Improved Modulation Classification Based on Hough Transforms of Constellation Diagrams Using CNN for the UWA-OFDM Communication System

Abstract

The Automatic Modulation Classification (AMC) for underwater acoustic signals enables more efficient utilization of the acoustic spectrum. Deep learning techniques significantly improve classification performance. Hence, they can be applied in AMC work to improve the underwater acoustic (UWA) communication. This paper is based on the adoption of Hough Transform (HT) and Edge Detection (ED) to enhance modulation classification, especially for a small dataset. Deep neural models based on basic Convolutional Neural Network (CNN), Visual Geometry Group-16 (VGG-16), and VGG-19 trained on constellation diagrams transformed using HT are adopted. The objective is to extract features from constellation diagrams projected onto the Hough space. In addition, we use Orthogonal Frequency Division Multiplexing (OFDM) technology, which is frequently utilized in UWA systems because of its ability to avoid multipath fading and enhance spectrum utilization. We use an OFDM system with the Discrete Cosine Transform (DCT), Cyclic Prefix (CP), and equalization over the UWA communication channel under the effect of estimation errors. Seven modulation types are considered for classification, including Phase Shift Keying (PSK) and Quadrature Amplitude Modulation (QAM) (2/8/16-PSK and 4/8/16/32-QAM), with a Signal-to-Noise Ratio (SNR) ranging from −5 to 25 dB. Simulation results indicate that our CNN model with HT and ED at perfect channel estimation, achieves a 94% classification accuracy at 10 dB SNR, outperforming benchmark models by approximately 40%.

1. Introduction

In recent years, there has been an increasing interest in UWA communications. Both military and civilian applications such as marine resource development [1,2], environmental research, commercial fishing, and surveillance systems [3,4], and marine climate monitoring [5,6,7] are the reasons for this interest. Communication over UWA channels is widely acknowledged as one of the most challenging tasks [8]. Time-space variations and multipath effects are features of UWA channels that cause signal distortion [9,10]. The utilization of OFDM is a more effective solution for UWA communications due to its robustness to channels having long delay spreads and frequency selectivity [11,12]. In many UWA communication signal processing methods, AMC is important. UWA communication signal modulation types are accurately and automatically classified by AMC, allowing the receiver to properly do demodulation without being informed of the modulation type. Two of the most popular AMC methods are Likelihood-Based (LB) and Feature-Based (FB) methods [13]. LB methods typically use perfect channel information to calculate the probability function for each modulation type under consideration. However, an underwater acoustic channel is usually a multipath channel with hundreds of taps [14]; therefore, LB methods could be impractical in this scenario due to computational complexity. However, rather than calculating the probability function, FB-based methods commonly extract a few important features for classification tasks, making them more suitable for underwater acoustic applications.

In recent years, AMC methods have made use of deep learning [15,16]. Deep learning algorithms can automatically extract hidden features from data to perform detection and recognition [17]. The augmented signal is reconstructed in radio modulation recognition using the inverse Fourier transform of the interference spectrum. By using both the original and augmented signals, CNNs can identify the modulation type of the signal. Wang Bin et al. [18] used CNN modulation recognition and Denoising Automatic-Encoder (DAE) methods. Initially, a DAE-based noise reduction module was designed to reduce the impact of alpha-stable distribution noise on modulation features. Secondly, the CNN recognizes the output signal power spectrum to complete the modulation recognition task. The proposed method, compared to the current algorithms, reduces the need for specialized knowledge, while increasing recognition rates in environments with impulse noise. Marcoux, Caitlyn N. et al. [19] discussed how CNNs and blind equalization can be used to automatically classify underwater signals. The suggested method uses less training data than previous methods and improves modulation classification by about 24%, when compared to methods without equalization.

The paper discusses several constant-modulus modulations, including Binary Phase shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), Minimum Shift Keying (MSK), Frequency Shift Keying (FSK), and eight Phase Shift Keying (8PSK). Xiao Y et al. [20] studied the applicability and effectiveness of a CNN-based AMC method over UWA channels. Three transmission modes have been used: Single-Carrier (SC) modulation, OFDM, and Direct Sequence Spread Spectrum (DSSS). The modulation methods include four coherent modulation formats (BPSK, QPSK, 8PSK, and 16QAM) and two non-coherent modulation formats (BFSK and QFSK). According to numerical simulations, their proposed method gives high recognition performance. Y. Li and S. Liang [21] presented a deep-learning-based modulation recognition network for aquatic communication signals. Combining ResNet with a modulation recognition network allows it capture deep features. Finally, the experiments show the effectiveness of this method. Zhang, Youwen et al. [22] developed a deep-learning-based UWA OFDM communication system. The deep-learning-based receiver, for the UWA OFDM communication system, can directly recover transmitted symbols without the requirement of explicit channel estimate and equalization after sufficient training, compared to the standard receiver. Many system metrics, such as the number of pilot symbols and the length of the CP, are used to evaluate the performance of deep-learning-based UWA OFDM. The simulation results reveal that the deep-leaning-based receiver outperforms the traditional UWA OFDM receiver. In this paper, the proposed AMC method depends on deep learning with a CNN trained on constellation diagrams transformed using HT. In addition, ED is performed on original constellation diagrams. The constellation diagram patterns are transferred into a different space using the HT, improving classification performance. Basic CNN, VGG-16, and VGG-19 are used for modulation classification over the UWA OFDM communication system with an SNR range of −5 to 25 dB. The following items summarize the main contributions of this paper:

• Utilization of the HT and edge detection to enhance modulation classification;
• Utilization of an OFDM system based on DCT, Linear Minimum Mean Square Error (LMMSE) equalizer, and CP to mitigate Inter-Symbol Interference (ISI) over the UWA communication channel;
• Performance comparison between the proposed method on a small dataset and existing deep-learning-based methods on large amounts of data;
• Classification of seven modulation schemes, namely 2/8/16-PSK and 4/8/16/32-QAM, which are accurately classified under the effect of estimation errors;
• Obtaining an average classification accuracy of 94% at 10 dB for perfect channel estimation with the UWA OFDM communication system. This represents an improvement of 40% compared to the benchmark model at 10 dB SNR.

The remaining sections of the paper are organized as follows. Section 2 describes the underwater channel model and describes also the proposed CNN-based classification over the UWA-OFDM system. Results from the simulation and a comparative analysis are presented in Section 3. Finally, Section 4 gives the conclusion of this study as well as the future work.

