I was wondering what would be the best waveform to generate for a phased array short range imaging radar? Square, sine, etc. Also what frequency would be best to operate at for the carrier wave given that this radar wants to point out people and dimensions of say a building or forest. So seeing through walls is an objective as well. I assume higher frequency for close range is best. Any info will help, thanks

• This is a really open question. You may need to focus it some more. But I do know that your frequency choices are limited to what the regulations allow. Jul 13, 2020 at 5:40

There's a many things you need to consider when designing a radar system. In your case it seems that you have some top-level requirements in mind!

You're seeking a solution for a short range radar using a phased array for the purpose of imaging. The words are in bold because we are considering these to be the main design considerations. We'll go over to what these words translate to in terms of overall radar architecture, receiver, waveforms, and some common trades associated with them.

## Short Range Considerations

"Classic" pulse radars are the ones we think of that transmit a simple rectangular pulse of length $$\\tau\$$ at some carrier frequency $$\f_c\$$. During this time, the receiver must be off in order to avoid damaging the receiver and/or to avoid self-interference.

Within this time since the receiver is off we must wait until our pulse is fully transmitted in order to turn on the receiver and begin receiving target returns. This minimum range is called the blind range is is given by

$$R_{blind} = \frac{c\tau}{2}$$

A 100 ns pulse would yield a blind range of 15 m. In other words, the pulse must travel at least 15 m before you can try and receive the return signal.

Keep in mind that "short range" means something very different to an automotive radar than it would to a traffic control radar.

We can avoid the blind range problem by considering a different kind of radar system: Frequency-Modulated Continuous Wave (FMCW). This type of system is continuously radiating a frequency-modulated wave and the receiver is always on. Below is an example of a linear up-chirp

This is the type of radar you see a lot in automotive applications (e.g. 77 GHz carrier) where we need to eliminate blind ranges for safety. In addition, we can also get the benefit of increased range resolution that we will talk more about below. This system requires a different kind of receiver that has its own challenges.

## Imaging Considerations

Whether "imaging" here means generic target separation in multiple measurement dimensions or actually forming a picture, we need good range, Doppler, and angle resolution to do so. We'll go over range resolution because it's the more straight-forward of the three in my opinion.

Range resolution is the measure of how two targets must be spaced in order to differentiate between them. For a lower range resolution of a system, the farther apart targets must be so that they do not meld into one during processing. For imaging, you generally want high resolution so you can differentiate between closely spaced targets.

Range resolution comes down to the bandwidth of the signal your transmit. For the case of a simple pulse, the range resolution is approximated by

$$\Delta R = \frac{c}{2B} = \frac{c\tau}{2}$$

Here we've made the approximation that the bandwidth of a rectangular pulse is the inverse of its pulse width so that $$\B \approx 1/\tau\$$. You can immediately see the trade-off: shorter pulse widths yield better range resolutions but we will suffer decreased energy on the target and thus decreased detection performance.

We can decouple the relationship between the pulse width and bandwidth. In order to do this, we introduce some kind of modulation to the rectangular pulse to increase its bandwidth. We've already went over one type: frequency modulation. Specifically, we looked at a linear frequency modulation (LFM) signal where we linearly increase the frequency during the pulse.

Consider two 100 ns pulses:

1. Rectangular pulse
2. LFM pulse with 100 MHz linear chirp

Using the range resolution equations

$$\Delta R_{Rect} = \frac{c}{2B} = \frac{c\tau}{2} = \frac{c}{2(10 \space MHz)} = 15 m$$

$$\Delta R_{LFM} = \frac{c}{2B} = \frac{c}{2(100 \space MHz)} = 1.5 m$$

You can see that using the LFM pulse gives us an order of magnitude in range resolution improvement and we get to keep the same pulse width! Visually we can see the range resolution performance from a nominal target return (zero delay) at the output of a matched filter, which is what is usually done in pulsed systems.

The rectangular matched filter output is very wide, so a second target must be spaced further in order to differentiate between the two, as expected. With the LFM pulse, the targets can get much closer as can be seen by how much narrower the main lobe is. There's no free lunch here: we increased our range resolution and maintained the same pulse width, but now our receiver bandwidth requirements have increased.

This was a rather high-level dump of some of the major aspects that must be considered. To summarize

1. Short range considerations - Find what your definition of "short" is and determine whether a traditional pulsed radar can be used or something like FMCW to eliminate blind ranges entirely.
2. Imaging considerations - Determine how close targets can be to each other when performing detection. Use this information to determine the range resolution you need which will then aid in waveform selection and bandwidth requirements.
3. Trade-offs - All of these benefits come with downsides. You will have to explore what effects these choices will have on your overall system design and how much it will cost.

This is not even close to being exhaustive but hopefully it will give you some orientation on the approach you want to take.

• this was a fantastic read, I really appreciate it. I am definitely left with, I love the idea of the FMCW for eliminating blind spots and gaining resolution with very short pulse width with the same pulse length (if I said that right). Having that pinpointing precision to basically stay out of your own way and to better separate objects is the way I'd choose to go, so I will have to be prepared for some heavy calculating on the receiver end. Will give this more rereads, thanks again
– Af91
Jul 13, 2020 at 23:50
• @Af91 This is exactly why close-range high resolution radar systems go with FMCW. You eliminate the blind ranges, get the resolution you required, and despite higher bandwidth requirements is actually quite simple to implement. Jul 14, 2020 at 0:26
• definitely makes sense. Will probably look into how to generate these waves, I'm guessing with MatLab or something. Really cool technology 👍👍
– Af91
Jul 14, 2020 at 3:26
• @Af91 If this answer sufficed please mark it as accepted to help the site out :) Jul 14, 2020 at 16:24
• do you know how I do that? I tried pushing the up arrow useful button but don't have enough reputation.
– Af91
Jul 15, 2020 at 0:07

Try 77 GHz sine waves. Thats what automotive radars use and it works very well.