You want to design a side looking synthetic aperture ultrasonic radar operating at f0 = 60 KHz and peak power Pt = 2 W. The antenna beam is conical with 3dB beam width θ3dB = 5˚. The maximum gain is 16. The radar is at a constant altitude h = 15 m and is moving at a velocity of 10 m/s. The elevation angle defining the footprint is β = 45˚. 

(a) Give an expression for the antenna gain assuming a Gaussian pattern. 

(b) Compute the pulse width corresponding to range resolution of 10 mm. 

(c) What are the footprint dimensions? 

(d) Compute and plot the Doppler history for a scatterer located on the central range bin. 

(e) Calculate the minimum and maximum PRFs. Do you need to use more than one PRF? 

(f) How will you design the system in order to achieve an azimuth resolution of 10 mm?