$*$write a Matlab code: Automatic Modulation Classification $($AMC$)$ plays a critical role in modern communication systems, enabling efficient signal processing and adaptation in dynamic environments. As the backbone of cognitive radio and adaptive communication technologies, AMC allows systems to identify the modulation techniques of incoming signals automatically, optimizing the use of available spectral resources and enhancing overall communication reliability.

Artificial Intelligence $($AI$)$ and Machine Learning $($ML$)$ are pivotal in advancing AMC, especially in noisy environments. Traditional AMC methods struggle with accuracy under such conditions, but AI$-$driven models, particularly those based on deep learning, excel by extracting subtle features from noisy signals that are often indiscernible to conventional techniques. These models can be trained on vast datasets to learn from complexity and variability, adapting to new, unseen conditions without explicit programming.

The integration of AI and ML into AMC not only improves signal classification accuracy but also enables real$-$time processing capabilities. This is essential for applications requiring quick adaptation to changing conditions, such as in military communications and mobile networks. By leveraging AI$,$ systems can automatically adjust to interference, signal fading, and other disruptions, ensuring stable and efficient communication links. This makes AI$-$enhanced AMC a cornerstone of modern digital communication strategies, driving forward innovations in connectivity and network resilience.

ML is a branch of $AI$ in which computer algorithms are designed to automatically improve models through experience and data utilization. These models are trained using input data paired with corresponding outputs, often referred to as ground$-$truth. These trained models are frequently employed for making predictions or decisions in various applications.

One of the most widely used subclasses of ML is the Artificial Neural Network $($ANN$).$ ANNs consist of one or more layers positioned between the input and output layers. These networks can take on various architectures and configurations. The selection of the appropriate ANN type depends on the data characteristics and the specific application requirements.

Figure $1$ illustrates the fundamental block diagram of an ANN. It comprises a fundamental unit known as a neuron, with multiple neurons forming a layer. ANNs typically have three types of layers: the input layer, hidden layers, and the output layer. There can be multiple hidden layers,

each with a varying number of neurons. Diverse optimization algorithms can be employed to adjust the network's parameters to ensure the final layer's output aligns with the desired output.

Figure $1$: Basic ANN diagram.

An ANN works as follows. Each neuron receives inputs from the preceding layers and produces one output. Neurons may linearly or non$-$linearly map their inputs to generate an output, which is often referred to as an activation function. In essence, the outputs from preceding layers are multiplied by weights $(w_k),$ summed, and then added to bias coefficients $(b_k)$ to compute the neuron's input. The non$-$linear mapping capability of ANNs empowers these networks to approximate the behavior of virtually any function.

In this exercise, you will work with a file named 'Data' which includes a matrix $\text{'}x\text{'}$ with dimensions $4200$x$250$ and a vector $\text{'}Y\text{'}$ of size $1$x$4200.$ Each row in the matrix $\text{'}x\text{'}$ represents a noisy binary sequence, either $\frac{0}{1}$ or $-\frac{1}{1},$ randomly generated under specific SNR ranging from $30$ to $10dB$ in increments of $2dB.$ For each SNR level, $100$ independent realizations were generated. The vector $\text{'}Y\text{'}$ is the ground$-$truth corresponding to the classification of each row of matrix $\text{'}x\text{'}.$ The value $\text{'}0\text{'}$ is set to represent the class of sequence $\frac{0}{1}$ and the value $\text{'}1\text{'}$ is set to represent the class of sequence $-\frac{1}{1}.$

Utilize the matrix $\text{'}x\text{'}$ and vector $\text{'}Y\text{'}$ to develop and train an ANN aimed at classifying the modulation type of a given sequence$-$whether it is $\frac{0}{1}$ or $-\frac{1}{1}.$ Your design should have high classification accuracy $)>(90\%$ with the minimum possible number of hidden layers.

Evaluate the performance of your ANN by computing the output of your model using the matrix $\text{'}$XT$\text{'},$ which is also found in the file 'Data'. This matrix contains $100$ rows with $250$ sample noisy sequences similar to those in $\text{'}$