ECEN5633 Radar Theory Lecture #16 5 March 2015 Dr. George Scheets n Read 12.1 n Problems 11.1, 3, & 4 n Corrected quizzes due 1 week after return n Exam #2, 31 March 2014 (< 4 April DL)

Coherent Detection n Analysis to date assumes constant P r u Or nearly so. n A not unreasonable assumption u If aspect angle remains ≈ same u Multiple pulses from same scan F Mach 2 aircraft moves ≈ 20 km/30 sec = m/sec 1000 pps → 2/3 m/pulse 10 pulses → 20/3 = 6 2/3 meter from start of scan n May not be reasonable u If target is turning u From one scan to the next

Coherent Detection, Fixed P r n Single Pulse Hit Probability P(Hit) = Q[ Q -1 [P(FA)] – SNR 0.5 ] n M Pulse Coherent Integration P(Hit) = Q[ Q -1 [P(FA)] – (M*SNR) 0.5 ] u Sum M outputs (same range bin) from Matched Filter n Binary Detection (a.k.a Integration) u Transmit M pulses, examine M (identical) range bins u Think > K echoes detected? Display a blip on PPI. u Think < K echoes detected? Display nothing. P(Hit M ) P(FA M )

PDF of Gaussian ☺ Rayleigh Source: math.stackexchange.com

P(Hit) Example, 2nd Order PDF P(Hit) =

Can't Always Trust Fancy Programs Here changing the integration bound yields erroneous results.

Terminology n P r u Received echo power from the Radar Equation F Peak (pulse) power is most appropriate F Expected value at RCVR antenna output n σ 2 n = kT o sys W n u Noise power with respect to front end of RCVR n SNR = P r /σ 2 n n Equations assume Direct Conversion RCVR

Coherent Detection, Fixed P r n Single Pulse Hit Probability P(Hit) = Q[ Q -1 [P(FA)] – SNR 0.5 ] u Signal (echo) PDF will be Gaussian with Var = σ 2 n u P(FA) set via Gaussian Noise PDF with Var = σ 2 n n M Pulse Coherent Integration P(Hit) = Q[ Q -1 [P(FA)] – (M*SNR) 0.5 ] u Transmit M pulses n Sum M outputs from Matched Filter u Make decision (Hit or Noise) based on sum u Signal (echo) PDF will be Gaussian with Var = Mσ 2 n u P(FA) set via Gaussian Noise PDF with Var = Mσ 2 n

Coherent Detection, Binary Integration n Transmit M pulses, look for echoes u Think > K echoes detected? Display a blip on PPI. u Think < K echoes detected? Display nothing. u P(Hit M )= desired Hit probability for display u P(FA M )= desired False Alarm probability for display u P(Hit 1 )= required single pulse Hit probability u P(FA 1 )= required single sample False Alarm probability u Adjust K, P(Hit 1 ), & P(FA 1 ) to find lowest SNR P(Hit M ) P(FA M )

Coherent Detection, Random P r n Exponentially distributed RCS & P r u Reasonable if many SI scatterers, none dominant u Results in Rayleigh distributed echo voltage PDF f S (r) u P(FA) set using Gaussian distributed noise PDF f N (r) u P(Hit): Integrate appropriate volume of f NS (n,s) F S.I., so f NS (n, s) = f N (n) f S (s) u P(Hit): Integrate appropriate area of f Z (z) = f N (r) ☺ f S (r) n In class example, Single Pulse u For fixed P r, P(Hit) = u For Rayleigh distributed P r, P(Hit) = 0.51