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ECEN5633 Radar Theory Lecture #13 24 February 2015 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen5633 Read 11.1 – 11.4 Problems 3.14, 18, 22 Exam 1 rework due 1 week after return Quiz #2, 3 March 2015 Live: 3 March DL no later than 10 March ECEN5633 Radar Theory Lecture #14 26 February 2015 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen5633 Read 11.5 & 11.6 Problems 4.1, 4.2, 11.10 Exam 1 rework due 3 March Quiz #2 Live: 3 March DL no later than 10 March Exam 1 Clarification Problem #1a) Radar Detector with 1 Mixer LO not phase locked? Followed by LPF? Signal Voltage & Power gain ↓ Problem #1b) Wording not tight enough. Only wideband noise n(t) input Mixer output = n(t) cos(ωct) → Low Pass Filter Mixer output = n(t) cos(ωct + 14º) → Low Pass Filter Does average noise power out of LPF differ? Matched Filters Seeks to maximize output SNR h(t) is matched to expected signal Direct Conversion Receiver Matched to baseband signal Output Signal Voltage (end of tp echo pulse) βtp(signal power in)0.5 Instantaneous Power is this voltage squared Noise Power Out = kToWn Easiest to analyze at Front End Using Pt and Tosys Square pulse of width tp expected? Noise BW = 1/(2tp) Hz Theory then says SNR = 2E/No Range Gate Usage Search Track 2 State Radar Search Mode (Looking for contacts) Multiple range bins required Bins ≈ tp seconds wide Need to monitor each bin Track Mode (You've got a contact) Range gate can predict location of next echo Only need to look there to maintain this contact May still want to watch for new contacts Search Mode Thomas Bayes Born circa 1701 Died 1761 English Statistician & Minister 1763 paper "An Essay towards Solving a Problem in the Doctrine of Chances" Provided statement of Baye's Rule Picture is from 1936 History of Life Insurance Previously… Baye's Concepts for Radar Costs; Hit & Miss Probabilities Known? Can get Optimum threshold. If Unknown, set allowable P(False Alarm) Go from there. False Alarm Rate ≈ P(False Alarm)*PRF If using Range Gating = P(False Alarm)*Sampling Rate Otherwise; Sampling Rate < 1/tp P(Hit) not good enough? Crank up pulse power out Pt Crank up antenna gain Gant Increase wavelength size λ Reduce System Temperature Tosys Decrease threshold γ Increase pulse width tp Put multiple pulses on the target Coherent Detection Single Pulse Hit Probability P(Hit) = Q[ Q-1[P(FA)] – SNR0.5 ] = 1 – Q(x) Can get SNR with Pr, Tosys, & Wn Want actual values out of Matched Filter? Go to back end. Q(-x) M Pulse Coherent Integration P(Hit) = Q[ Q-1[P(FA)] – (M*SNR)0.5 ] Sum M outputs from Matched Filter Want to sum outputs from identical range bins Compare sum to threshold Binomial PDF A random voltage is Binomially Distributed if… You've a two state experiment Success or Failure P(Success) & P(Failure) are constant Experimental Results are Statistically Independent You're interested in the number of successes Not the specific order of successes Coherent Detection Binary Detection (a.k.a Binary Integration) Transmit M pulses > K echoes* detected? Display a blip on operator's PPI scope. < K echoes* detected? Display nothing. *Or noise mistakenly thought to be an echo. Binary Detection: M = 10 Binary Detection: M = 10 Binary Detection: M = 10 Binary Detection: M = 10