CFAR using unfold

cfarunfold.md

Question:

Can you give me an example how I can implement a CFAR algorithm for radar using torch.nn.functional.unfold ?

Answer:

Certainly, let's dive right into how one might implement a Constant False Alarm Rate (CFAR) algorithm for radar data using PyTorch's torch.nn.functional.unfold. The CFAR algorithm is primarily used in radar systems to detect objects by varying the threshold dynamically, which allows for maintaining a constant false alarm rate.

Assumptions and Setup

1. You're familiar with the basics of radar signal processing and the CFAR algorithm.
2. You have a working knowledge of PyTorch and its functionalities.
3. Your radar data is a 2D matrix where the rows and columns correspond to range and azimuth bins.

Let's assume you have a 2D tensor radar_data representing the radar's power readings. This is what you're trying to apply CFAR to.

Approach

1. Use torch.nn.functional.unfold to extract sliding windows around each cell under test (CUT).
2. Compute the average noise level around each CUT.
3. Set a dynamic threshold based on this average noise level and the predefined false alarm rate.
4. Compare the CUT against this dynamic threshold to make a detection decision.

Here's some code to help illustrate these steps:

import torch
import torch.nn.functional as F

# Simulated radar_data (e.g., 10x10 matrix)
radar_data = torch.rand(10, 10)

# Kernel size (Window Size), let's say 3x3
kernel_size = 3

# Number of Training Cells (surrounding cells to be used to calculate the noise threshold), e.g., 4
num_train_cells = 4

# CFAR sensitivity, say 1.2
cfar_sensitivity = 1.2

# Use unfold to extract sliding windows
unfolded_data = F.unfold(radar_data.unsqueeze(0).unsqueeze(0), (kernel_size, kernel_size))

# Compute average noise level (mean) for each window
noise_level = unfolded_data.mean(dim=2)

# Select the middle value in the unfolded tensor as the CUT (Cell Under Test)
cut_value = unfolded_data[kernel_size // 2, kernel_size // 2, :]

# Calculate the dynamic threshold
threshold = noise_level * cfar_sensitivity

# Make detection decision
detection = (cut_value > threshold).float()

# Reshape detection tensor back to original shape (e.g., 10x10)
detection = detection.view(radar_data.size())

Caveats and Considerations

1. This example assumes the CFAR algorithm is applied across the entire radar_data matrix. In a real-world application, you'd likely apply this per range or azimuth.
2. The kernel size and the number of training cells should be selected based on your specific radar system's requirements.
3. CFAR sensitivity (cfar_sensitivity) will also depend on your specific requirements. Tuning this value will affect the performance of your CFAR algorithm.

By using torch.nn.functional.unfold, we can efficiently extract sliding windows for each CUT and apply the CFAR algorithm in a highly parallel manner, which is one of the advantages of using PyTorch for this task.

This should give you a good starting point for implementing a CFAR algorithm using PyTorch. Would you like to explore any part of this further?

Question

Can you show me the same example, but written in Rust ?

Answer

Certainly, translating this example to Rust will require using a suitable numerical library, as Rust doesn't have native matrix manipulation capabilities like Python's NumPy or PyTorch. One popular choice for numerical computing in Rust is the ndarray crate, though it doesn't provide out-of-the-box functionality similar to torch.nn.functional.unfold.

Assumptions

1. You're familiar with Rust and its package manager, Cargo.
2. You've already added the ndarray crate to your Cargo.toml.

Steps to Follow

1. Extract sliding windows around each Cell Under Test (CUT) by iterating over the 2D array.
2. Compute the average noise level around each CUT.
3. Set a dynamic threshold based on this average noise level and a predetermined false alarm rate.
4. Compare the CUT against this dynamic threshold.

Here's how you might implement this:

extern crate ndarray;
use ndarray::{Array2, ArrayView2, s};

fn main() {
    // Simulated radar data (10x10 matrix)
    let radar_data = Array2::from_shape_fn((10, 10), |_| rand::random::<f64>());

    // Window size (e.g., 3x3)
    let kernel_size = 3;

    // Number of Training Cells (e.g., 4)
    let num_train_cells = 4;

    // CFAR Sensitivity (e.g., 1.2)
    let cfar_sensitivity = 1.2;

    // Placeholder for detection results, initialized with zeros
    let mut detection = Array2::zeros((10, 10));

    for i in 0..(10 - kernel_size + 1) {
        for j in 0..(10 - kernel_size + 1) {
            // Extract window around CUT
            let window: ArrayView2<f64> = radar_data.slice(s![i..i+kernel_size, j..j+kernel_size]);
            
            // Calculate the mean noise level
            let noise_level: f64 = window.mean().unwrap();

            // Extract the CUT value
            let cut_value = window[(kernel_size / 2, kernel_size / 2)];

            // Calculate dynamic threshold
            let threshold = noise_level * cfar_sensitivity;

            // Make detection decision
            detection[(i + kernel_size / 2, j + kernel_size / 2)] = if cut_value > threshold { 1.0 } else { 0.0 };
        }
    }

    // Detection contains the CFAR applied results.
    println!("{:?}", detection);
}

Important Notes

1. The Rust example uses simple loops to implement the window sliding, which could be less efficient than PyTorch's unfold.
2. The ndarray crate is efficient but not designed for GPU acceleration like PyTorch.
3. To run the above example, you'll also need to include ndarray and ndarray-rand in your Cargo.toml.

This gives you a rudimentary but functional CFAR implementation in Rust. How well this scales will depend on your specific application and performance requirements. Would you like to delve into any aspect of this further?