2. The Proposed Method

2.1. Underwater Channel Model

There are many challenges, including attenuation, reflection losses, and spreading losses that affect the channel model. Sound waves face these challenges as they propagate in the ocean environment. At the same time, channel modeling helps the prediction and enhancement of real-field experiments. Both the multi-path signal propagation and the time-varying nature of each component of the multi-path signal propagation are important factors in the characterization of underwater channels. In addition to resulting in ISI, multi-path propagation generates dispersion in both time and frequency domains. Additionally, the reflections of the sound signals between the surface and the bottom cause multi-path propagation. Due to its dispersive nature, the UWA channel suffers frequency-dependent attenuation, which causes sound signals to propagate at a speed of around 1500 m/s. Other UWA channels could be deterministic, but the fading statistics may be Rayleigh [23], Rician [24], K-distributed [25], or log-normal distributed [26]. There are two categories of UWA channel modeling: large-scale channel modeling and small-scale channel modeling, according to [24,25]. In large-scale channel modeling, we assume smooth surfaces and bottoms in addition to the stationary positions of the transmitter and the receiver. However, scattering processes and Doppler shifts are included in small-scale channel modeling. The impulse response of the UWA channel was predicted, and calculated, and its statistical features were evaluated by the authors in [27]. The underwater channel characteristics used in the Mobile Acoustic Communications Experiment (MACE) are shown in

Table 1. The UWA-MACE channel parameters.

Parameter	Value	Parameter	Value
Chanel model	MACE	Central frequency	16 kHz
Transmitter height	45 m	Number of intra-paths	20
Receiver height	60 m	Mean of intra-paths	25 mv
Water depth	100 m	Variance of intra-paths	1 µv
Channel distance	1.0 km	Bandwidth of UWA channels	12 kHz
Surface variance	1.123 m2
Bottom variance	0.5625 m2

. The UWA channel transfer function is as follows [27]:

$$H\left(f\right)=H_o\left(f\right){\sum }_p{h}_p{\gamma }_p\left(f\right)e^{-j2\pi f{\tau }_p}$$

(1)

where

$${\gamma }_p\left(f\right)={\displaystyle \frac{1}{h_p}}{\sum }_{i\ge 0}{h}_{p,i}{e}^{-j2\pi f{\delta }_{{\tau }_{p,i}}}$$

(2)

The transfer function of the whole channel is denoted by $H\left(f\right)$, the small-scale fading coefficient by ${\gamma }_p\left(f\right)$, and the transfer function of the direct path by $H_o\left(f\right)$. Path gain and delay are denoted by $h_p$ and ${\tau }_p$, respectively. The intra-path gains and delays are denoted by $h_{p,i}$ and ${\delta }_{{\tau }_{p,i}}$, respectively. The estimated channel impulse response during the MACE is shown in Figure 1.

Figure 1 illustrates a sample channel impulse response drawn from the UWA-MACE dataset, which is widely used for simulating realistic underwater acoustic communication environments. The figure captures the temporal and multipath characteristics typical of shallow-water acoustic channels, including significant delay spreads and fluctuating path gains. These features reflect the complex propagation conditions caused by reflections from the sea surface and bottom. The specific impulse response shown is one of approximately 3500 realizations available in the dataset, each representing a unique combination of channel parameters. In our simulation framework, one impulse response is randomly selected for each run to emulate the time-varying nature of the UWA channel. This approach ensures statistical variability and robustness in the performance evaluation of the proposed system. Similar methods are commonly adopted in the literature to account for the highly-dynamic behavior of UAC channels, as seen in references [27,28,29].

2.2. Proposed CNN-Based UWA-OFDM System

We consider a Single-Input Single-Output (SISO-OFDM) scenario. As shown in Figure 2, the proposed system model is based on OFDM that is implemented at the transmitter side using Inverse DCT (IDCT). The first mapping of the original data streams to symbols for 2-, 8-, 16-PSK, 4-, 8-, 16- and 32-QAM (S/P) conversion is used to multiplex the data stream from transmit mapped symbols. To reduce the ISI, the mapped symbols are modulated using IDCT (${\mathbf{C}}_N^{-1}\in {\mathbb{R}}^{N\times N}$). Each symbol has the CP added at its beginning. The transmitted data vector is generated from the sender hydrophone through the UWA-MACE channel as in Figure 2. The SISO-OFDM system based on DCT is used for data transmission. Assume vector $\mathbf{X}$ of samples to be modulated via IDCT, the CP insertion can be expressed as follows:

$${\tilde{x}}_C={\mathbf{P}}_{+}{\mathbf{C}}_N^{-1}\mathbf{X}$$

(3)

where ${\mathbf{P}}_{+}$ is the CP incorporation matrix, and ${\tilde{x}}_C$ represents symbols with CP in the time domain.

Now, the UWA channel effect is added as follows:

$$\tilde{x}=h\ast {\tilde{x}}_C+n$$

(4)

where * is the convolution operator, $h$ is the UWA channel, and $n$ is the Additive White Gaussian Noise (AWGN). The first step at the receiver side is to remove the CP as follows:

$${\tilde{\mathbf{x}}}_1={\mathbf{P}}_{-}\tilde{\mathbf{x}}$$

(5)

where ${\mathbf{P}}_{-}$ is the CP removal matrix. Now, an N-point DFT matrix is used at the receiver part to transform the signal to the frequency domain to perform frequency-domain equalization. Here is an expression for the DFT output:

$${\mathbf{Y}}_C={\mathbf{F}}_N\left\{{\mathbf{P}}_{-}\mathbf{h}·{\mathbf{P}}_{+}{\mathbf{C}}_N^{-1}\mathbf{X}+\mathbf{n}\right\}$$

(6)

The previous equation can be re-expressed as follows:

$${\mathbf{Y}}_C=\mathbf{H} \overline{\mathbf{X}}+\mathbf{N}$$

(7)

where $\mathbf{N}={\mathbf{F}}_N\left\{\mathbf{n}\right\}$, $\mathbf{H}$ represents the composite paths in the frequency domain in the seawater UAW channel, $\overline{\mathbf{X}}=\left\{{\mathbf{C}}_N^{-1}\mathbf{X}\right\}$ represents the modulated IDCT symbols in the frequency domain. Now, the equalization process can be performed as follows:

$$\mathbf{\Psi }={\left({\mathbf{H}}^H\mathbf{H}+{\displaystyle \frac{1}{SNR}}{\mathbf{I}}_{N\times N}\right)}^{-1}{\mathbf{H}}^H$$

(8)

where ${\mathbf{I}}_{N\times N}$ is an N × N identity matrix. After the usage of the LMMSE equalizer expressed in the previous equation on the received vector, the equalized symbols can be rewritten as follows:

$${\mathbf{Y}}_1=\mathbf{\Psi }{\mathbf{Y}}_C=\overline{\mathbf{X}}+\mathbf{\Psi }\mathbf{N}$$

(9)

Afterward, the Inverse Discrete Fourier Transform (IDFT) matrix is applied to transform the signal from the frequency domain back to the time domain, effectively reversing the initial DFT operation performed at the transmitter. This step reconstructs the time-domain signal components. Subsequently, the DCT matrix is applied to the result to exploit its energy compaction property and further refine the signal, ultimately enabling the accurate recovery of the original transmitted data vector. It should be noted that the cosine transform requirement of orthogonality is given as follows [30]:

$${\displaystyle \frac{1}{N}}{\sum }_{n=0}^{N-1}\cos \left({\displaystyle \frac{2\mathit{\pi mn}}{N}}\right)\mathrm{c}\mathrm{o}\mathrm{s}\left({\displaystyle \frac{2\pi pn}{N}}\right)=\left\{\begin{array}{c}1 \mathrm{for} m=p\\ 0 \mathrm{for} m\ne p\end{array}\right.$$

(10)

The required interference matrix can be formulated in the case of DCT as follows [30]:

$${\left({\mathbf{\eta }}_{m,p}\right)}_{DCT}={\displaystyle \frac{1}{2N}}\left({\sum }_{n=0}^{N-1}{e}^{j{\displaystyle \frac{2\pi [\left(m-p\right)+\epsilon ]n}{N}}}+e^{-j{\displaystyle \frac{2\pi [\left(m-p\right)+\epsilon ]n}{N}}}+e^{j{\displaystyle \frac{2\pi [\left(m+p\right)+\epsilon ]n}{N}}}+e^{-j{\displaystyle \frac{2\pi [\left(m+p\right)+\epsilon ]n}{N}}}\right)$$

(11)

Then, a parallel-to-serial (P/S) conversion process converts the S/P sub-stream into a serial data stream, which is then sent to create the constellation diagram images, which are transformed using HT after ED for various modulation schemes. The deep learning models (Basic CNN, VGG-16, and VGG-19) then use these images as input. Then, the modulation scheme is decided, and used for demapping.

2.2.1. Dataset Description

For the experiments, we describe the dataset here. The signal processing toolbox of MATLAB 2020b is used. Of about 27,125 constellation images in the generated dataset, 70% are used for training, 20% are used for testing, and 10% are used for validation. Constellation diagrams, including 125 constellations at various SNRs for each modulation type over the UWA channel, are used. We analyze seven different types of modulation schemes, with an SNR step size of 1 dB from −5 to 25 dB.

2.2.2. Pre-Processing Phase

The constellation diagram is a color JPG image with a 227 × 227 size. To reduce the computational load, this image is first binarized to a grayscale image, and then an ED method is applied. The ED is an image-processing method that uses mathematical algorithms to identify object edges [31]. Curves in images can be identified using the HT [32]. Peaks that map to points in another space are formed by curves of the same shape in one coordinate space using a transformation between two coordinate systems. The parametric representation of a line is used by the Standard Hough Transform (SHT):

$$\rho =x\cos \left(\theta \right)+y\sin \left(\theta \right)$$

(12)

The center of the pixels in the upper left corner is considered to represent the origin of the coordinate system. The perpendicular distance between the line and the origin is represented by the variable $\rho$. The angle, shown in degrees clockwise from the positive x-axis, of the perpendicular projection from the origin to the line is the variable $\theta$. The $\theta$ range is 90° ≤ θ < 90°. About the positive x-axis, the angle of the line itself is θ + 90°, which is similarly measured clockwise. Figure 3 shows the basic concept of the HT. Important features are highlighted after the HT. For more reliable computation and improved line detection, Hart and Duda used HT with a defined parameter space [33]. In Figure 4, we provide samples of the constellation diagrams and their HTs at various SNRs.

2.2.3. Pre-Trained CNN Models

Basic CNN The Basic CNN model is created based on the pre-trained model in [34], which has three convolution layers. Although the number of filters in each layer varies (8, 16, and 32, respectively), they all have the same kernel size (3), stride (1), and padding (1). Furthermore, three batch normalization layers are used, one after each convolution layer except the final layer. The most valuable features are selected using the 2 × 2 Max pooling. The fully-connected layer of the proposed model has seven neurons in its output, each of which represents a class. Each convolution layer depends on the ReLU activation function, but the fully-connected layer depends on the Softmax activation function. Using the Basic CNN model that has already been trained in [34], the image input size has been changed to 227 × 227 × 3. To fit the variety of modulation types in our proposal, we decreased the number of outputs from 10 to 7 and changed the learning rate from 0.01 to 0.0001. For our optimizer, we raised the maximum number of epochs from 4 to 10 and the validation frequency from 30 to 100. The training statistical parameters are shown in

Table 2. Statistical Parameters of Training.

Parameter	Basic CNN	VGG-16	VGG-19
Training time (Min: s)	2:66	32:58	38:38
Epochs	10	6	6
Total Iterations	1970	15,150	15,150
Iterations/Epoch	197	2525	2525
Validation Frequency (Iterations)	100	100	100
Learning Rate	0.0001	0.0001	0.0001
Hardware Resources	Single GPU	Single GPU	Single GPU

. Using the UWA-OFDM communication system, the Basic CNN model is trained and tested using the preprocessed constellation images. To guarantee that there is sufficient data available to evaluate the algorithm performance, we divided the data into 70% for training, 20% for testing, and 10% for validation.

VGG-16 The pre-trained VGG-16 model in [35] has 13 convolutional layers. Each layer has a different number of filters (64, 64, 128, 128, 256, 256, 256, and each layer of the last 6 layers contains 512), but they all have the same kernel size of 3, stride of 1, and padding of 1. In addition, a ReLU layer is added after each convolution layer. A 2 × 2 Max pooling process selects the most effective features. The suggested model ends with a fully-connected layer that outputs 7 neurons representing 7 classes. The Softmax is employed in the fully-connected layer. Based on the pre-trained VGG-16 model in [35], the number of outputs changes from 5 to 7 to adjust for the system various modulation types. Then, in our optimizer, we increase the frequency of validation from three to one hundred. Table 2 shows the statistical parameters for training.

VGG-19 The pre-trained VGG-19 model from [36], which has 16 convolutional layers, is used. Each layer has a different number of filters (64, 64, 128, 128, 256, 256, 256, 256, and each layer of the last 8 layers contains 512), respectively. The same kernel size of 3, a stride of 1, and a padding of 1 are shared by all of them. After every convolution layer, a ReLU layer is also added. A 2 × 2 Max pooling selects the most effective features. A fully-connected layer with seven output neurons, each of which representing a class, represents the end of the proposed structure. The Softmax algorithm is used in the fully-connected layer. The pre-trained VGG-19 model in [36] is used to adjust the input size of the image to 227 × 227 × 3, and the number of outputs is decreased from 1000 to 7, to fit the modulation schemes in the proposed module. Table 2 shows the statistical parameters of training.

3. Results

3.1. Result Analysis for Different Modulation Schemes

The proposed AMC performance study is provided in this section. We consider seven modulation schemes, namely 4/8/16/32-QAM and 2/8/16-PSK. Using their constellation diagrams or certain image transforms performed on the constellation diagrams, we want to distinguish between them. Three CNN models were used for the modulation classification task: VGG-19, VGG-16, and the Basic CNN. Three cases are discussed: (1) SC modulation with no equalization; (2) SC with LMMSE equalization; and (3) OFDM-DCT with LMMSE, ED and HT under the effect of UWA channel. The classification accuracy of the CNN models for all simulation scenario are shown in Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 and

Table 3. Accuracy for BPSK modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for different modulation classifiers.

BPSK
	Basic CNN			VGG-16			VGG-19
SNR (dB)	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT
−5	0.08	0.96	1	0.28	1	1	0.48	0.96	1
0	0.52	1	1	0.8	1	1	0.84	1	1
5	0.84	1	1	1	1	1	1	1	1
10	0.84	1	1	0.96	1	1	0.96	1	1
15	0.88	1	1	1	1	1	1	1	1
20	0.96	1	1	1	1	1	1	1	1
25	1	1	1	1	1	1	1	1	1

,

Table 4. Accuracy for 4QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for different modulation classifiers.

4QAM
	Basic CNN			VGG-16			VGG-19
SNR (dB)	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT
−5	0.08	0.12	0	0	0	0	0	0	0
0	0.12	0.2	0.6	0	0.12	0.68	0	0	0.6
5	0	0.44	1	0	0.12	0.96	0	0.08	0.92
10	0.08	0.6	0.96	0	0.44	0.92	0.04	0.6	0.96
15	0.32	0.92	0.96	0.36	1	0.96	0.48	1	0.96
20	0.52	1	1	0.36	1	1	0.68	1	1
25	0.44	1	1	0.4	1	1	0.6	1	1

,

Table 5. Accuracy for 8PSK modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for different modulation classifiers.

8PSK
	Basic CNN			VGG-16			VGG-19
SNR (dB)	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT
−5	0.12	0.12	0.6	0	0.36	0	0	0	0.32
0	0.28	0.12	0.8	0	0.36	0.2	0.04	0	0.36
5	0.36	0.2	0.88	0	0.24	0.76	0.04	0	0.72
10	0.24	0.52	0.88	0	0.12	0.8	0.04	0.04	0.52
15	0.4	0.68	0.92	0	0.52	0.8	0.04	0.24	0.68
20	0.44	0.96	1	0.12	0.96	0.96	0.04	0.8	0.92
25	0.36	1	1	0.08	1	1	0	1	1

,

Table 6. Accuracy for 8QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for different modulation classifiers.

8QAM
	Basic CNN			VGG-16			VGG-19
SNR (dB)	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT
−5	0.2	0.12	0.52	0.08	0.36	0.72	0.84	0.12	0.64
0	0.16	0.16	0.96	0.04	0.6	0.96	0.88	0.32	1
5	0.12	0.4	1	0	0.88	1	0.88	0.76	1
10	0.04	0.88	1	0.08	1	1	0.84	1	1
15	0.16	1	1	0.04	1	1	0.72	1	1
20	0.12	1	1	0	1	1	0.64	1	1
25	0.24	1	1	0.08	1	1	0.48	1	1

,

Table 7. Accuracy for 16PSK modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for different modulation classifiers.

16PSK
	Basic CNN			VGG-16			VGG-19
SNR (dB)	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT
−5	0.04	0	0.36	0	0.04	0.88	0	0.24	0.6
0	0	0	0.36	0.04	0	0.48	0	0.08	0.6
5	0	0	0.52	0.12	0.04	0.72	0.2	0.08	0.56
10	0	0.16	0.88	0.16	0.68	1	0.24	0.72	0.92
15	0.04	0.68	1	0.36	0.96	1	0.6	1	0.96
20	0.04	0.76	0.96	0.56	1	1	0.44	1	1
25	0.08	0.88	1	0.32	1	1	0.44	1	1

,

Table 8. Accuracy for 16QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for different modulation classifiers.

16QAM
	Basic CNN			VGG-16			VGG-19
SNR (dB)	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT
−5	0.36	0.28	0	0.16	0.36	0	0	0.8	0
0	0.4	0.16	0.52	0.2	0.28	0.36	0	0.92	0.68
5	0.24	0.16	0.84	0.12	0.32	0.44	0.04	0.88	0.92
10	0.32	0.28	1	0.16	0.88	0.6	0	1	1
15	0.32	0.6	1	0.24	0.96	0.84	0	0.96	1
20	0.28	0.84	1	0.16	0.96	1	0	1	1
25	0.24	0.96	1	0.32	1	1	0.12	1	1

and

Table 9. Accuracy for 32QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for different modulation classifiers.

32QAM
	Basic CNN			VGG-16			VGG-19
SNR (dB)	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT
−5	0.04	0.56	0	0.6	0.04	0	0.04	0.08	0
0	0.04	0.64	0.12	0.8	0.12	0.2	0.08	0	0.08
5	0.12	0.68	0.6	0.76	0.36	0.72	0.08	0.12	0.4
10	0.04	0.72	0.88	0.48	0.56	0.72	0.24	0.28	0.84
15	0.12	0.96	1	0.48	0.92	0.92	0.44	0.72	1
20	0.08	0.96	1	0.48	1	0.96	0.16	0.96	0.96
25	0.04	1	1	0.68	1	1	0.16	1	0.96

. In general, the simulation results show that the best classification accuracy for the three CNN models occurs in case three of OFDM-DCT with LMMSE equalization, HT and ED. The simulation results were obtained with a 1 dB step at SNRs between −5 and 25 dB. Low-density constellation diagrams, like those of BPSK, are easier to classify at low SNRs than high-density constellation diagrams. It is recommended to use ED of constellation diagrams and the HT for the classification of high-density constellation diagrams at low SNRs. The HT of a point maps into a continuous line. HT is, therefore, expected to do well in the classification task. Furthermore, ED possesses a strong ability to accurately represent curved lines that represent object boundaries. For the BPSK, as shown in Figure 5 and Table 3, the classification accuracy with the Basic CNN, VGG-16, and VGG-19 in case three is about 100% for all SNRs. For the 4QAM, the performance of the Basic CNN in case three is the best with a classification accuracy of about 100% at 5 dB SNR as shown in Figure 6 and Table 4. For the 8PSK, for low SNR, at 0 dB, the Basic CNN gives the best performance of about 80% in case three as shown in Figure 7 and Table 5. For the 8QAM, at low SNR, VGG-16 provides the optimum performance in case three as shown in Figure 8 and Table 6. For the 16PSK, Figure 9 and Table 7 indicate clearly that the VGG-16 provides the best performance for all SNR values in case three. According to Figure 10 and Table 8, for the modulation classification accuracy of 16QAM at all SNR values, VGG-19 provides the best performance in case three. For the 32QAM, VGG-16 performs optimally at low SNR in case three as shown in Figure 11 and Table 9.

3.2. Result Analysis Under the Effect of Estimation Errors

This section includes the study of the accuracy of classification for seven modulation schemes over the UWA channel with the proposed algorithms under the effect of estimation errors at standard deviation values of $\sigma =0,\sigma =0.1$ and $\sigma =0.5$. Two proposed cases are considered: (1) SC with LMMSE equalization, and (2) OFDM-DCT, with LMMSE equalization, and HT. The classification accuracy of the models for all simulation scenarios is shown in Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18 and

Table 10. Accuracy for BPSK modulation classification at various SNRs for the UWA channel under the effect of estimation errors for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for Basic CNN classifier.

Basic CNN Accuracy (BPSK)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.96	0.96	0.28	1	0.96	0.84
0	1	0.99	0.37	1	1	0.84
5	1	1	0.43	1	1	0.83
10	1	1	0.51	1	1	0.87
15	1	1	0.56	1	1	0.93
20	1	1	0.62	1	1	0.94
25	1	1	0.64	1	1	0.92

,

Table 11. Accuracy for BPSK modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-16 classifier.

VGG-16 Accuracy (BPSK)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	1	0.96	0.76	1	0.96	0.92
0	1	1	0.9	1	1	0.88
5	1	1	0.88	1	1	0.88
10	1	1	0.96	1	1	0.92
15	1	1	0.97	1	1	0.95
20	1	1	0.98	1	1	0.96
25	1	1	1	1	1	0.92

,

Table 12. Accuracy for BPSK modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-19 modulation classifier.

VGG-19 Accuracy (BPSK)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.96	0.96	0.88	1	0.96	0.8
0	1	0.99	0.96	1	1	0.86
5	1	1	0.96	1	1	0.87
10	1	1	0.99	1	1	0.9
15	1	1	1	1	1	0.93
20	1	1	1	1	1	0.95
25	1	1	1	1	1	1

,

Table 13. Accuracy for 4QAM modulation classification at various SNRs for the UWA channel under the effect of estimation errors for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for Basic CNN classifier.

Basic CNN Accuracy (4QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.12	0.04	0	0	0.28	0
0	0.15	0.12	0	0.59	0.74	0.19
5	0.3	0.13	0	0.99	0.78	0.2
10	0.66	0.59	0	0.98	0.81	0.26
15	0.94	0.89	0	0.99	0.94	0.38
20	1	1	0	1	0.95	0.48
25	1	0.96	0	1	0.92	0.56

,

Table 14. Accuracy for 4QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-16 classifier.

VGG-16 Accuracy (4QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0	0.16	0	0	0.2	0
0	0.06	0.15	0.01	0.62	0.65	0.36
5	0.09	0.1	0.1	0.95	0.82	0.43
10	0.46	0.64	0.31	0.95	0.8	0.46
15	0.99	0.98	0.53	0.98	0.95	0.58
20	1	1	0.54	1	0.96	0.69
25	1	1	0.56	1	0.92	0.64

,

Table 15. Accuracy for 4QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-19 classifier.

VGG-19 Accuracy (4QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0	0.04	0.04	0	0.2	0
0	0	0.03	0.01	0.55	0.64	0.21
5	0.06	0.04	0.01	0.92	0.78	0.36
10	0.66	0.46	0.12	0.98	0.8	0.42
15	1	0.93	0.36	0.98	0.92	0.58
20	1	0.99	0.42	1	0.96	0.67
25	1	1	0.24	1	0.92	0.68

,

Table 16. Accuracy for 8PSK modulation classification at various SNRs for the UWA channel under the effect of estimation errors for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for Basic CNN classifier.

Basic CNN Accuracy (8PSK)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.12	0.2	0	0.6	0.08	0.28
0	0.12	0.26	0	0.69	0.22	0.24
5	0.21	0.29	0	0.87	0.38	0.37
10	0.39	0.42	0	0.89	0.42	0.41
15	0.66	0.6	0	0.92	0.42	0.52
20	0.94	0.79	0	0.98	0.6	0.59
25	1	0.72	0	1	0.52	0.76

,

Table 17. Accuracy for 8PSK modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-16 classifier.

VGG-16 Accuracy (8PSK)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.36	0.08	0	0	0.08	0.04
0	0.36	0.07	0	0.22	0.16	0.2
5	0.31	0.09	0.01	0.72	0.28	0.39
10	0.14	0.04	0.02	0.74	0.4	0.41
15	0.43	0.21	0.14	0.78	0.35	0.39
20	0.94	0.6	0.18	0.94	0.59	0.36
25	1	0.76	0.28	1	0.68	0.44

,

Table 18. Accuracy for 8PSK modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-19 classifier.

VGG-19 Accuracy (8PSK)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0	0.4	0.08	0.32	0.56	0.08
0	0	0.24	0.21	0.33	0.32	0.22
5	0.01	0.2	0.31	0.67	0.33	0.35
10	0.1	0.04	0.49	0.62	0.48	0.4
15	0.26	0.09	0.68	0.66	0.51	0.46
20	0.74	0.37	0.76	0.93	0.72	0.46
25	1	0.72	0.68	1	0.8	0.44

,

Table 19. Accuracy for 8QAM modulation classification at various SNRs for the UWA channel under the effect of estimation errors for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for Basic CNN classifier.

