ECEN5633 Radar Theory Lecture #25 14 April 2015 Dr. George Scheets n Read 5.3 n Problems 5.3, Web10 & 11 n Reworked Exams u Due 16 April (Live) u Due 23 April (DL) n Quiz #3 u Live on 21 April u DL < 28 April

ECEN5633 Radar Theory Lecture #26 16 April 2015 Dr. George Scheets n Read 5.5, 6.1 n Problems Web 12, 13, & 14 n Reworked Exams u Due 16 April (Live) u Due 23 April (DL) n Quiz #3 u Live on 21 April u DL < 28 April

h(t) Delays Low Frequency Output x(α) h(α) x(t-α)

Impulse Response h(t) h(t) Impulse In Matched Filter (FIR Filter) FIR weights = sampled values of h(t)

How does Chirping affect… n … the Ambiguity Function? n … a doppler shifted waveform? n … the P(Hit)? x(t) What you might see at: Direct Conversion Receiver Output of Mixer Low Pass Filter Up Chirp Local Oscillator tuned to f low Phases happen to match

Down Chirp Ambiguity Function

How does Chirping affect… n … the Ambiguity Function? u Tilts it x(t)

Chirp: No Doppler n Top: Matched Filter Output n Middle: Input n Bottom: Matched Filter Impulse Response n t p = 1 second n (Δf/2) *t 2 = 3t 2 (rate of phase change) Instantaneous Frequency = 6 Hz at t p seconds = Δf*t p at t p seconds

Chirp: 0.1 Hz Doppler n Top: Matched Filter Output n Middle: Input n Bottom: Matched Filter Impulse Response

Chirp: 1 Hz Doppler n Top: Matched Filter Output n Middle: Input n Bottom: Matched Filter Impulse Response

Chirp: 4 Hz Doppler n Top: Matched Filter Output n Middle: Input n Bottom: Matched Filter Impulse Response

Chirp Radar n Transmit a long pulse u Get range resolution of short pulse n Long pulse has > energy than short pulse n Can get by with lower voltages n Doppler Shift → Wrong range n Can get around this by… u Matching up chirp with down chirp

Down Chirp Ambiguity Function source: Levanon, Radar Principles

How does Chirping affect… n … the Ambiguity Function? u Tilts it n … a doppler shifted waveform? u MF peak is at wrong time Up Chirp

How does Chirping affect… n … the Ambiguity Function? u Tilts it n … a doppler shifted waveform? u MF peak is at wrong time n … the P(Hit)? x(t)

Some Equivalent E signals n 1 vp Square Pulse, t p = 1 microsecond Power = 1 watt, Energy = 1 μ joule n vp sinusoid, t p = 1 microsecond Power = 1 watt, Energy = 1 μ joule n 2 vp Square Pulse, t p = 0.25 microsecond Power = 4 watt, Energy = 1 μ joule n 0.2 vp sinusoid, t p = 25 microsecond Power = 0.04 watts, Energy = 1 μ joule

Matched Filter Output SNR n SNR < 2E/No u = at optimum sample time & input signal is perfectly matched u SNR = 2P r t p /N o = P r /(N o W N ) [Baseband Pulse] u SNR does depend on W N F WN depends on pulse envelope shape n SNR does depend on T o sys n Considerable Flexibility for Pulse Shape u What matters is the Energy

Radar Equation n Yields RF power at antenna output n No Chirp? No doppler? Direct Conversion Receiver Baseband pulse (out of Mixer LP Filter) n Chirp? Time Varying Sinusoid n Sinusoid packs less energy n Do we need to adjust P(Hit) equations?

How does Chirping affect… n … the Ambiguity Function? n … a doppler shifted waveform? n … the P(Hit)? u Direct Conversion Receiver? u P r effectively takes a 3 dB hit