Examples of Correlation Detection 2.10 2001/06/27 2005/09/20 10:10:00.899 GMT-5 Behnaam Aazhang aaz@ece.rice.edu Roy Ha rha@rice.edu Behnaam Aazhang aaz@ece.rice.edu correlation correlator demodulation detection modulation receiver Examples of the use of a correlator-type receiver The implementation and theory of correlator-type receivers can be found in Detection.

m ^ 2 since D r s 1 D r s 2 or s 1 2 s 2 2 and r s 2 r s 1 .

Data symbols "0" or "1" with equal probability. Modulator s 1 t s t for 0 t T and s 2 t s t for 0 t T .

ψ 1 t s t A 2 T , s 11 A T , and s 21 A T m m 1 2 r t s m t N t

r 1 A T η 1 or r 1 A T η 1 η 1 is Gaussian with zero mean and variance N 0 2 .

m ^ A T r 1 A T r 1 , since A T 0 and s 1 s 1 then the MAP decision rule decides. s 1 t was transmitted if r 1 0 s 2 t was transmitted if r 1 0 An alternate demodulator: r t s m t N t r s m η