Basic CNN Accuracy (8QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.12	0.32	0.28	0.52	0.4	0.28
0	0.26	0.34	0.26	0.94	0.8	0.41
5	0.55	0.6	0.18	0.99	0.96	0.39
10	0.91	0.86	0.13	1	0.98	0.51
15	1	0.98	0.08	1	1	0.63
20	1	1	0.12	1	0.98	0.62
25	1	1	0	1	1	0.72

,

Table 20. Accuracy for 8QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-16 classifier.

VGG-16 Accuracy (8QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.36	0.44	0.48	0.72	0.32	0.24
0	0.57	0.57	0.45	0.97	0.78	0.44
5	0.91	0.86	0.48	1	0.97	0.41
10	1	0.99	0.59	1	0.98	0.58
15	1	1	0.68	1	0.98	0.69
20	1	1	0.73	1	0.98	0.69
25	1	1	0.84	1	1	0.56

,

Table 21. Accuracy for 8QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-19 classifier.

VGG-19 Accuracy (8QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.12	0.64	0.24	0.64	0.32	0.12
0	0.34	0.73	0.26	0.99	0.85	0.28
5	0.82	0.92	0.34	1	0.97	0.25
10	1	1	0.53	1	0.98	0.37
15	1	1	0.65	1	1	0.6
20	1	1	0.66	1	0.98	0.55
25	1	1	0.88	1	1	0.28

,

Table 22. Accuracy for 16PSK modulation classification at various SNRs for the UWA channel under the effect of estimation errors for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for Basic CNN classifier.

Basic CNN Accuracy (16PSK)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0	0.08	0.64	0.36	0.04	0
0	0.05	0.14	0.68	0.35	0.28	0.02
5	0.04	0.2	0.68	0.46	0.34	0.02
10	0.15	0.23	0.76	0.88	0.57	0.02
15	0.5	0.35	0.91	0.98	0.78	0.04
20	0.8	0.32	0.88	0.97	0.86	0.07
25	0.88	0.56	0.92	1	0.64	0.16

,

Table 23. Accuracy for 16PSK modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-16 classifier.

VGG-16 Accuracy (16PSK)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.04	0	0.16	0.88	0.2	0
0	0.01	0.01	0.38	0.67	0.29	0.02
5	0.24	0.23	0.51	0.68	0.44	0.07
10	0.76	0.68	0.54	0.92	0.62	0.25
15	0.9	0.9	0.67	0.96	0.8	0.34
20	0.98	0.87	0.59	0.98	0.88	0.34
25	1	0.96	0.64	1	0.8	0.4

,

Table 24. Accuracy for 16PSK modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-19 classifier.

VGG-19 Accuracy (16PSK)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.24	0	0.04		0.6	0
0	0.2	0.02	0.09		0.6	0.22
5	0.34	0.28	0.12		0.64	0.45
10	0.76	0.7	0.1		0.92	0.61
15	0.97	0.94	0.08		0.95	0.73
20	1	0.98	0.02		0.94	0.76
25	1	1	0.04		1	0.84

,

Table 25. Accuracy for 16QAM modulation classification at various SNRs for the UWA channel under the effect of estimation errors for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for Basic CNN classifier.

Basic CNN Accuracy (16QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.28	0.04	0	0	0.36	0.2
0	0.16	0.11	0	0.39	0.55	0.23
5	0.13	0.12	0	0.86	0.77	0.32
10	0.27	0.3	0	1	0.89	0.36
15	0.58	0.47	0	0.99	0.92	0.37
20	0.84	0.62	0	1	0.94	0.42
25	0.96	0.72	0	1	0.88	0.52

,

Table 26. Accuracy for 16QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-16 classifier.

VGG-16 Accuracy (16QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.36	0.2	0	0	0.12	0.08
0	0.29	0.35	0	0.25	0.38	0.09
5	0.46	0.54	0.02	0.44	0.66	0.2
10	0.81	0.74	0.02	0.59	0.85	0.27
15	0.94	0.86	0.16	0.89	0.9	0.33
20	0.99	0.96	0.24	0.98	0.92	0.36
25	1	0.96	0.32	1	0.96	0.28

,

Table 27. Accuracy for 16QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for VGG-19 classifier.

VGG-19 Accuracy (16QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.8	0.2	0.04	0	0.24	0.08
0	0.82	0.28	0.03	0.59	0.52	0.17
5	0.9	0.49	0.1	0.95	0.78	0.28
10	0.99	0.7	0.24	1	0.93	0.39
15	0.94	0.84	0.43	1	0.94	0.45
20	1	0.96	0.5	1	0.95	0.44
25	1	0.96	0.52	1	0.96	0.36

,

Table 28. Accuracy for 32QAM modulation classification at various SNRs for the UWA channel under the effect of estimation errors for the cases of (1) SC with LMMSE equalization, and (2) OFDM-DCT with LMMSE equalization and HT for Basic CNN classifier.

Basic CNN Accuracy (32QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.56	0.4	0.04	0	0.2	0.16
0	0.61	0.36	0.01	0.06	0.35	0.32
5	0.62	0.43	0.02	0.53	0.48	0.37
10	0.7	0.45	0.01	0.85	0.74	0.35
15	0.84	0.54	0	0.99	0.83	0.47
20	0.97	0.74	0	1	0.81	0.37
25	1	0.8	0	1	0.88	0.64

,

Table 29. Accuracy for 32QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with LMMSE equalization, and (2) OFDM-DCT with LMMSE equalization and HT for VGG-16 classifier.

VGG-16 Accuracy (32QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.04	0.04	0.12	0	0.76	0.52
0	0.14	0.18	0.18	0.19	0.63	0.53
5	0.33	0.28	0.21	0.68	0.8	0.52
10	0.52	0.51	0.16	0.74	0.86	0.56
15	0.87	0.82	0.27	0.9	0.89	0.64
20	0.98	0.95	0.34	0.97	0.92	0.52
25	1	0.92	0.56	1	0.96	0.56

and

Table 30. Accuracy for 32QAM modulation classification at various SNRs for the UWA channel for the cases of (1) SC with LMMSE equalization, and (2) OFDM-DCT with LMMSE equalization and HT for VGG-19 classifier.

