slide 16

If two objects are not too close, we can distinguish their signals based on the peaks of the correlation after matched filtering. But if they are too close, we cannot see two peaks and cannot distinguish the signals. This is why the range resolution is limited. Shortening the pulse width can increase resolution, but it reduces signal-to-noise ratio. So, it's not a good solution. Then, we look at the case of two received signals. The left figure is the case when two objects are not too close. It means that their distance is longer than half of the light speed times pulse width. After matched filtering, we can see there are two high-density correlations. We are able to distinguish two received signals based on the peaks of the correlation. However, if the two objects are too close, their distance is shorter than half of the light speed times pulse width, we cannot see two peaks of the correlation. We thus cannot distinguish the two received signals because they are not too tight correlations. It is the reason why the range resolution is half of the light speed times pulse width. Viewing the figure, one obvious way to increase the range resolution is to shorten the pulse width. However, it leads to the lower SNR of the signal. Despite that the resolution increases, the signal becomes noise. So, it is not a good idea.