuracy at each SNR point; the whole symbol rate range and roll-off value range were covered in each classification task. We tested each modulation type at each SNR point; the accuracy of one modulation type at one SNR point is Acc 1 . Furthermore, the accuracy of all modulation types at one SNR point (Acc 2 ), and the average accuracy of all modulation types at all SNR points (Acc 3 ) are calculated from Acc 1 . The calculation method can be described as where N m is the number of modulation types, N snr is the number of SNR points.

Influence Analysis of Underwater Acoustic Channel
We first analyzed the influence of underwater acoustic channels on communication signals and the performance of AMC. An example of the underwater acoustic channel with multi-path fading (Ch1) and OAN influencing a QPSK signal is illustrated in Figure 6. It is clear that underwater acoustic channel has a great influence on communication signals, especially multi-path fading.
The influence of underwater acoustic channels on the performance of AMC was analyzed through a series of contrastive experiments, in which multi-path fading effect and additive noise were considered individually. We trained an ordinary DCN without DCMF and DCCE in this section as a benchmark for subsequent experiments. Figure 7 has shown the AMC performance comparison between different channels, which include AWGN channel, OAN channel (OAN), two channels include multi-path fading and AWGN (Ch1+AWGN,  Ch2+AWGN), and two channels include multi-path fading and OAN (Ch1+OAN and Ch2+OAN). We can see from Figure 7: (1) There is an obviously positive correlation between classification accuracy and SNR.
(2) Acc 3 in AWGN channel is 14.7% higher than that in OAN channel.
Similar results can be observed when using OAN as the additive noise, in which Ch1 and Ch2 reduce the Acc 3 by 17.6% and 18.9%, respectively. This illustrates that OAN has a greater influence on the AMC performance than AWGN, especially at low SNR. The multi-path fading effect can reduce the AMC performance significantly, even at high SNR.  We also analyzed the performance of each modulation type individually in the underwater acoustic channel. Figure 8 has shown the confusion matrix charts of each modulation type in the underwater acoustic channel (Ch1+OAN). It is obvious that BPSK can be identified correctly, and the mean accuracy of PSK is higher than QAM. QPSK and 8PSK are misclassified from each other. 16QAM, 32QAM, and 64QAM are also misclassified for each other, especially 16QAM and 64QAM. The AMC accuracy improves gradually with the increase in SNR. We can conclude from the classification results that the underwater acoustic channel greatly influences the performance of AMC, especially on the high-order modulation types. The main classification errors occurred in the in-class identification of PSK and QAM.

Comparison with Real-Valued DNN
We investigated the performance of DCN by comparing DCN with classical realvalued DNN. Two DNNs with different numbers of hidden units are built for contrastive experiments. Since DCMF and DCCE are unsuitable for real-valued DNN, an ordinary DCN without DCMF and DCCE is used for a fair comparison. The first DNN (DNN-1) is structurally similar to the DCN, and they have the same number of hidden units; the second DNN (DNN-2) is a scaled-up version of DNN-1 to keep the actual complexity and trainable parameters equal to that of the DCN. The contrastive experiments were carried out with the AWGN channel and the underwater acoustic channel (Ch1+OAN), respectively. Figure 9 has illustrated the performance comparison of DCN, DNN-1, and DNN-2 under different conditions. It can be observed that the DCN has an advantage over DNN, both in the AWGN channel and underwater acoustic channel. Acc 3 of the DCN at all SNR is higher than DNN-1 and DNN-2 at 5% and 3.4%, respectively, in the AWGN channel. In the underwater acoustic channel, DCN has a larger advantage, Acc 3 of DCN is higher than DNN-1 and DNN-2 at 8.7% and 4.3%, respectively. Acc 3 of the DCN in all conditions is higher than real-valued DNN at 5.3%. The results demonstrate that it is more appropriate to use DCN in AMC of underwater acoustic communication signals.

Performance Analysis of Deep Complex Matched Filter
We analyzed the performance of DCMF in this section. A contrastive experiment was carried out between two DCNs with and without DCMF in the Ch1+OAN channel. In the DCN without DCMF, an ordinary CConv layer was used to ensure the parameters of the two DCNs are equal. We tracked the kernels of DCMF during the training to monitor the filtering process of the DCMF. The variations of the first kernel at different training stages are visualized in Figure 10, which includes the variation of kernel shape and spectrum. As we can see from Figure 10a that the real and imaginary parts of the complex kernel gradually approximate sine waves with the training process going. The spectrum of the complex kernel converges to a matched filter, as is shown in Figure 10b. Figure 11 has compared filtering processes between the DCMF kernel and an ordinary CConv kernel. It is obvious that the proposed DCMF can significantly remove the noise and preserve the communication signal in the received signal, while the ordinary CConv layer tends to preserve features of the full frequency band.
Spectrum of DCMF kernel Spectrum of DCMF kernel

