1. ECEN5633 Radar Theory Lecture #13 24 February 2015 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen5633 n Read 11.1 – 11.4 n Problems 3.14, 18, 22 n Exam 1 rework due 1 week after return n Quiz #2, 3 March 2015 u Live: 3 March u DL no later than 10 March

2. ECEN5633 Radar Theory Lecture #14 26 February 2015 Dr. George Scheets www.okstate.edu/elec-eng/scheets/ecen5633 n Read 11.5 & 11.6 n Problems 4.1, 4.2, 11.10 n Exam 1 rework due 3 March n Quiz #2 u Live: 3 March u DL no later than 10 March

3. Exam 1 Clarification n Problem #1a) Radar Detector with 1 Mixer u LO not phase locked? Followed by LPF? u Signal Voltage & Power gain ↓ n Problem #1b) Wording not tight enough. u Only wideband noise n(t) input u Mixer output = n(t) cos(ω c t) → Low Pass Filter u Mixer output = n(t) cos(ω c t + 14º) → Low Pass Filter u Does average noise power out of LPF differ?

4. Matched Filters n Seeks to maximize output SNR n h(t) is matched to expected signal u Direct Conversion Receiver Matched to baseband signal u Output Signal Voltage (end of t p echo pulse) βt p (signal power in) 0.5 Instantaneous Power is this voltage squared u Noise Power Out = kT o W n u Easiest to analyze at Front End F Using P t and T o sys n Square pulse of width t p expected? u Noise BW = 1/(2t p ) Hz n Theory then says SNR = 2E/No

5. Range Gate Usage Search Track

6. 2 State Radar n Search Mode (Looking for contacts) u Multiple range bins required u Bins ≈ t p seconds wide u Need to monitor each bin n Track Mode (You've got a contact) u Range gate can predict location of next echo u Only need to look there to maintain this contact u May still want to watch for new contacts F Search Mode

7. Thomas Bayes n Born circa 1701 n Died 1761 n English Statistician & Minister n 1763 paper "An Essay towards Solving a Problem in the Doctrine of Chances" u Provided statement of Baye's Rule n Picture is from 1936 History of Life Insurance

8. Previously… n Baye's Concepts for Radar u Costs; Hit & Miss Probabilities Known? Can get Optimum threshold. u If Unknown, set allowable P(False Alarm) Go from there. n False Alarm Rate u ≈ P(False Alarm)*PRF If using Range Gating u = P(False Alarm)*Sampling Rate Otherwise; Sampling Rate < 1/t p

9. P(Hit) not good enough? n Crank up pulse power out P t n Crank up antenna gain G ant n Increase wavelength size λ n Reduce System Temperature T o sys n Decrease threshold γ n Increase pulse width t p n Put multiple pulses on the target

10. Coherent Detection n Single Pulse Hit Probability P(Hit) = Q[ Q -1 [P(FA)] – SNR 0.5 ] u Q(-x) = 1 – Q(x) u Can get SNR with P r, T o sys, & W n u Want actual values out of Matched Filter? Go to back end. n M Pulse Coherent Integration P(Hit) = Q[ Q -1 [P(FA)] – (M*SNR) 0.5 ] u Sum M outputs from Matched Filter F Want to sum outputs from identical range bins u Compare sum to threshold

11. Binomial PDF A random voltage is Binomially Distributed if… n You've a two state experiment u Success or Failure n P(Success) & P(Failure) are constant n Experimental Results are Statistically Independent n You're interested in the number of successes u Not the specific order of successes

12. Coherent Detection n Binary Detection (a.k.a Binary Integration) u Transmit M pulses u > K echoes* detected? Display a blip on operator's PPI scope. u < K echoes* detected? Display nothing. *Or noise mistakenly thought to be an echo.

13. Binary Detection: M = 10