Extract and process related features
Accurately estimate each M-PSK and M-QAM waveform signal \({\textbf {y}} _{d ^(j)} \) in \(j^{\textrm {th}} \) It is essential to select an antenna, an associated set of important features. Higher order statistics (HO) including high-order moments (HOMS) and high-order cumulative accumulation (HOC) are considered effective features of AMC tasks26,27,28. As a result, we choose to use the host for the proposed AMC method up to the 8th time27.
In this work, we will calculate \(m^{\textrm {th}} \)– Order the home of the received signal \(j^{\textrm {th}} \) The antenna used16
$$\begin{aligned}\hat{\mu}_{mk}\left({\textbf{y}}_{d}^{(j)}\right)=\frac{1}{n_s}\overset{n_s}{\sumperset}}\left(y_{d,i}^{(j)}\right)^{mk}\left(\overline{y_{d,i}^{(j)}}\right)^{k},\end{aligned}$$
(13)
where \(n_s \) The sample count is as follows \({\textbf {y}} _ {d}^{(j)} \). \(m^{\textrm {th}} \)– Order \({\textbf {y}} _ {d}^{(j)} \) It can be expressed like a household with equally low order
$$\begin{aligned}\textrm{cum}\left[ {\textbf{y}}_{d1}^{(j)},\ldots ,{\textbf{y}}_{dm}^{(j)}\right] =\Underset {\ theta} {{\textStyle \sum}} \left(-1 \right) ^{\kappa -1} \left(\kappa -1 \right)! {e}} \Left[ \underset{c\in \vartheta }{{\textstyle \prod }}{\textbf{y}}_{dc}^{(j)}\right] ,\end {aligned} $$
(14)
where \(\ theta \) Passes a list of all partitions of \(1, \ ldots, m \), \(\ vartheta \) Run a list of all blocks in a partition \(\ theta \)and \(\ kappa \) The number of elements in a partition \(\ theta \). Here, each HOC is increased to power \(\frac {2} {m} \) This is because the size of the HOCS increases with orders29.
It also incorporates differential nonlinear phase peak coefficients (PF) as a function, as it has the ability to distinguish between different modulations in the considered list.30. The PF metric is defined as the ratio of the sum of normalized peak values for differential nonlinear phases to the normalized mean values for differential nonlinear phases. It can be expressed as
$$\begin{aligned}\textrm{pf}=\frac{\textrm{sum}\left(\text{nor}\left(\text{diff}\left(\phi_{nl}(i)\right)\right)\mir\text{diff}\left(\phi_{nl}(i)\right)\right)\gamma_{th}}}}{\text{mean}\left(\text{nor}\left(\text{diff}}\left(right)\right)\}\end{aligned}$$
(15)
where
$$\begin{aligned}\phi_{\text{nl}}(i)=\phi(i) -\frac{2\pi if_{c}}{f_{s}},\end{aligned}$$
(16)
and
$$\begin{aligned}\phi(i)=\theta(i)+c(i). \end {aligned} $$
(17)
here, \(\text {diff}(\phi_{nl}(i))\) Refers to the treatment of differences in nonlinear phases \(\phi _{nl}(i)\) and \(\text {nor}(\cdot)\) The function normalizes the data by limiting the range to a value between 0 and 1. operator \(\text {sum}(\cdot | _{\textrm {condition}})\) Compare the differences and normalization results with the condition and sum up the parts above the threshold (\(\ gamma _ {th} \)) Next, calculate the ratio with the normalized differential nonlinear phase average. \(\ phi(i)\), \(f_c \) and \(f_s \) The unpacked phase, the carrier frequency of the signal, and the sampling frequency, respectively. \(\ theta(i)\) Represents instantaneous phase and is calculated using the Hilbert transform. Finally, \(c(i)\) Shows the modified phase sequence.
Select a set of features using the Gramschmidt orthogonal procedure to enhance the classification performance of the proposed AMC-based DL method, while minimizing computational complexity.31. The simulation results show that selecting just 11 of the total 29 features is sufficient to achieve a good compromise between classification performance and training speed.
To classify the modulation type of an unknown signal, a training phase based on a CNN classifier must first begin. This phase involves constructing classifiers from the learning set. Once the classifier is constructed, a test phase is performed to identify modulation schemes for unknown signals. The following subsections provide details of the CNN architecture considered.
CNN Classifier
To identify the modulation scheme employed by the source node of the destination node from the set of modulations indicated by \({\mathscr {m}} \)6-layer CNN model is used. This model is followed by two convolutional layers and four fully connected layers, as shown in Table 1 and Figure 3. The first convolutional layer uses 128 filters (i.e., f = 128) of kernel size of 8 (i.e., k = 8), followed by batch normalization (BN). The second convolutional layer employs 64 filters and 4 kernel sizes with the same BN, Relu and dropout scheme. This is followed by three dense layers with 256, 128, and 64 neurons, respectively, using BN, Relu, and dropout (0.5) respectively. The final density layer matches the number of modulation classes and uses the SoftMax activation function.