Performance Analysis of Proposed Method
The AMC performance comparison between DCN with and without DCMF is shown in Figure 12. The contrastive experiments were carried out using AWGN and OAN, respectively. Acc 3 of DCN with DCMF are 1.2%, 4%, and 5.7% higher than that without DCMF in AWGN, Ch1+AWGN, and Ch2+AWGN channels, respectively. Acc 3 of DCN with DCMF are 9.5%, 4.4%, and 6.1% higher than that without DCMF in OAN, Ch1+OAN and Ch2+OAN channels, respectively. The overall Acc 3 of DCN with DCMF is 5.1% higher than that without DCMF in all conditions. It is obvious that DCMF can improve the AMC performance at low SNR(about SNR < −6 dB). The comparison results have shown the advantages of the proposed DCMF in denoising and improving the performance of AMC.   Other contrastive experiments were carried out to evaluate the performance of DCCE. The DCCE was embedded in the DCN and followed the DCMF. Multi-path fading channels Ch1 and Ch2 were considered individually. The comparison of the AMC accuracies is illustrated in Figure 13. In Figure 13a, DCCE can improve the Acc 3 in Ch1+AWGN and Ch1+OAN channels by 5.8% and 8.4%, respectively. The accuracies increments are 10.1% and 13.2% when Ch1 is replaced by Ch2, as is shown in Figure 13b. The overall Acc 3 of DCN with DCMF and DCCE is 9.3% higher than that with only DCMF in all conditions, and it is 14.3% higher than the ordinary DCN in all multi-path fading channels. The results have suggested that the proposed DCMF and DCCE can overcome the multi-path fading effect and improve the AMC performance significantly. Another classification experiment was carried out on a real-world dataset, which was recorded in the South China Sea. The data were recorded using an omnidirectional hydrophone placed under the surface of about 10 m, the transmitter was about 3 km far away from the receiver, and the relative speed of the transmitter and receiver was less than 5 m/s. The modulation types of real-world signals include BPSK, QPSK, 16QAM, and 32QAM. The SNR of the received signals is about 3-5 dB. The received signals were down-converted and expressed as the sampled complex baseband, and all the signals were resampled and divided into 0.5 s to keep the same dimension as the simulated signals. The number of each modulation type is 100. The signals were classified by the proposed method; the classification results are shown in Table 3. The AMC performance comparison between the proposed method and some others achieved AMC methods were carried out. There were three AMC methods based on deep neural networks (include VGGnet [40], ResNet [41,42], LSTM [43,44]) and one AMC method using feature extraction based on HOC [45,46] (which is usually used for AMC of PSK and QAM signals) for comparison. The AMC method based on HOC used SVM as the classifier. The trainable parameters of VGGnet, ResNet, and LSTM were kept nearly to the DCN with DCMF and DCCE. The contrastive experiments were carried out with the two underwater acoustic channels (Ch1+OAN and Ch2+OAN), respectively. Table 4 and Figure 14 have illustrated the performance comparison in the two underwater acoustic channels of these mentioned AMC methods. In Figure 14a, Acc 3 of each AMC method is 50.78%, 54.94%, 55.95%, 51.48%, and 65.1%. In Figure 14b, Acc 3 of each AMC method is 59.95%, 65.79%, 65.82%, 55.17%, and 70.27%. The proposed method obtained higher classification accuracy than the other methods in the two underwater acoustic channels.

Limitations of the Proposed Method
We carried out one experiment to analyze the SNR limitation of the proposed method. We used the combination dataset in the channels Ch1+OAN and Ch2+OAN. Figure 15 has illustrated the classification performance at lower SNR, as we can see that in multi-path fading channels when the SNR ≤ −15 dB, the method can not classify the modulation types anymore.

Conclusions
In this paper, we adopted DCN into AMC of underwater acoustic communication signals, two physical signal processing layers based on DCN were proposed to improve the AMC performance. The two physical signal processing layers include DCMF and DCCE, DCMF can remove the noise from the received signals, and the DCCE can reduce the influence of multi-path fading. The proposed method can integrate the signal processing method with deep learning. Real-world underwater acoustic communication scenario was fully considered in this paper.
The results of the experiments indicated that multi-path fading and OAN in the underwater acoustic channels have a great influence on underwater acoustic communication signal and the AMC performance, especially the multi-path fading effect. DCN showed a larger advantage than real-valued DNN in AMC of underwater acoustic communication signals. By tracking and visualizing the filters of DCMF, we can observe that DCMF can significantly remove the noise in the received signals. The proposed method yielded certain performance gains and achieved robustness to the underwater acoustic channel.

Data Availability Statement:
The data presented in this paper are available after contacting the corresponding author.

Acknowledgments:
The Argo date used in this study came from China Argo Real-time Data Center.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript: