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ELEC ENG 4069/7059 Radar Principles & Systems Assignment 1 Due 3pm Friday 31 August Question 1. Obtain an expression for the range to the horizon as a function of altitude h and earth radius re, where h < re. calculate the range at which a ground-based radar with suitable parameters could detect (i) a low-flying target at an altitude of 100 m; (ii) a target at 10,000 m; (iii) a satellite orbiting in a low earth orbit with altitude of 800 km. in this case, how many radars would be required to give round-the-clock coverage? assume straight line propagation, i.e. neglect effects such as atmospheric refraction, and re = 6, 371 km. [3 marks] question 2. consider a radar which uses linear fm waveform with b = 200 mhz, and τ = 1µs. (a) what is the waveform’s time-bandwidth product; (b) assume a baseband coherent detector, determine the minimum sampling rate required for the adc. (c) given a 2 km range window, compute the minimum collection time to avoid eclipsing returns within the window. (d) compute the number of complex samples obtained over the collection time in (c) given the sampling rate in (b). (e) compute the pulse compression integration gain in db. if the snr prior to the matched filter is -3 db, compute the snr at the output of the matched filter. (f) compute the doppler shift required to displace this lfm waveform by 3 rayleigh range resolution cells. if the centre frequency is 10 ghz, compute the radial velocity associated with the doppler shift. [3 marks] question 3. determine the autocorrelation function of the five-element barker code + + + - +, and calculate the relative sidelobe levels. plot the acf on matlab and include it in your submission. now suppose the received signal has undergone a doppler induced phase shift of 360 degrees across the uncompressed pulse. sketch the distorted autocorrelation function. if the width of the transmitted pulse is 10µs and the radar frequency is 10 ghz, what would be the required target radial velocity to produce this phase shift? [3 marks] question 4. a simple pulse radar operating at 10 ghz with vertical polarisation is required to have an unambiguous range of 100 km, a range resolution of 75 m, and 12 db (single pulse) snr for a 1 m2 target at 60 km. it is to scan a sector 60◦ in azimuth and 15◦ in elevation (above the horizon) in 4 s with a minimum of 10 hits per target per scan. determine 1. the prf; 2. the pulse width; 3. the receiver bandwidth; 4. the solid angle scanned by the antenna; 5. the maximum antenna gain; 1 6. the corresponding e and h plane beamwidths assuming a square aperture; 7. the approximate size of the antenna; 8. the transmitter power assuming a system loss of 7 db, an antenna with the gain calculated above, and a noise temperature at the receiver input of 600 k; 9. the noise spectral density at the receiver input; 10. the energy in the received pulse (at the receiver input) at 60 km range; 11. the range for unity snr; 12. the snr at the maximum unambiguous range for a target rcs of 10 m2. assume an ‘ideal’ antenna with g = 4πaλ2 . [3 marks] question 5. derive the ambiguity functions for (i) rectangular pulse and (ii) linear fm chirp waveforms. in both cases, assume the waveform to have a pulse length of 1µs, and assume the chirp to vary from 0 to 1 mhz (baseband). plot these using matlab and include them in your submission. [3 marks] bwn 14/08/2018. 2 re.="" calculate="" the="" range="" at="" which="" a="" ground-based="" radar="" with="" suitable="" parameters="" could="" detect="" (i)="" a="" low-flying="" target="" at="" an="" altitude="" of="" 100="" m;="" (ii)="" a="" target="" at="" 10,000="" m;="" (iii)="" a="" satellite="" orbiting="" in="" a="" low="" earth="" orbit="" with="" altitude="" of="" 800="" km.="" in="" this="" case,="" how="" many="" radars="" would="" be="" required="" to="" give="" round-the-clock="" coverage?="" assume="" straight="" line="" propagation,="" i.e.="" neglect="" effects="" such="" as="" atmospheric="" refraction,="" and="" re="6," 371="" km.="" [3="" marks]="" question="" 2.="" consider="" a="" radar="" which="" uses="" linear="" fm="" waveform="" with="" b="200" mhz,="" and="" τ="1µs." (a)="" what="" is="" the="" waveform’s="" time-bandwidth="" product;="" (b)="" assume="" a="" baseband="" coherent="" detector,="" determine="" the="" minimum="" sampling="" rate="" required="" for="" the="" adc.="" (c)="" given="" a="" 2="" km="" range="" window,="" compute="" the="" minimum="" collection="" time="" to="" avoid="" eclipsing="" returns="" within="" the="" window.="" (d)="" compute="" the="" number="" of="" complex="" samples="" obtained="" over="" the="" collection="" time="" in="" (c)="" given="" the="" sampling="" rate="" in="" (b).="" (e)="" compute="" the="" pulse="" compression="" integration="" gain="" in="" db.="" if="" the="" snr="" prior="" to="" the="" matched="" filter="" is="" -3="" db,="" compute="" the="" snr="" at="" the="" output="" of="" the="" matched="" filter.="" (f)="" compute="" the="" doppler="" shift="" required="" to="" displace="" this="" lfm="" waveform="" by="" 3="" rayleigh="" range="" resolution="" cells.="" if="" the="" centre="" frequency="" is="" 10="" ghz,="" compute="" the="" radial="" velocity="" associated="" with="" the="" doppler="" shift.="" [3="" marks]="" question="" 3.="" determine="" the="" autocorrelation="" function="" of="" the="" five-element="" barker="" code="" +="" +="" +="" -="" +,="" and="" calculate="" the="" relative="" sidelobe="" levels.="" plot="" the="" acf="" on="" matlab="" and="" include="" it="" in="" your="" submission.="" now="" suppose="" the="" received="" signal="" has="" undergone="" a="" doppler="" induced="" phase="" shift="" of="" 360="" degrees="" across="" the="" uncompressed="" pulse.="" sketch="" the="" distorted="" autocorrelation="" function.="" if="" the="" width="" of="" the="" transmitted="" pulse="" is="" 10µs="" and="" the="" radar="" frequency="" is="" 10="" ghz,="" what="" would="" be="" the="" required="" target="" radial="" velocity="" to="" produce="" this="" phase="" shift?="" [3="" marks]="" question="" 4.="" a="" simple="" pulse="" radar="" operating="" at="" 10="" ghz="" with="" vertical="" polarisation="" is="" required="" to="" have="" an="" unambiguous="" range="" of="" 100="" km,="" a="" range="" resolution="" of="" 75="" m,="" and="" 12="" db="" (single="" pulse)="" snr="" for="" a="" 1="" m2="" target="" at="" 60="" km.="" it="" is="" to="" scan="" a="" sector="" 60◦="" in="" azimuth="" and="" 15◦="" in="" elevation="" (above="" the="" horizon)="" in="" 4="" s="" with="" a="" minimum="" of="" 10="" hits="" per="" target="" per="" scan.="" determine="" 1.="" the="" prf;="" 2.="" the="" pulse="" width;="" 3.="" the="" receiver="" bandwidth;="" 4.="" the="" solid="" angle="" scanned="" by="" the="" antenna;="" 5.="" the="" maximum="" antenna="" gain;="" 1="" 6.="" the="" corresponding="" e="" and="" h="" plane="" beamwidths="" assuming="" a="" square="" aperture;="" 7.="" the="" approximate="" size="" of="" the="" antenna;="" 8.="" the="" transmitter="" power="" assuming="" a="" system="" loss="" of="" 7="" db,="" an="" antenna="" with="" the="" gain="" calculated="" above,="" and="" a="" noise="" temperature="" at="" the="" receiver="" input="" of="" 600="" k;="" 9.="" the="" noise="" spectral="" density="" at="" the="" receiver="" input;="" 10.="" the="" energy="" in="" the="" received="" pulse="" (at="" the="" receiver="" input)="" at="" 60="" km="" range;="" 11.="" the="" range="" for="" unity="" snr;="" 12.="" the="" snr="" at="" the="" maximum="" unambiguous="" range="" for="" a="" target="" rcs="" of="" 10="" m2.="" assume="" an="" ‘ideal’="" antenna="" with="" g="4πAλ2" .="" [3="" marks]="" question="" 5.="" derive="" the="" ambiguity="" functions="" for="" (i)="" rectangular="" pulse="" and="" (ii)="" linear="" fm="" chirp="" waveforms.="" in="" both="" cases,="" assume="" the="" waveform="" to="" have="" a="" pulse="" length="" of="" 1µs,="" and="" assume="" the="" chirp="" to="" vary="" from="" 0="" to="" 1="" mhz="" (baseband).="" plot="" these="" using="" matlab="" and="" include="" them="" in="" your="" submission.="" [3="" marks]="" bwn="" 14/08/2018.="">