lec43 - Simple Radar Pasive reflectors 1 u(t) Receiver...

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Unformatted text preview: Simple Radar Pasive reflectors 1 u(t) Receiver Output r(t) Radar transmitter Are waveforms r(τ + t) and u(τ ) equal for some delay t? Compute the crosscorrelation function: y (t) = u(τ )r(τ + t)dτ Find t s.t. |y (t)| > η for some threshold η . Lecture 43 Simple Radar 2 Uniform grid (sj , ti ) with spacing ∆, sj = T0 + j ∆ , ti = i∆, i = 0, 1, ..., N − 1, j = 0, 1, ..., M . N y (ti ) = c · j =1 u(sj )r (ti + sj ) 8N 2 flops for y = [y0 , y1 , ..., yN −1 ], 10N log2 N for fast linear convolution via FFT. Lecture 43 Linear Sensor Array d’=dsin(ψ) τ = d’ c s(t-3τ) ψ d’ d d d s(t-2τ) s(t-τ) s(t)=Ae j2πf0t 3 s(t − τ ) = Ae N −1 k=0 2π jf0 (t− d sin ψ ) c = s(t)e −2π j f0 c d sin ψ = s(t)e−jα 1 − e−jN α = s(t)GN (α) s(t − kτ ) = s(t) −jα 1−e GN (α) looks like frequency response of a MA filter! In radar this is a function of angle of arrival. Lecture 43 Beam Pattern 4 PN (α) = 20 · log10 0 0 |GN (α)| N −20 −20 −40 −40 −60 −60 −80 −100 −50 0 50 100 −80 −100 −50 0 50 100 0 0 −20 −20 −40 −40 −60 −60 −80 −100 −50 0 50 100 −80 −100 −50 0 50 100 Lecture 43 Shift in Beam Pattern 5 PN (α − γ ) 0 0 −10 −20 −20 −40 −30 −40 −60 −50 −80 −100 −50 0 50 100 −60 −100 −50 0 50 100 0 −10 −20 −30 −40 −50 −60 −100 −50 0 50 100 0 −10 −20 −30 −40 −50 −60 −100 −50 0 50 100 Lecture 43 Array Steering - weighting s2(t)=Ae j2πft 6 j2πft s1(t)=Ae d w1 w2 d w3 Σ y d w4 4 y (t) = s1 (t) i=1 wi e−j(i−1)2πα1 + s2 (t) 4 i=1 wi e−j(i−1)2πα2 Choose weights wi so s1 is preserved while s2 is rejected. 4 i=1 wi e−j(i−1)2πα1 = 1 , 4 i=1 wi e−j(i−1)2πα2 = 0 Lecture 43 ...
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This note was uploaded on 03/02/2011 for the course ECE 2200 taught by Professor Johnson during the Spring '05 term at Cornell University (Engineering School).

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lec43 - Simple Radar Pasive reflectors 1 u(t) Receiver...

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