Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Digital Communication Systems » Performance Analysis of Antipodal Binary signals with Correlation

Navigation

Lenses

What is a lens?

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.

Who can create a lens?

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

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.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

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.
  • Rice Digital Scholarship

    This collection is included in aLens by: Digital Scholarship at Rice University

    Click the "Rice Digital Scholarship" link to see all content affiliated with them.

Recently Viewed

This feature requires Javascript to be enabled.
 

Performance Analysis of Antipodal Binary signals with Correlation

Module by: Behnaam Aazhang. E-mail the author

Summary: Bit-error analysis for an antipodal signal set by using a correlator-type receiver.

Figure 1
Figure 1 (Figure4-32.png)

The bit-error probability for a correlation receiver with an antipodal signal set (Figure 1) can be found as follows:

P e =Pr m ̂ m=Pr b ̂ b= π 0 Pr r 1 <γ| m =1+ π 1 Pr r 1 γ| m =2= π 0 γf r 1 s 1 t rd r + π 1 γf r 1 s 2 t rd r P e m ̂ m b ̂ b π 0 m 1 r 1 γ π 1 m 2 r 1 γ π 0 r γ f r 1 s 1 t r π 1 r γ f r 1 s 2 t r
(1)
if π 0 = π 1 =1/2 π 0 π 1 12 , then the optimum threshold is γ=0 γ 0 .
f r 1 | s 1 t r=𝒩 E s N 0 2 f | r 1 s 1 t r E s N 0 2
(2)
f r 1 | s 2 t r=𝒩 E s N 0 2 f | r 1 s 2 t r E s N 0 2
(3)
If the two symbols are equally likely to be transmitted then π 0 = π 1 =1/2 π 0 π 1 12 and if the threshold is set to zero, then
P e =1/2012π N 0 2e|r E s |2 N 0 d r +1/2012π N 0 2e|r+ E s |2 N 0 d r P e 12 r 0 1 2 π N 0 2 r E s 2 N 0 12 r 0 1 2 π N 0 2 r E s 2 N 0
(4)
P e =1/22 E s N 0 12πe| r |22d r +1/22 E s N 0 12πe| r |22d r P e 12 r 2 E s N 0 1 2 π r 2 2 12 r 2 E s N 0 1 2 π r 2 2
(5)
with r =r E s N 0 2 r r E s N 0 2 and r =r+ E s N 0 2 r r E s N 0 2
P e =12Q2 E s N 0 +12Q2 E s N 0 =Q2 E s N 0 P e 1 2 Q 2 E s N 0 1 2 Q 2 E s N 0 Q 2 E s N 0
(6)
where Qb=b12πex22d x Q b x b 1 2 π x 2 2 .

Note that

Figure 2
Figure 2 (Figure4-34_1.png)
P e =Q d 1 2 2 N 0 P e Q d 1 2 2 N 0
(7)
where d 1 2 =2 E s =s1s22 d 1 2 2 E s s 1 s 2 2 is the Euclidean distance between the two constellation points (Figure 2).

This is exactly the same bit-error probability as for the matched filter case.

A similar bit-error analysis for matched filters can be found here. For the bit-error analysis for correlation receivers with an orthogonal signal set, refer here.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

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.

Who can create a lens?

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

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.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

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.

Who can create a lens?

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

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.

| External bookmarks