VGG-19 Accuracy (32QAM)
	SC, LMMSE			OFDM-DCT, LMMSE, HT
SNR (dB)	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Perfect Channel Estimation	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.08	0	0.24	0	0.44	0.8
0	0.04	0.03	0.35	0.14	0.48	0.74
5	0.09	0.08	0.27	0.53	0.71	0.62
10	0.29	0.46	0.2	0.81	0.83	0.59
15	0.71	0.83	0.32	0.98	0.87	0.63
20	0.96	0.96	0.34	0.97	0.91	0.54
25	1	0.92	0.68	0.96	0.92	0.52

. In general, the simulation results show that the best classification accuracy of the three models occurs in case of OFDM-DCT with LMMSE equalization, HT and ED.

For example, for the BPSK, as shown in Figure 12a and Table 10, at SNR 15 dB, the Basic CNN in case one at perfect channel estimation (σ = 0) gives a classification accuracy of 1. When σ = 0.1, the classification accuracy is also 1, and this means that the accuracy reduction is 0. When σ = 0.5, the classification accuracy is 0.56, and this means that the accuracy reduction is 0.44. In case two, at perfect channel estimation (σ = 0). Moreover, the classification accuracy is still 1, when σ = 0.1, which means that the accuracy reduction is 0. When σ = 0.5, the classification accuracy is 0.93 revealing a low accuracy reduction of 0.07 compared with case one. It is concluded that the classification accuracy in case two is better compared with that in case one. Similar results are obtained for 8PSK and 16PSK.

For 4QAM, as shown in Figure 13a and Table 13, at SNR 15 dB, the CNN in case one at perfect channel estimation (σ = 0) gives a classification accuracy of 0.94. When σ = 0.1, the classification accuracy is 0.89. This means that the accuracy reduction is 0.05. When σ = 0.5, the classification accuracy is 0, which represents a large accuracy reduction of 0.94. In case two, at perfect channel estimation (σ = 0), the classification accuracy is 0.99. When σ = 0.1, the classification accuracy is 0.94. This means an accuracy reduction of 0.05. When σ = 0.5, the classification accuracy is 0.38 with a reduction of 0.61 compared with case one. This means that the classification accuracy in case two is better compared with that of case one. Similar results are obtained for 8QAM, 16QAM and 32QAM.

3.3. Comparison Results

3.3.1. Comparison Results Under the Effect of Perfect Channel Estimation

The average classification accuracies for the three proposed CNN models (Basic CNN, VGG-16, and VGG-19) are compared as shown in Figure 19 and

Table 31. Average accuracy of the three proposed models at different SNRs for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for different modulation classifiers over UWA channel.

Accuracy of the Three Proposed Models over UWA Channel
	Basic CNN			VGG-16			VGG-19
SNR (dB)	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT	SC, No Equalization	SC, LMMSE	OFDM-DCT, LMMSE, HT
−5	0.15	0.29	0.35	0.16	0.31	0.37	0.19	0.31	0.37
0	0.22	0.33	0.62	0.27	0.35	0.55	0.26	0.33	0.62
5	0.24	0.41	0.83	0.29	0.42	0.8	0.32	0.42	0.79
10	0.27	0.59	0.94	0.26	0.67	0.86	0.34	0.66	0.89
15	0.33	0.79	0.98	0.35	0.91	0.93	0.47	0.85	0.94
20	0.34	0.94	0.99	0.38	0.99	0.99	0.42	0.97	0.98
25	0.36	0.98	1	0.41	1	1	0.4	1	0.99

for the three cases of (1) SC, with no equalization, and (2) SC, with LMMSE equalization, and (3) OFDM-DCT, with LMMSE equalization, and HT under the effect of the UWA channel. According to Figure 19 and Table 31, the Basic CNN gives the optimum performance in case three for the UWA-OFDM communication system.

3.3.2. Comparison Results Under the Effect of Estimation Errors

The average classification accuracies for the three proposed models are compared as shown in Figure 20 and

Table 32. Average classification accuracies for different modulation types at various SNRs under the effect of estimation errors for the cases of (1) SC with no equalization, and (2) SC with LMMSE equalization, and (3) OFDM-DCT with LMMSE equalization and HT for Basic CNN classifier.

Basic CNN Accuracy
	SC, LMMSE		OFDM-DCT, LMMSE, HT
SNR (dB)	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.29	0.18	0.33	0.25
0	0.33	0.19	0.56	0.32
5	0.4	0.19	0.67	0.34
10	0.55	0.2	0.78	0.38
15	0.69	0.22	0.84	0.48
20	0.78	0.23	0.88	0.5
25	0.82	0.22	0.83	0.61

,

Table 33. Average classification accuracies for different modulation types at various SNRs under the effect of estimation errors for the cases of (1) SC with LMMSE equalization, and (2) OFDM-DCT with LMMSE equalization and HT for VGG-16 classifier.

VGG-16 Accuracy
	SC, LMMSE		OFDM-DCT, LMMSE, HT
SNR (dB)	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.27	0.22	0.38	0.26
0	0.33	0.28	0.55	0.35
5	0.44	0.32	0.71	0.4
10	0.66	0.36	0.79	0.47
15	0.82	0.49	0.84	0.56
20	0.91	0.52	0.89	0.56
25	0.94	0.6	0.9	0.54

and

Table 34. Average classification accuracies for different modulation types at various SNRs under the effect of estimation errors for the cases of (1) SC with LMMSE equalization, and (2) OFDM-DCT with LMMSE equalization and HT for VGG-19 classifier.

VGG-19 Accuracy
	SC, LMMSE		OFDM-DCT, LMMSE, HT
SNR (dB)	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5	Channel Estimation Error at Standard Deviation (σ) = 0.1	Channel Estimation Error at Standard Deviation (σ) = 0.5
−5	0.32	0.22	0.39	0.27
0	0.33	0.27	0.58	0.34
5	0.43	0.3	0.72	0.4
10	0.62	0.38	0.8	0.44
15	0.8	0.5	0.85	0.56
20	0.89	0.53	0.9	0.56
25	0.94	0.58	0.92	0.53

, for the two cases of (1) SC with LMMSE equalization; and (2) OFDM-DCT with LMMSE equalization and HT under the effect of estimation errors. According to Figure 20 and Table 32, Table 33 and Table 34, the Basic CNN gives the optimum performance at σ = 0.1 in two cases. When σ = 0.5, the VGG-19 gives the optimum performance in case one and the VGG-16 gives the optimum performance in case two.