Block diagram of the considered CNN model.
The conv1d layer performs a one-dimensional convolution operation, while the dense layer acts as a fully connected component. BN is applied to improve training efficiency. This stabilizes learning and accelerates convergence. Additionally, the Relu Activation function is expanded to introduce nonlinearity, reduces the problem of annihilation gradients and improves training speed. Dropout normalization is incorporated to reduce the risk of overfitting. Extensive experiments show that this CNN configuration effectively balances modulation recognition accuracy and training efficiency. An intensive training approach is adopted. A single CNN is trained using the total received signals from multiple antennas rather than individually training the individual CNN models for each antenna. Considering the training set \(\left \{t_{i}, l_{i}\right \}_{i=1}^{t}\)it consists of t Along with the observation and corresponding one-hot encoded label, the loss function can be defined as follows:
$$\begin{aligned}{\mathscr{l}}(f_{\text{cnn}},\theta;\{t_{i},l_{i}\}_{i=1}^{t})=-\frac{1}}_{i=1}^{t} l_{i}\log(f_{\text{cnn}}(\theta;l_{i})+\lambda J(f_{\text{cnn}},\ theta)
(18)
where \(f _ {\text {cnn}} \) Mapping functions and \(\ theta \) Model the CNN parameters. The second term, \(\lambda j(f_{\text {cnn}},\theta)\) It acts as a normalization term to prevent overfitting \(\lambda\) Controls its impact. Adaptive Moment Estimation (ADAM) optimizer is employed to minimize loss functions and utilize adaptive learning rates and momentum characteristics to increase convergence efficiency.
The testing process consists of two main phases: First, the trained CNN generates \(n_ {3} \) Probability density function denoted by \(\{p_ {j} \} _ {j = 1}^{n_3} \)Based on the test sample of \(n_ {3} \) The destination node antenna. Next, these \(\{p_ {j} \} _ {j = 1}^{n_3} \) It is handled by the decision module. This applies cooperative decision rules to determine the modulation type, as shown in Figure 4. In fact, each antenna independently determines a modulation scheme, and the final decision is made based on numerous rules. We also believe that decisions made at each antenna are equally important.
An illustration of the voting decision module used in the proposed AMC system.
Figure 5 shows the complete modulation classification process of the received signal on a J-Th antenna. \({\textbf {y}} _ {d}^{(j)} \).
A block diagram of a complete AMC pipeline using the proposed DL technique.
Complexity of inference in the proposed CNN model
The sum of the inference complexity of the proposed CNN model for each sample batch is given as follows:
$$\begin{aligned}{\mathscr{o}}\left(b\cdot\left(l\cdot 1024+l'\cdot 32{,}768+32{,}768+8{,}192+64\cdot | {mathscr | \right)\end{aligned}$$
(19)
where:
-
b Batch size (i.e. the number of samples processed simultaneously during inference),
-
l The length of the input feature vector is the vector of the first convolutional layer.
-
\(l '\) Shortening of the output length after the first convolution layer;
-
\(| {\mathscr {m}} | \) The number of modulation types to be classified.
Since l, \(l '\) and \(| {\mathscr {m}} | \) The constants of the expansion scenarios have overall linear inference complexity in the batch size of the model \({\mathscr {o}}(b)\). Therefore, the considered model has a linear batch size that makes it easy to manage per-sample complexity, making it suitable for real-time inference in 5G systems. We also find that the proposed CNN-based AMC methods are inherently scalable for more complex scenarios, such as large MIMOs and systems using multiple relays. In our framework, feature extraction and classification processes are applied independently to each antenna. The number of features extracted per antenna remains fixed, so the dimensions of the input to the CNN do not grow in the number of antennas, thanks to Hoss and Gram-Schmidt orthogonalization procedures. Therefore, the computational complexity of the classification model per antenna remains constant. When scaling to multiple antennas or relays, classification is performed in parallel across the antenna stream, followed by a centralized decision-making process based on majority votes. This increases the overall computational load linearly with the number of antennas, but allows workloads to be efficiently distributed and parallelized. Furthermore, having more antennas can improve diversity and increase the reliability of majority voting schemes, making the system robust. As a result, the proposed method is computationally efficient in more complex 5G scenarios and may increase performance.
Considered as a rating metric
In this work, we conduct a comparative study between proposed algorithms using the related benchmark algorithms.16,21 It is based on several rating metrics including true positive (TP) rate, false positive (FP) rate, accuracy, recall, and F-major. Recall, accuracy, and F measures are defined as follows:
$$\begin{aligned}&\text{recall}=\frac{\text{tp}}{\text{tp}+\text{fn}},\end{aligned}$$
(20)
$$\begin{aligned}&\text{precision}=\frac{\text{tp}}{\text{tp}+\text{fp}},\end{aligned}$$
(twenty one)
$$\begin{aligned}&\text{f-measure}=2\cdot\frac{\text{recall}\cdot\text{precision}}{\text{recall}+\text{precision}},\end}”
(twenty two)
where \(\ text {fn} \) It's a false negative.
