ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #25 14 April 2015Lecture #25 14 April 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633

ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #25 14 April 2015Lecture #25 14 April 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633 Read 5.3Read 5.3 Problems 5.3, Web10 & 11 Problems 5.3, Web10 & 11 Reworked Exams Reworked Exams

Due 16 April (Live)Due 16 April (Live) Due 23 April (DL)Due 23 April (DL)

Quiz #3Quiz #3 Live on 21 AprilLive on 21 April DL DL << 28 April 28 April

ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #26 16 April 2015Lecture #26 16 April 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633

ECEN5633 Radar TheoryECEN5633 Radar TheoryLecture #26 16 April 2015Lecture #26 16 April 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-eng/scheets/ecen5633www.okstate.edu/elec-eng/scheets/ecen5633 Read 5.5, 6.1Read 5.5, 6.1 Problems Web 12, 13, & 14Problems Web 12, 13, & 14 Reworked Exams Reworked Exams

Due 16 April (Live)Due 16 April (Live) Due 23 April (DL)Due 23 April (DL)

Quiz #3Quiz #3 Live on 21 AprilLive on 21 April DL DL << 28 April 28 April

h(t) Delays Low Frequency Outputh(t) Delays Low Frequency Output

x(α) h(α)

x(t-α)

Impulse Response h(t)Impulse Response h(t)

h(t)

Impulse In

MatchedFilter

(FIR Filter)

FIR weights = sampled values of h(t)

How does Chirping affect…How does Chirping affect… … … the Ambiguity Function?the Ambiguity Function? … … a doppler shifted waveform?a doppler shifted waveform? … … the P(Hit)?the P(Hit)?

x(t)

What you might see at:Direct Conversion ReceiverOutput of Mixer Low Pass FilterUp ChirpLocal Oscillator tuned to flow

Phases happen to match

Down Chirp Ambiguity FunctionDown Chirp Ambiguity Function

How does Chirping affect…How does Chirping affect…

… … the Ambiguity Function?the Ambiguity Function? Tilts itTilts it

x(t)

Chirp: No DopplerChirp: No Doppler Top: Matched Filter OutputTop: Matched Filter Output Middle: InputMiddle: Input Bottom: Matched Filter Bottom: Matched Filter

Impulse ResponseImpulse Response

ttpp = 1 second = 1 second

(Δf/2) *t(Δf/2) *t2 2 = 3t= 3t2 2

(rate of phase change)(rate of phase change)Instantaneous Frequency Instantaneous Frequency

= 6 Hz at t= 6 Hz at tpp seconds seconds

= = ΔΔf*tf*tpp at t at tpp seconds seconds

Chirp: 0.1 Hz DopplerChirp: 0.1 Hz Doppler Top: Matched Filter OutputTop: Matched Filter Output Middle: InputMiddle: Input Bottom: Matched Filter Bottom: Matched Filter

Impulse ResponseImpulse Response

Chirp: 1 Hz DopplerChirp: 1 Hz Doppler Top: Matched Filter OutputTop: Matched Filter Output Middle: InputMiddle: Input Bottom: Matched Filter Bottom: Matched Filter

Impulse ResponseImpulse Response

Chirp: 4 Hz DopplerChirp: 4 Hz Doppler Top: Matched Filter OutputTop: Matched Filter Output Middle: InputMiddle: Input Bottom: Matched Filter Bottom: Matched Filter

Impulse ResponseImpulse Response

Chirp RadarChirp Radar Transmit a long pulseTransmit a long pulse

Get range resolution of short pulseGet range resolution of short pulse Long pulse has > energy than short pulseLong pulse has > energy than short pulse Can get by with lower voltagesCan get by with lower voltages Doppler Shift → Wrong rangeDoppler Shift → Wrong range Can get around this by…Can get around this by…

Matching up chirp with down chirpMatching up chirp with down chirp

Down Chirp Ambiguity FunctionDown Chirp Ambiguity Function

source: Levanon, Radar Principles

How does Chirping affect…How does Chirping affect… … … the Ambiguity Function?the Ambiguity Function?

Tilts itTilts it

… … a doppler shifted waveform?a doppler shifted waveform? MF peak is at MF peak is at

wrong timewrong time Up Chirp

How does Chirping affect…How does Chirping affect… … … the Ambiguity Function?the Ambiguity Function?

Tilts itTilts it

… … a doppler shifted waveform?a doppler shifted waveform? MF peak is at wrong timeMF peak is at wrong time

… … the P(Hit)?the P(Hit)?

x(t)

Some Equivalent E signalsSome Equivalent E signals 1 vp Square Pulse, t1 vp Square Pulse, tpp = 1 microsecond = 1 microsecond

Power = 1 watt, Energy = 1 Power = 1 watt, Energy = 1 μμ joule joule 220.50.5 vp sinusoid, t vp sinusoid, tpp = 1 microsecond = 1 microsecond

Power = 1 watt, Energy = 1 Power = 1 watt, Energy = 1 μμ joule joule 2 vp Square Pulse, t2 vp Square Pulse, tpp = 0.25 microsecond = 0.25 microsecond

Power = 4 watt, Energy = 1 Power = 4 watt, Energy = 1 μμ joule joule 0.2 vp sinusoid, t0.2 vp sinusoid, tpp = 25 microsecond = 25 microsecond

Power = 0.04 watts, Energy = 1 Power = 0.04 watts, Energy = 1 μμ joule joule

Matched Filter Output SNRMatched Filter Output SNR SNR SNR << 2E/ 2E/No No

= at optimum sample time= at optimum sample time& input signal is perfectly matched& input signal is perfectly matched

SNR = 2PSNR = 2Prrttpp//NNoo = P = Prr/(/(NNooWWNN) [Baseband Pulse]) [Baseband Pulse]

SNR does depend on WSNR does depend on WNN

WN depends on pulse WN depends on pulse envelopeenvelope shape shape

SNR does depend on TSNR does depend on Toosyssys

Considerable Flexibility for Pulse ShapeConsiderable Flexibility for Pulse Shape What matters is the EnergyWhat matters is the Energy

Radar EquationRadar Equation Yields RF power at antenna outputYields RF power at antenna output No Chirp? No doppler?No Chirp? No doppler?

Direct Conversion ReceiverDirect Conversion ReceiverBaseband pulse (out of Mixer LP Filter)Baseband pulse (out of Mixer LP Filter)

Chirp? Chirp? Time Varying SinusoidTime Varying Sinusoid

Sinusoid packs less energySinusoid packs less energy Do we need to adjust P(Hit) equations?Do we need to adjust P(Hit) equations?

How does Chirping affect…How does Chirping affect…

… … the Ambiguity Function?the Ambiguity Function? … … a doppler shifted waveform?a doppler shifted waveform? … … the P(Hit)?the P(Hit)?

Direct Conversion Receiver?Direct Conversion Receiver? PPrr effectively takes a 3 dB hit effectively takes a 3 dB hit