1. For the next 4 problems, consider the following:
Homework #3
Problem 1. Derive the limitation on the maximum unfocused synthetic-aperture length, from the constraint that the maximum phase shift variation across the aperture is 45º and using the figure shown at right.
For the next 4 problems, consider the following:
An airborne side-looking strip-map SAR is flying north (y direction) 1 km above the local terrain.
The SAR collects data over a 4-km synthetic aperture, L.
A point target is offset 2 km east of the SAR’s ground track.
Assume flat, i.e., ignore Earth’s curvature.
The SAR parameters are listed below.
Center frequency: 1 GHz
Antenna 3-dB azimuth beamwidth, az: 34
Antenna’s azimuth pattern:
where  is the azimuth angle measured from broadside

2. Homework #3
Problem 2. Plot the variation in the normalized received power P(y) as a function of SAR position y. Consider only the effects of G2 and R-4 effects on P(y).
Problem 3. Compute target’s complex phase history vector s(y). Plot the real part of the target’s phase history vector s(y).
Include the received power variations found in problem 2 and remember that power  (amplitude)2.
Problem 4. From the phase history vector s(y) produced in problem 3, use unfocused SAR processing to obtain the impulse response for the point target.
Problem 5. From the phase history vector s(y) produced in problem 3, use stretch processing to obtain the fully-focused impulse response for the point target.