Why buffer to delay the filtered receiving signal in the Monte Carlo ROC Simulation?

When I was leraning how to plot ROC curve in the page of Help Center : Monte Carlo ROC Simulation, I can't understand why we need to delay the receiving signal after filtering in the Loop Over Pulses section.

The code is given by

rcv_pulses = buffer(rcv_pulses(matchingdelay+1:end),size(rcv_pulses,1));

Could anyone help me here?

Answer 1

[Jack]

Hi,

The reason for delaying the receiving signal after filtering in the Loop Over Pulses section in Monte Carlo ROC simulation is to align the pulse with the template used for detection.

In a typical radar or sonar system, the transmitted pulse is sent out and then the receiver collects the reflected pulses after a certain amount of time. The reflected pulse is delayed with respect to the transmitted pulse due to the time it takes for the pulse to travel to the target and back.

In order to detect the reflected pulse, the receiver needs to align the received pulse with a template pulse that is used for detection. If the received pulse is not properly aligned with the template, the detection performance can be degraded.

In the Monte Carlo ROC simulation, the delay is simulated by delaying the received pulse by a certain amount of time. The matchingdelay variable in the code represents the time delay between the transmitted and received pulse. By delaying the received pulse by matchingdelay samples, the pulse is aligned with the template pulse used for detection, which improves the detection performance.

The buffer function is used to shift the samples of the received pulse by matchingdelay samples and discard the first matchingdelay samples. The remaining samples are then used for detection. The size(rcv_pulses,1) argument in the buffer function specifies the size of the buffer used for shifting the samples.

[奥 刘]

@Jack Thanks, I checked the code and you are right. We have to align the received signal here. However, I now have an another question. For the rcvsig that is the received signal before filtering, the signal (the rising edge) shows up at the exact range index of the target. But why after filtering the signal is delayed, for the parameter in the page, the target range index shows up at 140. Then we have to use the matchingdelay and buffer to align. Is this delay caused by matched filtering?

[Jack]

Yes, the delay you are seeing in the filtered signal is caused by the matched filtering process.

Matched filtering is a signal processing technique that is used to detect signals in noisy environments. The basic idea behind matched filtering is to convolve the received signal with a filter that is matched to the shape of the expected signal. This process enhances the signal-to-noise ratio of the received signal and makes it easier to detect the desired signal.

However, the matched filter introduces a delay in the received signal. This delay is proportional to the length of the filter and the shape of the expected signal. In other words, the longer the filter and the more complex the expected signal, the greater the delay introduced by the matched filter.

In your case, the delay introduced by the matched filter is causing the signal to appear at a later range index than expected. This delay can be compensated for by using the matching delay and buffer to align the filtered signal with the expected signal.

It's worth noting that the delay introduced by the matched filter is typically small compared to the time of flight of the radar signal. Therefore, it does not significantly affect the accuracy of the range measurement. However, it is important to account for this delay when processing the received signal to ensure that the signal is correctly aligned with the expected signal.

[奥 刘]

Really thanks! I think I get your basic point here.