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# lec44 - Doppler shift Received signal 1 Transmitted signal...

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Doppler shift 1 Received signal Transmitted signal λ 0 λ v r λ 0 is the wavelength which is the distance traveled in one time period T 0 = 1 f 0 . For electromagnetic waves in free space c = f 0 λ 0 . Lecture 44

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Doppler shift 2 In T 0 seconds, the receiver moves a distance v r f 0 to the transmitter. Receiver measures the distance of λ = λ 0 - v r f 0 between peaks. This provides a means of measuring velocity. Also f = c λ = (1 + v r c - v r ) f 0 = f 0 + f D f D is called the Doppler shift . Lecture 44
Time Processing 3 s(t) = e j2 π ft s(t-3 τ ) s(t-2 τ ) s(t- τ ) s(t) w 4 w 3 w 2 Σ y(t) w 1 Time snapshot: c ( t ) = s ( t )[1; e j 2 πf ; ... ; e j ( M 1)2 πf ] = s ( t ) H M ( f ) Array gain: y ( t ) = s ( t ) w H H M ( f ) y ( t ) = s 1 ( t ) w H H M ( f 1 ) + s 2 ( t ) w H H M ( f 2 ) Problem: Preserve s 1 while rejecting s 2 . Lecture 44

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Space-Time Processing 4 PRI’s / Delay Taps Channels/ Sensors 1 2 M-1 M 1 1 2 M-1 2 1 2 M-1 N M M Σ Filter Vector Output H M ( f ) G N ( α ) is called a space-time steering vector Space-Time processing provides ability to probe the direction ( α ) , velocity ( f ) and distance ( t ) .
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