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Course by: Behnaam Aazhang. E-mail the author

Performance Analysis of Binary Antipodal Signals with Matched Filters

Module by: Behnaam Aazhang. E-mail the author

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

Recall r t = s m t+ N t r t s m t N t where m=1 m 1 or m=2 m 2 and s 1 t= s 2 t s 1 t s 2 t (see Figure 1).

Y 1 T= E s + ν 1 Y 1 T E s ν 1
(1)
Y 2 T= E s + ν 2 Y 2 T E s ν 2
(2)
since s 1 t= s 2 t s 1 t s 2 t then ν 1 ν 1 is 𝒩0 N 0 2 E s 0 N 0 2 E s . Furthermore ν 2 = ν 1 ν 2 ν 1 . Given ν 1 ν 1 then ν 2 ν 2 is deterministic and equals ν 1 ν 1 . Then Y 2 T= Y 1 T Y 2 T Y 1 T if s 1 t s 1 t is transmitted.

If s 2 T s 2 T is transmitted

Y 1 T= E s + ν 1 Y 1 T E s ν 1
(3)
Y 2 T= E s + ν 2 Y 2 T E s ν 2
(4)
ν 1 ν 1 is 𝒩0 N 0 2 E s 0 N 0 2 E s and ν 2 = ν 1 ν 2 ν 1 .

The receiver can be simplified to (see Figure 2)

If s 1 t s 1 t is transmitted Y 1 T= E s + ν 1 Y 1 T E s ν 1 .

If s 2 t s 2 t is transmitted Y 1 T= E s + ν 1 Y 1 T E s ν 1 .

P e =1/2Pr Y 1 T<0| s 1 t +1/2Pr Y 1 T0| s 2 t =1/2012π N 0 2 E s e|y E s |2 N 0 E s d y +1/2012π N 0 2 E s e|y+ E s |2 N 0 E s d y =Q E s N 0 2 E s =Q2 E s N 0 P e 12 s 1 t Y 1 T 0 12 s 2 t Y 1 T 0 12 y 0 1 2 N 0 2 E s y E s 2 N 0 E s 12 y 0 1 2 N 0 2 E s y E s 2 N 0 E s Q E s N 0 2 E s Q 2 E s N 0
(5)
This is the exact bit-error rate of a correlation receiver. For a bit-error analysis for orthogonal signals using a matched filter receiver, refer here.

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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.

Who can create a lens?

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

What are tags?

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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| 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?

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