ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #22 2 April 2015Lecture #22 2 April 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633

ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #22 2 April 2015Lecture #22 2 April 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633

Read 4.3Read 4.3 Problems 4.10, Web 8 & 9Problems 4.10, Web 8 & 9 Design Problem due 7 April (Live), 9 April (DL)Design Problem due 7 April (Live), 9 April (DL)

Late turn in fee = -1 per working dayLate turn in fee = -1 per working day Reworked exams due 14 April (Live)Reworked exams due 14 April (Live) Quiz #2 ResultsQuiz #2 Results

Hi = 13.6, Low = 6.50, Ave = 11.33, Hi = 13.6, Low = 6.50, Ave = 11.33, σσ =2.71 =2.71

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Coherent DetectionCoherent Detection RCVR Local OscillatorRCVR Local Oscillator

PLL seeks echo frequency & phase lockPLL seeks echo frequency & phase lockttpp = 1 = 1 μμsec, fsec, fcc = 10 GHz → 10,000 cycles = 10 GHz → 10,000 cycles

Will take some time Will take some time Some echo energy is lost Some echo energy is lost Matched Filter fed sinusoid until lockMatched Filter fed sinusoid until lock

Area around zeroArea around zero

Locked → Matched Filter fed baseband pulse Locked → Matched Filter fed baseband pulse Best Potential PerformanceBest Potential Performance

Non-coherent DetectionNon-coherent Detection

RCVR Local Oscillator at transmitted fRCVR Local Oscillator at transmitted fcc

Stationary target with respect to radarStationary target with respect to radarZero doppler, baseband pulse to Matched FilterZero doppler, baseband pulse to Matched Filter

Moving target with respect to radarMoving target with respect to radarWide variety of signals fed to Matched FilterWide variety of signals fed to Matched Filter

May get almost nothing when sampledMay get almost nothing when sampled Quadrature DetectionQuadrature Detection

If energy not in I channel, it's in Q channelIf energy not in I channel, it's in Q channel

Ambiguity FunctionAmbiguity Function

X(X(ττ,,νν) = g(t)g*(t - ) = g(t)g*(t - ττ) e) ej2j2πνπνt t dtdt

X(X(ττ,0) = Autocorrelation ,0) = Autocorrelation of complex envelope g(t)of complex envelope g(t)

= Matched Filter output envelope= Matched Filter output envelope at Zero dopplerat Zero doppler

X(0,X(0,νν) = F.T. of signal's magnitude (AM)) = F.T. of signal's magnitude (AM)

∫-∞

+∞

Ambiguity FunctionAmbiguity Function

X(X(ττ,,νν) = g(t)g*(t - ) = g(t)g*(t - ττ) e) ej2j2πνπνt t dtdt

For most accurate range estimatesFor most accurate range estimates Want narrow width along Want narrow width along ττ (time) axis (time) axis

For most accurate radial velocity estimateFor most accurate radial velocity estimate Want narrow width along Want narrow width along νν (frequency) axis (frequency) axis

Since X(0,0) = 1 &Since X(0,0) = 1 &Volume of |X(Volume of |X(ττ,,νν)|)|22 = 1 (if complex E = 1) = 1 (if complex E = 1)May not be able to do both May not be able to do both

∫-∞

+∞

Selected e IntegralsSelected e Integrals

Gaussian Pulse Ambiguity FunctionGaussian Pulse Ambiguity Function ttpp = 1.0 = 1.0

source: west 5633 notes

Matched Filter Outputs as fd ↑ Matched Filter Outputs as fd ↑

fd = 1

fd = 2fd = 3

fd = 5

Rectangular Pulse Ambiguity FunctionRectangular Pulse Ambiguity Function

source: skolnik, Introduction to Radar Systems