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ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #9 10 February 2015Lecture #9 10 February 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633
ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #9 10 February 2015Lecture #9 10 February 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633
Read 8.4, 3.1 – 3.5Read 8.4, 3.1 – 3.5 Problems 2.38, 14.2, web1 & 2 Problems 2.38, 14.2, web1 & 2 Reworked Quizzes due 1 week after returnReworked Quizzes due 1 week after return Exam #1: Open book & notesExam #1: Open book & notes
17 February 2015 (Live)17 February 2015 (Live) Not later than 24 February (DL)Not later than 24 February (DL)
ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #10 12 February Lecture #10 12 February 20152015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633
ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #10 12 February Lecture #10 12 February 20152015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633 Read 3.6 & 3.7Read 3.6 & 3.7
Problems 8.9, 8.10, old exam #1Problems 8.9, 8.10, old exam #1 Reworked Quizzes DueReworked Quizzes Due
Today – LiveToday – Live 1 week after return - Dl1 week after return - Dl
Exam #1, 19 February 2015Exam #1, 19 February 2015 Open book & notesOpen book & notes
OSI IEEEOSI IEEE
February General MeetingFebruary General Meeting 5:30-6:30 pm, Wednesday, 18 February5:30-6:30 pm, Wednesday, 18 February ES201bES201b Reps from Tinker AFB willReps from Tinker AFB will
presentpresent Dinner will be served + 3 points extra creditDinner will be served + 3 points extra credit All are invited All are invited
Signal * Wideband NoiseSignal * Wideband Noise
Last Time…Last Time… Radar Horizon Radar Horizon
≈ (8*Earth Radius*height/3) ≈ (8*Earth Radius*height/3) 0.50.5
General Receiver ConfigurationsGeneral Receiver Configurations Super HeterodyneSuper Heterodyne
RF brought to IF for processingRF brought to IF for processing Homodyne (a.k.a. Direct Conversion)Homodyne (a.k.a. Direct Conversion)
RF brought to baseband for processingRF brought to baseband for processing Coherent DetectionCoherent Detection
One Mixer which must be phase & freq lockedOne Mixer which must be phase & freq locked• Phased Locked LoopsPhased Locked Loops
Syncs Receiver LO with received RF echoSyncs Receiver LO with received RF echo
Quadrature DetectionQuadrature Detection Two mixers instead of oneTwo mixers instead of one
Leonhard EulerLeonhard Euler
Born 1707Born 1707 Died 1783Died 1783 Swiss Mathematician Swiss Mathematician
& Physicist& Physicist Mostly worked in Prussia Mostly worked in Prussia
& Russia& Russia Considered Greatest Mathematician Considered Greatest Mathematician
of 18of 18thth Century Century
Joseph FourierJoseph Fourier
Born 1768Born 1768 Died 1830Died 1830 French Mathematician French Mathematician
& Physicist& Physicist Researched Heat FlowResearched Heat Flow
1822 published "Analytical Theory of Heat"1822 published "Analytical Theory of Heat" Postulated any function = bunch of sinusoidsPostulated any function = bunch of sinusoids
Not Named after Oscar MyerNot Named after Oscar Myer
Norbert WienerNorbert Wiener
Born 1894Born 1894 Died 1964Died 1964 American Mathematician American Mathematician
M.I.T. ProfessorM.I.T. Professor Proposed filter in a 1949 paperProposed filter in a 1949 paper
Minimizes the average squared error between Minimizes the average squared error between the filter output and a "desired response".the filter output and a "desired response".
Error SignalError Signal
Filter Output y(n)
‘Desired’ Response d(n)
Error e(n) = d(n) – y(n)-
+
Wiener Filter seeks to minimize <e(n)Wiener Filter seeks to minimize <e(n)22>.>.
‘‘Desired’ Response not always easy to find.Desired’ Response not always easy to find.
FIR Adaptive FilterFIR Adaptive Filterx(n) x(n-1)
z-1 z-1 z-1
w1wNw2
Filter Output y(n)
Adaptive Linear Predictor Adaptive Linear Predictor
z-1 FIRAdaptive
Filter
‘Desired Response’ d(n)
x(n)= d(n-1)
y(n)
+
-
e(n)
= d(n)^
z-1 FIRAdaptive
Filter
input d(n)
d(n-1)Estimateof d(n)
+
-
e(n)
FIR Filter unable to predict future behavior.Best option, set all weights = 0.
