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So, I already understand that the maximum resolution of a radar system is λ R / L, where lambda is the wavelength, R is the range to the target, and L is the diameter of the antenna, and that for a phased array, L would be the maximum distance between antennas (correct me if I'm wrong :) ). But there are two things I don't know:

1) How would one go about calculating the maximum bandwidth of a phased-array system? I know that they can be retargetted "in milliseconds" and different portions of the array can be used to track different targets at the same time. But when sweeping across terrain, what determines how many return datapoints you can read per second?

2) How does one calculate / estimate range accuracy when measuring distances to the target? Again the multiple antennas throws me off a bit because I know that in a single antenna system you generally have the antenna switch between pulses and waiting for returns, but I imagine that on a phased array when you have many antennas that it might be different.

This is all concerning terrain mapping from a lighter-than-air vehicle. Just trying to calculate what sort of data quality could be gathered, and it seems that most radar questions on stack exchange are in this section. :)

On that front...

3) Am I wrong that phased array is the ideal radar choice for this application? I know aerial terrain mapping is usually done with SAR, but a) a lighter than air vehicle moves much slower than an airplane or spacecraft (bad for SAR), and 2b) spreads out over a large physical area (good for phased array). Correct me if I'm wrong and SAR or some other type of radar else would be superior from a mass perspective for a given resolution.

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Radar systems emit STRONG radio waves, usually as tone-bursts of the RF carrier.

The target reflects the radio wave, usually in all directions, with only a tiny bit of energy returning to the Antenna.

If you receive -100 dBm reflected energy (with 0 dBm across 50 ohms being 0.623 Vpp), you have 0.632 Cpp/105 or 632,000 uVpp/100,000 = 6.32 uVpp.

To detect that, after just one pulse, you need a rather clean signal, good signal-to-noise ratio, such as 20 dB SNR, thus noise needs to be -100, -20, or -120 dB noise power. Some people will balk at a 20 dB SNR, but you'll like the cleanliness of the signal.

Now...............the key..........noise power increases with bandwidth.

1 hertz produces -174 dBm (comes from 10*log10(KT))
10 hertz produces -164 dBm
100 hertz produces -154 dBm
1 kHz produces -144 dBm
10 kHz produces -134 dBm
100 kHz produces -124 dBm.
200 kHz produces -121 dBm. 

Thus we know 1/200 kHz, or 5 microsecond observation time, is what we can afford.

For range accuracy, you need narrow pulses (far as I know). Pulse Compression, using SAW devices, is one way. You need some sort of correlation.

To map the terrain, you could use a LIDAR.

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Phased array radars are generally composed of a single antenna. However the antenna consists of a number of individually addressable radiating elements. By varying the phases of the signals that drive each element, the resulting radar beam can be steered, usually in both elevation and azimuth. This eliminates the need for a mechanically movable antenna. The beam can also be steered electronically much faster than a mechanical antenna can be steered. The amplitude distribution of the individual elements can also be varied which allows shaping of the beam; in particular the side lobes can be reduced using a variety of shading functions which can trade off side lobe level to beamwidth. The bandwidth of a phased array is not necessarily any different than for a mechanically steered antenna of the same diameter. That depends more on the electronics and the transmitted wave shapes.

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