# Connexions

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# Examples of Correlation Detection

Module by: Behnaam Aazhang. E-mail the author

Summary: Examples of the use of a correlator-type receiver

The implementation and theory of correlator-type receivers can be found in Detection.

## Example 1

m ^ =2 m ^ 2 since Dr s 1 >Dr s 2 D r s 1 D r s 2 or s 1 2= s 2 2 s 1 2 s 2 2 and r, s 2 >r, s 1 r s 2 r s 1 .

## Example 2

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

ψ 1 t=stA2T ψ 1 t s t A 2 T , s 11 =AT s 11 A T , and s 21 =(AT) s 21 A T

m ,m=12: r t = s m t+ N t m m 1 2 r t s m t N t
(1)

r 1 =AT+ η 1 r 1 A T η 1
(2)
or
r 1 =(AT)+ η 1 r 1 A T η 1
(3)
η 1 η 1 is Gaussian with zero mean and variance N 0 2 N 0 2 .

m ^ =argmaxAT r 1 (AT r 1 ) m ^ A T r 1 A T r 1 , since AT>0 A T 0 and Pr s 1 =Pr s 1 s 1 s 1 then the MAP decision rule decides.

s 1 t s 1 t was transmitted if r 1 0 r 1 0

s 2 t s 2 t was transmitted if r 1 <0 r 1 0

An alternate demodulator:

( r t = s m t+ N t )(r= s m +η) r t s m t N t r s m η
(4)

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