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Simple Radar 1 Pasive reflectors Radar transmitter Receiver Output r(t) u(t) Are waveforms r ( τ + t ) and u ( τ ) equal for some delay t ? Compute the crosscorrelation function: y ( t ) = integraldisplay u ( τ ) r ( τ + t ) Find t s.t. | y ( t ) | > η for some threshold η . Lecture 43

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Simple Radar 2 Uniform grid ( s j , t i ) with spacing Δ , s j = T 0 + j Δ , t i = i Δ , i = 0 , 1 , ..., N - 1 , j = 0 , 1 , ..., M . y ( t i ) = c · N summationdisplay j =1 u ( s j ) r ( t i + s j ) 8 N 2 flops for y = [ y 0 , y 1 , ..., y N - 1 ] , 10 N log 2 N for fast linear convolution via FFT. Lecture 43
Linear Sensor Array 3 d d d s(t)=Ae j2 π f 0 t s(t- τ ) d’ d’=dsin( ψ ) τ = d’ c s(t-3 τ ) s(t-2 τ ) ψ s ( t - τ ) = Ae 2 π j f 0 ( t - d sin ψ c ) = s ( t ) e - 2 π j f 0 c d sin ψ = s ( t ) e - j α N - 1 summationdisplay k =0 s ( t - ) = s ( t ) 1 - e - j 1 - e - j α = s ( t ) G N ( α ) G N ( α ) looks like frequency response of a MA filter! In radar this is a function of angle of arrival . Lecture 43

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Beam Pattern 4 P N ( α ) = 20 · log 10 | G N ( α ) | N -100 -50 0 50 100 -80 -60 -40 -20 0 -100 -50 0 50 100 -80 -60 -40 -20 0 -100 -50 0 50 100 -80 -60 -40 -20 0 -100 -50 0 50

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