Skip to content Skip to navigation

OpenStax-CNX

You are here: Home » Content » Pulse Amplitude Modulation Through Bandlimited Channel

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 module is included in aLens by: Digital Scholarship at Rice UniversityAs a part of collection: "Digital Communication Systems"

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

Recently Viewed

This feature requires Javascript to be enabled.
 

Pulse Amplitude Modulation Through Bandlimited Channel

Module by: Behnaam Aazhang. E-mail the author

Summary: A description of the functionality of a pulse amplitude modulated transmission system in a bandlimited channel. The bandlimited nature of the channel causes it to have memory which causes intersymbol interference, which can be dealt with in a number of ways.

Consider a PAM system b -10 b -10 ,…, b -1 b -1 , b 0 b 0 b 1 b 1 ,…

This implies

a n , a n M levels of amplitude: x t =n= a n stnT a n a n M levels of amplitude x t n a n s t n T
(1)

The received signal is

r t =n= a n st(τnT)gτdτ+ N t =n= a n st(τnT)gτdτ+ N t =n= a n s ˜ tnT+ N t r t τ n a n s t τ n T g τ N t n a n τ s t τ n T g τ N t n a n s ˜ t n T N t
(2)

Since the signals span a one-dimensional space, one filter matched to s ˜ t=s¯gt s ˜ t s g t is sufficient.

The matched filter's impulse response is

t: h opt t=s¯gTt t h opt t s g T t
(3)
The matched filter output is
yt=n= a n s ˜ t(τnT) h opt τdτ+νt=n= a n s ˜ t(τnT) h opt τdτ+νt=n= a n utnT+νt y t τ n a n s ˜ t τ n T h opt τ ν t n a n τ s ˜ t τ n T h opt τ ν t n a n u t n T ν t
(4)

The decision on the k th k th symbol is obtained by sampling the MF output at kT k T :

ykT=n= a n ukTnT+νkT y k T n a n u k T n T ν k T
(5)
The k th k th symbol is of interest:
ykT= a k u0+n= a n ukTnT+νkT y k T a k u 0 n a n u k T n T ν k T
(6)
where nk n k .

Since the channel is bandlimited, it provides memory for the transmission system. The effect of old symbols (possibly even future signals) lingers and affects the performance of the receiver. The effect of ISI can be eliminated or controlled by proper design of modulation signals or precoding filters at the transmitter, or by equalizers or sequence detectors at the receiver.

Content actions

Download module as:

Add 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