ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #13 24 February 2015Lecture #13 24 February 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633 Read 11.1 – 11.4Read 11.1 – 11.4 Problems 3.14, 18, 22Problems 3.14, 18, 22 Exam 1 rework due 1 week after returnExam 1 rework due 1 week after return Quiz #2, 3 March 2015Quiz #2, 3 March 2015

Live: 3 MarchLive: 3 March DL no later than 10 MarchDL no later than 10 March

ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #14 26 February 2015Lecture #14 26 February 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633 Read 11.5 & 11.6Read 11.5 & 11.6 Problems 4.1, 4.2, 11.10Problems 4.1, 4.2, 11.10 Exam 1 rework due 3 MarchExam 1 rework due 3 March Quiz #2Quiz #2

Live: 3 MarchLive: 3 March DL no later than 10 MarchDL no later than 10 March

Exam 1 Clarification Problem #1a) Radar Detector with 1 MixerProblem #1a) Radar Detector with 1 Mixer

LO not phase locked? Followed by LPF?LO not phase locked? Followed by LPF? Signal Voltage & Power gain ↓Signal Voltage & Power gain ↓

Problem #1b) Wording not tight enough.Problem #1b) Wording not tight enough. Only wideband noise n(t) input Only wideband noise n(t) input Mixer output = n(t) cos(Mixer output = n(t) cos(ωωcct) → Low Pass Filtert) → Low Pass Filter Mixer output = n(t) cos(Mixer output = n(t) cos(ωωcct + 14º) → t + 14º) →

Low Pass FilterLow Pass Filter Does average noise power out of LPF differ?Does average noise power out of LPF differ?

Matched Filters Seeks to maximize output SNRSeeks to maximize output SNR h(t) is matched to expected signalh(t) is matched to expected signal

Direct Conversion ReceiverDirect Conversion ReceiverMatched to baseband signalMatched to baseband signal

Output Signal Voltage (end of tOutput Signal Voltage (end of tpp echo pulse) echo pulse)ββttpp(signal power in)(signal power in)0.50.5 Instantaneous Power is this voltage squaredInstantaneous Power is this voltage squared

Noise Power Out = kTNoise Power Out = kTooWWn n

Easiest to analyze at Front EndEasiest to analyze at Front End Using PUsing Ptt and T and Too

syssys

Square pulse of width tSquare pulse of width tpp expected? expected? Noise BW = 1/(2tNoise BW = 1/(2tpp) Hz) Hz

Theory then says SNR = 2E/Theory then says SNR = 2E/NoNo

Range Gate Usage

Search

Track

2 State Radar Search Mode (Looking for contacts)Search Mode (Looking for contacts)

Multiple range bins requiredMultiple range bins required Bins ≈ tBins ≈ tpp seconds wide seconds wide Need to monitor each binNeed to monitor each bin

Track Mode (You've got a contact)Track Mode (You've got a contact) Range gate can predict location of next echoRange gate can predict location of next echo Only need to look there to maintain this contactOnly need to look there to maintain this contact May still want to watch for new contactsMay still want to watch for new contacts

Search ModeSearch Mode

Thomas Bayes

Born circa 1701Born circa 1701 Died 1761Died 1761 English Statistician English Statistician

& Minister& Minister 1763 paper "An Essay towards Solving a 1763 paper "An Essay towards Solving a

Problem in the Doctrine of Chances"Problem in the Doctrine of Chances" Provided statement of Baye's RuleProvided statement of Baye's Rule

Picture is from 1936 History of Life InsurancePicture is from 1936 History of Life Insurance

Previously… Baye's Concepts for RadarBaye's Concepts for Radar

Costs; Hit & Miss Probabilities Known?Costs; Hit & Miss Probabilities Known?Can get Optimum threshold.Can get Optimum threshold.

If Unknown, set allowable P(False Alarm)If Unknown, set allowable P(False Alarm)Go from there.Go from there.

False Alarm RateFalse Alarm Rate ≈ ≈ P(False Alarm)*PRF P(False Alarm)*PRF

If using Range GatingIf using Range Gating = P(False Alarm)*Sampling Rate= P(False Alarm)*Sampling Rate

Otherwise; Sampling Rate Otherwise; Sampling Rate << 1/t 1/tpp

P(Hit) not good enough? Crank up pulse power out PCrank up pulse power out Ptt

Crank up antenna gain GCrank up antenna gain Gantant

Increase wavelength size Increase wavelength size λλ Reduce System Temperature TReduce System Temperature Too

syssys

Decrease threshold Decrease threshold γγ Increase pulse width tIncrease pulse width tpp

Put multiple pulses on the target Put multiple pulses on the target

Coherent Detection Single Pulse Hit ProbabilitySingle Pulse Hit Probability

P(Hit) = Q[ QP(Hit) = Q[ Q-1-1[P(FA)] – SNR[P(FA)] – SNR0.50.5 ] ] Q(-x) = 1 – Q(x)Q(-x) = 1 – Q(x) Can get SNR with PCan get SNR with Prr, T, Too

syssys, & W, & Wnn

Want actual values out of Matched Filter?Want actual values out of Matched Filter?Go to back end.Go to back end.

M Pulse Coherent IntegrationM Pulse Coherent IntegrationP(Hit) = Q[ QP(Hit) = Q[ Q-1-1[P(FA)] – (M*SNR)[P(FA)] – (M*SNR)0.50.5 ] ] Sum M outputs from Matched FilterSum M outputs from Matched Filter

Want to sum outputs from Want to sum outputs from identical range binsidentical range bins Compare sum to thresholdCompare sum to threshold

Binomial PDF

A random voltage is Binomially Distributed if…A random voltage is Binomially Distributed if…You've a two state experimentYou've a two state experiment

Success or FailureSuccess or FailureP(Success) & P(Failure) are constantP(Success) & P(Failure) are constantExperimental Results are Statistically IndependentExperimental Results are Statistically IndependentYou're interested in the number of successesYou're interested in the number of successes

Not the specific order of successesNot the specific order of successes

Coherent Detection Binary Detection (a.k.a Binary Integration)Binary Detection (a.k.a Binary Integration)

Transmit M pulsesTransmit M pulses >> K echoes* detected? K echoes* detected?

Display a blip on operator's PPI scope.Display a blip on operator's PPI scope. < K echoes* detected?< K echoes* detected?

Display nothing.Display nothing.

*Or noise mistakenly thought to be an echo.*Or noise mistakenly thought to be an echo.

Binary Detection: M = 10

Binary Detection: M = 10

Binary Detection: M = 10

Binary Detection: M = 10