【Practical Exercise】SAR Imaging Point Target Simulation in MATLAB — RD Algorithm and CS Algorithm

# 1. Basics of SAR Radar Imaging

Synthetic Aperture Radar (SAR) is an active microwave remote sensing system that utilizes the synthetic aperture effect of a radar antenna on a moving platform to achieve high-resolution imaging of the ground. The SAR imaging process mainly includes the following steps:

- **Pulse Emission:** The radar antenna emits a series of high-frequency electromagnetic pulses, illuminating the target area.
- **Echo Reception:** The radar antenna receives the echo signals reflected back from the target area.
- **Signal Processing:** The received echo signals are processed, including matched filtering, phase compensation, and focusing.
- **Image Reconstruction:** The processed echo signals are converted into radar images, displaying the ground features of the target area.

# 2. Principles of RD Algorithm and CS Algorithm

### 2.1 Principles of RD Algorithm

#### 2.1.1 Mathematical Model of RD Algorithm

The RD algorithm (Range Doppler algorithm) is an SAR imaging algorithm based on time-domain correlation processing. Its mathematical model is as follows:

s(r, d) = ∫∫f(x, y)exp(-j2π(rX/λ + dY/λ))dxdy

Where:

- `s(r, d)`: SAR image
- `f(x, y)`: Target scattering function
- `r`: Range direction
- `d`: Azimuth direction
- `λ`: Radar wavelength

This model represents the SAR image `s(r, d)` as the convolution of the target scattering function `f(x, y)` with a two-dimensional phase factor `exp(-j2π(rX/λ + dY/λ))`.

#### 2.1.2 Steps of RD Algorithm Implementation

The steps to implement the RD algorithm are as follows:

1. **Range Compression:** Apply matched filtering to the received signals to remove pulse compression modulation.
2. **Azimuth Compression:** Perform a Fourier transform on the range-compressed signals to remove azimuth modulation.
3. **Image Reconstruction:** Apply an inverse Fourier transform to the azimuth-compressed signals to obtain SAR images.

### 2.2 Principles of CS Algorithm

#### 2.2.1 Mathematical Model of CS Algorithm

The CS algorithm (Compressed Sensing algorithm) is an SAR imaging algorithm based on sparse representation. Its mathematical model is as follows:

s(r, d) = ΦΨ(f(x, y))

Where:

- `Φ`: Measurement matrix
- `Ψ`: Sparse transform matrix
- `f(x, y)`: Target scattering function

This model represents the SAR image `s(r, d)` as the product of the target scattering function `f(x, y)` after sparse transform `Ψ` and the measurement matrix `Φ`.

#### 2.2.2 Steps of CS Algorithm Implementation

The steps to implement the CS algorithm are as follows:

1. **Data Acquisition:** Use the measurement matrix `Φ` to acquire target scattering data.
2. **Sparse Reconstruction:** Perform sparse reconstruction on the acquired data to obtain the sparse representation of the target scattering function `f(x, y)`.
3. **Image Reconstruction:** Apply an inverse sparse transform to the scattered function to obtain SAR images.

# 3.1 Practice of RD Algorithm

### 3.1.1 MATLAB Implementation of RD Algorithm

The MATLAB implementation steps of the RD algorithm are as follows:

1. Import SAR raw data: Read SAR raw data