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Example of Correlation Detection

Module by: Tuan Do-Hong. E-mail the author

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

Example 1

Figure 1
Figure 1 (Figure4-20.png)

m ^ =2 m ^ 2 since D⁢r s 1 >D⁢r 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 .

Figure 2
Figure 2 (Figure4-21_1.png)

Example 2

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

Figure 3
Figure 3 (Figure4-21_2.png)

ψ 1 ⁢t=s⁢tA2⁢T ψ 1 t s t A 2 T , s 11 =A⁢T s 11 A T , and s 21 =−(A⁢T) 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)

Figure 4
Figure 4 (Figure4-22_1.png)

r 1 =A⁢T+ η 1 r 1 A T η 1 (2)
or
r 1 =−(A⁢T)+ 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 .

Figure 5
Figure 5 (Figure4-22_2.png)

m ^ =argmaxA⁢T⁢ r 1 −(A⁢T⁢ r 1 ) m ^ A T r 1 A T r 1 , since A⁢T>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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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

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What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

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