MIT16_36s09_lec07

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MIT OpenCourseWare http://ocw.mit.edu 16.36 Communication Systems Engineering Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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Lectures 7: Modulation with 2-D signal Eytan Modiano Eytan Modiano Slide 1
Two-dimensional signals S 1 =(1,1) S 2 =(-1,-1) S 3 =(1,-1) S 4 =(-1,1) S i = (S i1 , S i2 ) Set of signal points is called a constellation 2-D constellations are commonly used Large constellations can be used to transmit many bits per symbol More bandwidth efficient More error prone The “shape” of the constellation can be used to minimize error probability by keeping symbols as far apart as possible Common constellations QAM: Quadrature Amplitude Modulation PAM in two dimensions PSK: Phase Shift Keying Eytan Modiano Slide 2 Special constellation where all symbols have equal power

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Symmetric M-QAM Eytan Modiano S m = ( A m x , A m y ), A m x , A m y ! + / " 1, + / " 3,..., + / " ( M " 1) { } M is the total number of signal points (symbols) M signal levels on each axis Constellation is symmetric # M =K 2 , for some K Signal levels on each axis are
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