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I'm writing an essay about imaging radar. I was wondering the possible consequences that the bandwidth at which the radar operates could have on the measurements, and therefore on the image.
One effect of the choice of the bandwidth is e.g. longer wavelength can penetrate better through materials, having a lower energy (since frequency is low) and so not showing interaction with the external material layer, but with the inner one (medical application).
On the other side high frequency means high resolution, therefore more accurate image. Another point that has crossed my mind is that depending on the frequency, the atmosphere will show different attenuation properties.

Would you have other effects/consequences regarding the radar bandwidth choice which could be relevant? If you would have some helpful external resources to consult, that would be welcome too.

Thanks in advance!

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of the choice of the bandwidth is e.g. longer wavelength

I'm going to stop you there: The bandwidth is not directly related to wavelength. You're probably confusing center frequency with bandwidth. You need to get the difference very straight!

longer wavelength can penetrate better through materials, having a lower energy (since frequency is low) and so not showing interaction with the external material layer, but with the inner one (medical application).

Uff. While the tendency is true, it's by far not true for radio frequencies you might be using. (2.45 GHz is excellently absorbed by watery material, 3 GHz less so, see: microwave oven). Also, not quite true in other medical applications, too: hard (i.e. short-wavelength, high photon energy) X-ray penetrates further than soft.

So, not quite that easy. It's a common lie-to-children that popular medical literature tells, but your job is to write a good, not a popular essay ;)

On the other side high frequency means high resolution, therefore more accurate image.

In radar context, this is a consequence of bandwidth, not frequency, usually.

You can actually resolve sub-wavelength features with radar, too, given coherent post-processing.

Another point that has crossed my mind is that depending on the frequency, the atmosphere will show different attenuation properties.

Yes, exactly. See the thing about 2.4 GHz and absorption in water. You can find absorption spectra that show the general tendency (higher frequencies getting stronger absorption), but clear dips for specific frequency ranges.

Would you have other effects/consequences regarding the radar bandwidth choice which could be relevant?

Radartutorial.eu will teach you about how bandwidth and radar processing relate, but you first should make very clear in your head how bandwidth and carrier or center frequency are different things. You're conflating stuff there.

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Marcus already identified that you are confusing bandwidth and frequency, which are of course related but mean different things. In short, people refer signals as having some bandwidth centered around a carrier frequency. The carrier frequency could very well be zero, making it a baseband signal.

Assuming you're comfortable with that, let's answer the last part of your question:

Would you have other effects/consequences regarding the radar bandwidth choice which could be relevant? If you would have some helpful external resources to consult, that would be welcome too.

Regulatory and Spectrum Management

Countries and their respective governing bodies usually have regulations that dictate what frequencies and bandwidths radar and communication systems can operate on. These regulations are meant to mitigate the effects of interference between systems. Many times, military applications take priority and exclusively take up certain frequency bands.

Size Limitation

In microwave and antenna engineering, there are special relationships that involve the wavelength $\lambda$ in use. For example, a dipole antenna whose length is $\lambda/2$ will have an antenna gain of approximately 2.15 dBi. So depending on the frequency of choice, this antenna can be physically large.

At a frequency of 100 MHz, the wavelength is 3 meters. If you wanted to achieve the 2.15 dBi gain, the antenna would need to be 1.5 meters long. Contrast this to achieving this at 10 GHz, where the antenna need only be 15 cm long.

These types of relationships apply to the entire RF chain, effecting the size of waveguides, circulators, isolators, quater-wave transformers, etc. Many times this is why systems at lower operating frequencies are physically very large.

Depending on the application, you may need to consider certain frequencies, such as for atmospheric absorption properties. In other applications, the sizes required to achieve certain performance metrics (like antenna gain), immediately eliminates an entire set of frequencies from use. An example being airborne radars, that must fit within tight space constraints.

Bandwidth Limitations

In many radar and communication systems, being able to observe a large bandwidth is desirable. With large bandwidths, one can achieve higher data transfer rates, accommodate multiple signals simultaneously, and in radar systems, achieve good range resolution.

However achieving larger and larger bandwidths becomes more difficult. For starters, the RF hardware must be able to accomodate it, and doing so is expensive and some performance trades must be made. In addition, high sampling rates are required from analog-to-digital (ADC) converters, which can be prohibitively expensive. Observing large bandwidths also increases the probability of encountering interference.

Having too large of a bandwidth violates some assumptions made in microwave engineering. An example being how an antenna is designed, usually around a single frequency. Transmitting a high bandwidth signal now changes the antenna pattern significantly as the signal is being sent out, which is usually undesirable. There are high bandwidth antennas that can handle this, but are usually more exotic and expensive.

There are many more reasons that determine one's choice of bandwidth/frequency. There are many free online sources of information, such as microwaves101.com, RFCafe.com, Radartutorial.eu, and university sites.

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