# Connexions

You are here: Home » Content » Transmission through AWGN Channels

### Recently Viewed

This feature requires Javascript to be enabled.

# Transmission through AWGN Channels

Module by: Roy Ha, Mohammad Borran, Dinesh Rajan. E-mail the authors

Summary: (Blank Abstract)

Consider the problem of transmitting data through a simple additive white Gaussian noise (AWGN) channel.

X t X t , N t N t , and r t r t represent the transmitted, noise and received signals respectively. The received signal r t = X t + N t r t X t N t .

At the transmitter, we need to map the digital bits onto analog signals before they can be transmitted through the channel. This mapping is usually known as modulation.

Since we are considering a channel with no bandwidth restrictions, we can use rectangular pulses to represent information. On of the simplest ways of mapping the signal is to let to vary the amplitude of the pulse based on the data. Mappings based on the amplitude of the transmit pulse are called pulse amplitude modulation (PAM).

The data rate in fig2 is 1T 1 T bits per second. To change the data rate using PAM, we can change the symbol period TT or change the number of amplitude levels. For example, to make the data rate 2T 2 T bits per second, we can reduce the symbol period by half or we can use four amplitude levels to map the data as shown in Figure 3.

Another method of modulation is to use the position of the pulse to represent data. Mappings based on the position of the transmit pulse are called pulse position modulation (PPM).

At the receiver the problem is of mapping from the analog signals to the digital bits. Unsurprisingly, this mapping process is known as demodulation. Demodulation, consists of recovering the digital bit transmitted in each time slot of duration TT seconds given the received signal r t r t .

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

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

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?

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

### Reuse / Edit:

Reuse or edit module (?)

#### Check out and edit

If you have permission to edit this content, using the "Reuse / Edit" action will allow you to check the content out into your Personal Workspace or a shared Workgroup and then make your edits.

#### Derive a copy

If you don't have permission to edit the content, you can still use "Reuse / Edit" to adapt the content by creating a derived copy of it and then editing and publishing the copy.