【Advanced】Signal Modulation Recognition and Classification in MATLAB

# 1. Fundamentals of Signal Modulation Recognition in MATLAB

Signal modulation recognition is a critical task in communication systems that involves identifying and classifying different types of signal modulation techniques. In MATLAB, signal modulation recognition can be achieved through a variety of algorithms and techniques that leverage the signal's time-frequency, statistical, and machine learning characteristics.

# 2. Signal Modulation Recognition Algorithms

Signal modulation recognition algorithms are the core part of the modulation recognition system, and their performance directly affects the system'***mon modulation recognition algorithms are mainly divided into three categories: time-frequency analysis methods, statistical feature extraction, and machine learning classifiers.

### 2.1 Time-Frequency Analysis Methods

Time-frequency analysis methods extract the time-frequency features of signals by decomposing them into the time-frequency domain, ***mon time-frequency analysis methods include:

#### 2.1.1 Short-Time Fourier Transform (STFT)

STFT divides the signal into a series of overlapping time windows and performs a Fourier transform on each window, obtaining a time-frequency spectrum. The changes in the signal energy distribution in the time-frequency spectrum reflect the characteristics of the modulation signal, which can be used to identify the modulation type.

import numpy as np
from scipy import signal

# Signal sampling frequency
fs = 1000

# Signal time
t = np.linspace(0, 1, fs)

# Signal
x = np.sin(2 * np.pi * 100 * t) + np.sin(2 * np.pi * 200 * t)

# STFT window length
window_length = 128

# STFT overlap rate
overlap = 0.5

# STFT
stft = signal.stft(x, fs, window='hann', nperseg=window_length, noverlap=int(window_length * overlap))

# Time-frequency spectrum
spectrogram = np.abs(stft[2])

#### 2.1.2 Wavelet Transform

Wavelet transform is a time-frequency analysis method that decomposes signals using a series of wavelet basis functions to extract the time-frequency local features of the signal. Wavelet transform has a good analysis capability for non-stationary signals and can be used to identify the transient changes of modulation signals.

import pywt

# Wavelet basis function
wavelet = 'db4'

# Wavelet decomposition levels
levels = 5

# Wavelet transform
coeffs = pywt.wavedec(x, wavelet, level=levels)

# Wavelet coefficients
cA = coeffs[0]
cD = coeffs[1:]

### 2.2 Statistical Feature Extraction

Statistical feature extrac***mon statistical features include:

#### 2.2.1 Time-Domain Features

Time-domain features describe the statistical characteristics of the signal in the time domain, such as mean, variance, kurtosis, and skewness. These features can be used to identify the amplitude and phase changes of modulation signals.

# Mean
mean_x = np.mean(x)

# Variance
var_x = np.var(x)

# Kurtosis
kurtosis_x = np.mean(((x - mean_x) / np.std(x)) ** 4)

# Skewness
skewness_x = np.mean(((x - mean_x) / np.std(x)) ** 3)

#### 2.2.2 Frequency-Domain Features

Frequency-domain features describe the statistical characteristics of the signal in the frequency domain, such as spectral energy distribution, peak frequency, and bandwidth. These features can be used to identify the carrier frequency and modulation bandwidth of modulation signals.

# Spectral energy distribution
psd_x = np.abs(np.fft.fft(x)) ** 2

# Peak frequency
peak_freq = np.argmax(psd_x)

# Bandwidth
bandwidth = np.sum(psd_x > 0.5 * np.max(psd_x))

#### 2.2.3 Higher-Order Statistics

Higher-order statistics describe the higher-order statistical characteristics of the signal, such as the cross-correlation function, cross-power spectrum, and bispectrum. These features can be used to identify the nonlinear characteristics and phase coupling relationships of modulation signals.

# Cross-correlation function
acf_x = np.correlate(x, x, mode='full')

# Cross-power spectrum
cpsd_x = np.cross_spectral_density(x, x, fs=fs)

# Bispectrum
bispectrum_x = np.fft.fft2(np.abs(cpsd_x))

### 2.3 Machine Learning Classifiers

Machine learning classifiers use the features extracted by statis***mon machine learning classifiers include:

#### 2.3.1 Support Vector Machine (SVM)

SVM is a binary classifier that separates samples of different categories by finding a hyperplane. SVM has strong generalization ability and can be used to recognize complex modulation signals.

from sklearn.svm import SVC

# Training data
X_train = np.array([[mean_x, var_x, kurtosis_x, skewness_x],
                     [mean_y, var_y, kurtosis_y, skewness_y]])

# Training labels
y_train = np.array([0, 1])

# SVM classifier
clf = SVC()

# Training
clf.fit(X_train, y_train)

#### 2.3.2 Decision Tree

A decision tree is a non-parametric classifier that recursively divides the feature space to establish decision rules. Decision trees are easy to interpret and can be used to identify the modulation type and parameters of modulation signals.

from sklearn.tree import DecisionTreeClassifier

# Training data
X_train = np.array([[mean_x, var_x, kurtosis_x, skewness_x],
                     [mean_y, var_y, kurtosis_y, skewness_y]])

# Training labels
y_train = np.array([0, 1])

# Decision tree classifier
clf = DecisionTreeClassifier()

# Training
clf.fit(X_train, y_train)

#### 2.3.3 Neural Networks

Neural networks are deep learning models that learn complex relationships between features through layers of nonlinear transformations. Neural networks have strong feature extraction and classification capabilities and can be used to recognize complex