Connexions

You are here: Home » Content » Examples of Correlation Detection
Content Actions
Lenses

What is a lens?

Lenses

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

What is in a lens?

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

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

This content is ...
Affiliated with (?)
This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.

  • This module is included inLens: Rice University OpenCourseWare
    By: OpenCourseWare ConsortiumAs a part of collection:"Digital Communication Systems"

    Click the "Rice University OCW" link to see all content affiliated with them.

    Rice University OCW
Tags

(?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Examples of Correlation Detection

Module by: Behnaam Aazhang

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 
Figure4-20.png
Figure 1
m ^ =2 m ^ 2 since Drs1>Drs2 D r s 1 D r s 2 or ∥s1∥2=∥s2∥2 s 1 2 s 2 2 and <r,s2>><r,s1> r s 2 r s 1 .
Figure4-21_1.png
Figure 2
Example 2 
Data symbols "0" or "1" with equal probability. Modulator s 1 t=st s 1 t s t for 0≤t≤T 0 t T and s 2 t=-st s 2 t s t for 0≤t≤T 0 t T .
Figure4-21_2.png
Figure 3
ψ 1 t=stA2T ψ 1 t s t A 2 T , s11=AT s 11 A T , and s21=-AT s 21 A T
∀m,m=12:rt= s m t+ N t m m 1 2 r t s m t N t (1)
Figure4-22_1.png
Figure 4
r1=AT+ η 1 r 1 A T η 1 (2)
or
r1=-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 .
Figure4-22_2.png
Figure 5
m ^ =argmaxATr1-ATr1 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 r1≥0 r 1 0
s 2 t s 2 t was transmitted if r1<0 r 1 0
An alternate demodulator:
rt= s m t+ N t ⇒r=sm+η r t s m t N t r s m η (4)

Comments, questions, feedback, criticisms?

Send feedback