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ECEN5633 Radar Theory
Lecture #13
24 February 2015
Dr. George Scheets
www.okstate.edu/elec-eng/scheets/ecen5633
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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
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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
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Problem #1a) Radar Detector with 1 Mixer
 LO
not phase locked? Followed by LPF?
 Signal Voltage & Power gain ↓
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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
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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
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Search Mode (Looking for contacts)
 Multiple
range bins required
 Bins ≈ tp seconds wide
 Need to monitor each bin
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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"
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 Provided
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statement of Baye's Rule
Picture is from 1936 History of Life Insurance
Previously…
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Baye's Concepts for Radar
 Costs;
Hit & Miss Probabilities Known?
Can get Optimum threshold.
 If Unknown, set allowable P(False Alarm)
Go from there.
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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
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Coherent Detection
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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)
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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
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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