3.4. Model Complexity

The Basic CNN, VGG-16, and VGG-19 include 3, 13, and 16 convolutional layers, respectively. A system with a 32 GB MSI RTX 3090 Suprim X GPU card (Micro-Star International, Cairo, Egypt) and a Ryzen 9 5950x CPU (Advanced Micro Devices, Cairo, Egypt) with a maximum boost rate of 4.9 GHz and a base frequency of 3.4 is used to build, train, and test the models. After training, the Basic CNN, VGG-16, and VGG-19 require around 320, 1430, and 1914 ms, respectively, as shown in

Table 35. Comparison of Computational Complexity.

Network	Prediction Time (ms/Example)	Number of Convolution Layers
Proposed CNN Model	320	3
Proposed VGG-16 Model	1430	13
Proposed VGG-19 Model	1914	16
DL-SMI [37]	260	2
ResNet [38]	105	32
TRNN [39]	79	42

, to predict the modulation class of an input image. Comparing the proposed models to DL-SMI [37], TRNN [38], and ResNet [36], they are more time-complex. However, ResNet [36] has 32 convolutional layers, while TRNN [39] has 42 convolutional layers, making them more computationally complex than the proposed models.

3.5. Comparative Analysis

A comparative analysis of the three proposed CNN-based models and the recent related study of [40] for the same type of dataset and UWA-MACE channel parameters is shown in

Table 36. Comparison of the proposed models at 0 dB SNR with other related works.

Modulation Type	BPSK	4QAM	8PSK	8QAM	16PSK	16QAM	32QAM	Total
Basic CNN with Gabor filtering [40]	1	0.24	0.09	0.09	0.05	0.25	0.32	0.29
AlexNet with Gabor filtering [40]	1	0.01	0.12	0.52	0	0.46	0.29	0.34
ResNet 50 with Gabor filtering [40]	1	0.36	0	0.36	0.16	0.12	0	0.29
The proposed Basic CNN with OFDM-DCT, LMMSE equalization, and HT	1	0.6	0.8	0.96	0.36	0.52	0.12	0.62
VGG-16 with OFDM-DCT, LMMSE equalization, and HT	1	0.68	0.2	0.96	0.48	0.36	0.2	0.55
VGG-19 with OFDM-DCT, LMMSE equalization, and HT	1	0.6	0.36	1	0.6	0.68	0.08	0.62

,

Table 37. Comparison of the proposed models at 10 dB SNR with other related works.

Modulation Type	BPSK	4QAM	8PSK	8QAM	16PSK	16QAM	32QAM	Total
Basic CNN with Gabor filtering [40]	1	0.66	0.4	0.4	0.32	0.53	0.49	0.54
AlexNet with Gabor filtering [40]	1	0.52	0.48	0.97	0.31	0.71	0.57	0.65
ResNet 50 with Gabor filtering [40]	1	0.8	0.28	1	0.56	0.32	0.4	0.62
The proposed Basic CNN with OFDM-DCT, LMMSE equalization, and HT	1	0.96	0.88	1	0.88	1	0.88	0.94
VGG-16 with OFDM-DCT, LMMSE equalization, and HT	1	0.92	0.8	1	1	0.6	0.72	0.86
VGG-19 with OFDM-DCT, LMMSE equalization, and HT	1	0.96	0.52	1	0.92	1	0.84	0.89

and

Table 38. Comparison of the proposed models at 20 dB SNR with other related works.

Modulation Type	BPSK	4QAM	8PSK	8QAM	16PSK	16QAM	32QAM	Total
Basic CNN with Gabor filtering [40]	1	1	0.87	0.87	0.9	0.96	0.9	0.93
AlexNet with Gabor filtering [40]	1	1	0.79	1	0.92	1	0.99	0.96
ResNet 50 with Gabor filtering [40]	1	1	0.6	1	0.88	1	0.92	0.91
The proposed Basic CNN with OFDM-DCT, LMMSE equalization, and HT	1	1	1	1	0.96	1	1	0.99
VGG-16 with OFDM-DCT, LMMSE equalization, and HT	1	1	0.96	1	1	1	0.96	0.99
VGG-19 with OFDM-DCT, LMMSE equalization, and HT	1	1	0.92	1	1	1	0.96	0.98

. It is clear from the tables that the proposed models outperform the existing deep-learning-based ones. The CNNs are trained on constellation diagrams transformed using HT and ED in the proposed models. A point in the constellation diagram is transformed into a continuous line by the HT, and the ED helps to capture curved lines that represent object boundaries, accurately. Cyclic Prefix (CP) and LMMSE equalization are used in the UWA-OFDM communication system to reduce ISI. According to Table 36, the average classification accuracies at 0 dB for the proposed Basic CNN, VGG-16, and VGG-19 models are 62%, 55%, and 62%, respectively, and the average classification accuracies for the models in [40] are 29%, 34%, 29% for Basic CNN, AlexNet, and ResNet 50, respectively. When comparing the proposed models with the models in [40], the classification accuracies are improved by 33% for the proposed Basic CNN compared with the Basic CNN model in [40], 21% for VGG-16 compared with AlexNet model in [40], and 33% for VGG-19 compared with ResNet 50 model in [40]. Similarly, according to Table 37, at 10 dB, the classification accuracies are improved by 40% for the proposed Basic CNN, 21% for VGG-16, and 27% for VGG-19 compared with the models in [40]. Similarly, according to Table 38, at 20 dB, the classification accuracies are improved by 6% for the proposed Basic CNN, 3% for VGG-16, and 7% for VGG-19 compared with the models in [40].

4. Conclusions

In this work, we presented automatic modulation classification over underwater acoustic (UWA) channels using three different CNN models: Basic CNN, VGG-16, and VGG-19. To use a small dataset, and efficiently and accurately detect the modulation type of underwater acoustic signals, the proposed CNN models are trained on constellation diagrams, which are transformed using HT and edge detection. Furthermore, we use an OFDM system over the UWA communication channel that includes equalization, cyclic prefixes, and the Discrete Cosine Transform (DCT). Seven modulation schemes at different SNRs are classified, including 2/8/16-PSK and 4/8/16/32-QAM under the effect of estimation errors. The main advantage of the proposed method is that it can recognize modulation schemes with high performance levels without the need for complex feature engineering or data augmentation. Additionally, the effects of the channel are removed by equalizing the received data and using DCT with cyclic prefix before classification. The proposed Basic CNN model using HT and edge detection has an average classification accuracy of 94% at 10 dB for the UWA-OFDM communication system. It has an improvement of 40% compared to the benchmark model at 10 dB SNR. In the future, we aim to include modulation classification in more complicated marine environments and create a method based on deep learning for modulation classification that is appropriate for underwater communication with low signal-to-noise ratios.