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ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #24 9 April 2015Lecture #24 9 April 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633 Read 5.1 & 5.2Read 5.1 & 5.2 Problems 4.3, 4.4, 5.1Problems 4.3, 4.4, 5.1 Reworked exams due 16 April (Live)Reworked exams due 16 April (Live)
Around 23 April (DL)Around 23 April (DL)
Coherent Detection (PLL) Single EchoSingle Echo
Will operate along X(Will operate along X(ττ,0),0) Matched Filter output envelopeMatched Filter output envelope Zero dopplerZero doppler
Multiple Echoes in ≈ same range binMultiple Echoes in ≈ same range bin Strong will operate along X(Strong will operate along X(ττ,0),0) Weak will operate in X(Weak will operate in X(ττ,,νν) ) If equal strength, both may operate in X(If equal strength, both may operate in X(ττ,,νν) )
Noncoherent DetectionNoncoherent Detection All echoes operate in X(All echoes operate in X(ττ,,νν) )
Rectangular Pulse Ambiguity Function
source: skolnik, Introduction to Radar Systems
Nulls at 1/tp Hz Doppler Blind SpeedsDoppler Blind Speeds Moving Target IndicatorMoving Target Indicator
Delay Line CancelerDelay Line Canceler Has Blind Speeds at n(PRF), n a + integerHas Blind Speeds at n(PRF), n a + integer
Ambiguity Function Blind SpeedsAmbiguity Function Blind Speeds h(t) = 1; 0 < t < tp?h(t) = 1; 0 < t < tp? Doppler Frequency of 1/tp Hz?Doppler Frequency of 1/tp Hz? 1 complete Sinusoid Cycle in tp seconds1 complete Sinusoid Cycle in tp seconds Area under h(t)p(t) = Matched Filter Output = 0Area under h(t)p(t) = Matched Filter Output = 0
M = 5 Pulse Integration One way to do this is with a filter matched to 5 pulses.One way to do this is with a filter matched to 5 pulses.
What will the Ambiguity time axis look like?What will the Ambiguity time axis look like? X(X(ττ,0) = ,0) = AutocorrelationAutocorrelation of complex envelope g(t)of complex envelope g(t)
t
g(t) & h(t)
source: Levanon, Radar Principles
M = 5 Pulse Integration One way to do this is with a filter matched to 5 pulses.One way to do this is with a filter matched to 5 pulses.
What will the Ambiguity frequency axis look like? X(0,What will the Ambiguity frequency axis look like? X(0,νν) = ) = F.T. of signal's magnitudeF.T. of signal's magnitude
t
g(t) & h(t)
source: Levanon, Radar Principles
Frequency Domain Processing
Doppler shift is 0 Hz here.Dashed Line Sinc Function: Set by Pulse ShapeInside smaller Sinc Function: Set by Pulse train LengthDistance between small Sinc Functions: Set by PRF
PRF
Source: Communication and Radar Systems. Nicolaos Tzannes
Main lobe is 1/(2Window) Hz wide
1/tp
"3D" View, 5 Pulse Ambiguity
source: Levanon, Radar Principles
Top Down View, 5 Pulse Ambiguity
source: Levanon, Radar Principles
Plenty of opportunities to track wrong peak.
5 Pulse Ambiguity Function Of Academic InterestOf Academic Interest
Integration typically not done this wayIntegration typically not done this way Matched Filter usually set for single pulseMatched Filter usually set for single pulse
Integrate by adding M outputs togetherIntegrate by adding M outputs together Make decision based on sumMake decision based on sum
But…But… Center pulse can be made arbitrarily narrowCenter pulse can be made arbitrarily narrow
Along the time axis
source: Levanon, Radar Principles
Pulse width tPulse width tpp can be made real small can be made real small Slowing PRF will move triangles apartSlowing PRF will move triangles apart
Along the Frequency Axis
PRFSource: Communication and Radar Systems. Nicolaos Tzannes
Main lobe is 1/(2Window) Hz wide
1/tp
Number of pulses can be made largeNumber of pulses can be made large Window (function of M, tWindow (function of M, tpp & 1/PRF) gets larger & 1/PRF) gets larger Small sinc functions become spikierSmall sinc functions become spikier
Slowing PRF not good hereSlowing PRF not good here
M Pulse Ambiguity Function
Shows center pulse can be made arbitrarily Shows center pulse can be made arbitrarily narrownarrow
Ambiguity Function volume must go Ambiguity Function volume must go elsewhereelsewhere Goes into other spikesGoes into other spikes
Is there another technique that can yield Is there another technique that can yield good time and doppler accuracy?good time and doppler accuracy? I.E. a narrow spike centered at X(0,0) ?I.E. a narrow spike centered at X(0,0) ?
Baseband Linear Up-Chirp Signal
ffss = 100 sps = 100 sps ttpp = 1 second = 1 second Start at 0 HzStart at 0 Hz End at 6 HzEnd at 6 Hz
RCVR LO set RCVR LO set to run at fto run at flowlow. .
Autocorrelation of Up-ChirpRight Hand Side
Right Hand SideRight Hand Side Pulse lasted 100 Pulse lasted 100
samplessamples Autocorrelation Autocorrelation
hits zero around 7 hits zero around 7 samplessamples
Matched filter Matched filter output & output & Ambiguity Ambiguity Function should Function should look similarlook similar
Chirped Pulse ffss = 100 sps = 100 sps ttpp = 1 second = 1 second Start at 0 HzStart at 0 Hz End at 6 HzEnd at 6 Hz
Equal Energy Equal Energy Unchirped Pulse Unchirped Pulse Output. Output.