Range estimation for radar system.

I am writting a code on range estimation of radar syatem. I an sending a data frim transmitter and receive it after some delay. Now I write it as

% Parameters

fs = 1e6; % Sampling frequency (1 MHz)

T = 1e-3; % Pulse duration (1 ms)

fc = 10e6; % Carrier frequency (10 MHz)

PRI = 10e-3; % Pulse repetition interval (10 ms)

pulse_width = 1e4; % Pulse width (1 us)

c = 3e8; % Speed of light (m/s)

target_range1 = 200;

target_range2 = 100;

target_rcs = 1; % Target radar cross-section (RCS) in square meters

SNR_dB = 20; % Signal-to-noise ratio (in dB)

% Create a time vector for one pulse

num_symbols = 100; % Number of QAM symbols

snr_dB = 20; % Signal-to-noise ratio in dB

sigma_x=1;

% Generate QAM symbols

qam_order = 32; % 16-QAM

qam_symbols = randi([0, qam_order-1],1, num_symbols);

transmitted_pulse= qam_symbols;

% Simulate received signal with target echo and noise

target_delay1 = 2 * target_range1 / c; % Two-way propagation delay

target_delay2 = 2 * target_range2 / c; % Two-way propagation delay

% received_pulse = zeros(1, length(t_pulse));

% Time delay in samples

Fs = 1 / (target_delay1 + (1 / fc)); % Sampling frequency based on the delay and carrier frequency

time_delay_samples = round(target_delay1 * Fs); % Round to the nearest integer for discrete time

shifted_signal = circshift(transmitted_pulse, time_delay_samples);

% Add Gaussian noise to the received signal to achieve the desired SNR

SNR_linear = 10^(SNR_dB / 10); % Convert SNR from dB to linear scale

noise_power = var(shifted_signal) / SNR_linear; % Calculate noise power

noise = sqrt(noise_power) .* randn(1, length(shifted_signal)); % Generate noise

received_signal_with_noise = shifted_signal + noise;

% data indexing

transmitted_pulse1=reshape(transmitted_pulse,1,[]);

shifted_signal1=reshape(shifted_signal,1,[]);

received_signal_with_noise1=reshape(received_signal_with_noise,1,[]);

% Matched filtering (correlation) to detect target

correlation_result = conv(received_signal_with_noise1, fliplr(transmitted_pulse1));

threshold = max(correlation_result) * 0.5; % Adjust the threshold as needed

% Find target detection point

detection_index = find(correlation_result > threshold, 1);

del_t=detection_index/fs; %detection index*sampling frequency

% Calculate detected target range

detected_target_range = c * del_t /2;

% Display results

fprintf('Detected Target Range: %.2f meters\n', detected_target_range);

Here I am using match filter for detection. The code is running but not giving the proper range estimation. Kindly help me to to understand where I am missing.

Answer 1

[Rangesh]

Hi Soumita,

I understand that you are seeking to determine the correct value for the range.

Based on my understanding, it seems that there is no doppler shift present in the problem. Therefore, there is no need to calculate the frequency (Fs). Given that the sampling frequency (fs) is 1e6, the resolution of the detected range would be 300m for a delay in the received signal.

To find the target detection point, you can use the following:

[value, index] = max (correlation result)

If there is no delay, the matched filter would obtain a peak at the middle index, which in this case would be 100. However, with a delay, the peak would shift. So, we would obtain a peak at 101. Knowing that the time_delay is 1 (101-100), the detected target range can be calculated using the below mentioned formula:

c * time_delay / (2 * fs).

For a better understanding of radar signals, you can refer to the following link:

• https://youtu.be/UCir6mOW2OU?si=iWflIy_b3al1zj6a
• https://youtu.be/NtyU6aKZ-cY?si=zFFi5dEwZBwdYaP9

I hope this resolves your query.

Thanks,

Rangesh.

[SOUMITA NASKAR]

Thank you for replying and your valuable suggestion.