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