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.