Suppose d(n) is White NoiseSuppose d(n) is White Noise
z-1 FIRAdaptive
Filter
input d(n)
d(n-1)Estimateof d(n)
+
-
e(n)
There is some predictability between d(n-1) & d(n).FIR weights can be adjusted to reduce error power.
Suppose d(n) is a Narrow Band SignalSuppose d(n) is a Narrow Band Signal
Suppose x1(n) is a Narrowband Signal & x2(n) is Wideband Noise
Suppose x1(n) is a Narrowband Signal & x2(n) is Wideband Noise
z-1 FIRAdaptive
Filter
input d(n) =x1(n) + x2(n)
d(n-1)
+
-
e(n)
Adaptive Filter adjusts to minimize the A[e(n)2]
y(n)
Suppose x1(n) is a Narrowband Signal & x2(n) is Wideband Noise
Suppose x1(n) is a Narrowband Signal & x2(n) is Wideband Noise
z-1 FIRAdaptive
Filter
input d(n) =x1(n) + x2(n)
d(n-1)
+
-
Estimate of
the noise
Adaptive Filter adjusts to minimize the A[e(n)2]
Estimateof Signal
e(n)
Adaptive Linear PredictorAdaptive Linear Predictor
z-1 FIRAdaptive
Filter
input d(n) =x1(n) + x2(n)
d(n-1)
+
-
Estimate of less
correlatedsignal
Adaptive (Wiener) Filter adjusts to minimize the A[e(n)2]
Estimate of more correlated signal
e(n)
Commo System Multipath SuppressionCommo System Multipath Suppression
FIRAdaptive
Filter
Received Signal r(t)
+
-
e(n)
FIR Filter attempts to undo Multipath Distortion.
y(n)Periodically ReceiveKnown Sequence ofDistorted Logic 1's and 0's
Periodically InjectKnown Sequence ofClean Logic 1's and 0's
Hermann SchwarzHermann Schwarz Born 1843Born 1843 Died 1921Died 1921 German MathematicianGerman Mathematician Modern Proof of Integral InequalityModern Proof of Integral Inequality
Published in 1888Published in 1888 In Vector Form || A∙B || In Vector Form || A∙B || << ||A||∙||B|| ||A||∙||B||
(3∟0(3∟0oo)∙(4∟90)∙(4∟90oo) = 0 ) = 0 << 3∙4 = 12 3∙4 = 12Equality holds iff A = Equality holds iff A = kkB, B, kk a scalar constant a scalar constant
Radar Signal RepresentationRadar Signal Representation s(t) = p(t)∙cos(s(t) = p(t)∙cos(ωωcct + t + θθ(t) + (t) + φφ))
Amplitude Modulation p(t)Amplitude Modulation p(t) Frequency Modulation Frequency Modulation θθ(t) (t)
For CW and fixed XMTR fFor CW and fixed XMTR fcc Pulse Radar, Pulse Radar, θθ(t) = 0(t) = 0
s(t) = p(t)∙coss(t) = p(t)∙cosθθ(t)∙cos((t)∙cos(ωωcct + t + φφ) -) -
p(t)∙sinp(t)∙sinθθ(t)∙sin((t)∙sin(ωωcct + t + φφ))
Complex Envelope c(t)Complex Envelope c(t)= p(t)[cos= p(t)[cosθθ(t) + j∙sin(t) + j∙sinθθ(t)](t)]
These terms modulate carrier frequency fThese terms modulate carrier frequency fcc
They define (envelope) shape of S(f)They define (envelope) shape of S(f)
Marc-Antoine ParsevalMarc-Antoine Parseval
Born 1755Born 1755 Died 1836Died 1836 French MathematicianFrench Mathematician Published 5 papers in his lifePublished 5 papers in his life
#2 in 1799 stated, but did not prove#2 in 1799 stated, but did not prove Said was self-evidentSaid was self-evident
Picture not
Available
Sinc2 Function & Noise BWSinc2 Function & Noise BW
f(Hz)… …
Noise BW = 1/(2Tp)
1/Tp
0
Tp2
Matched FiltersMatched 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
Square pulse of width tSquare pulse of width tpp expected? expected? Noise BW = 1/(2tNoise BW = 1/(2tpp) Hz) Hz
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