# Connexions

You are here: Home » Content » Digital Communication Systems » Homework 6

### 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?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

#### 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.

Inside Collection (Course):

Course by: Behnaam Aazhang. E-mail the author

# Homework 6

Module by: Behnaam Aazhang. E-mail the author

Summary: (Blank Abstract)

Homework set 6 of ELEC 430, Rice University, Department of Electrical and Computer Engineering

## Problem 1

Consider the following modulation system

s 0 t=A P T t1 s 0 t A P T t 1
(1)
and
s 1 t=((A P T t))1 s 1 t A P T t 1
(2)
for 0tT 0 t T where P T t={1  if  0tT0  otherwise   P T t 1 0 t T 0

The channel is ideal with Gaussian noise which is μ N t=1 μ N t 1 for all t t, wide sense stationary with R N τ=b2e|τ| R N τ b 2 τ for all τR τ . Consider the following receiver structure

• a) Find the optimum value of the threshold for the system (e.g., γγ that minimizes the P e P e ). Assume that π 0 = π 1 π 0 π 1
• b) Find the error probability when this threshold is used.

## Problem 2

Consider a PAM system where symbols a 1 a 1 , a 2 a 2 , a 3 a 3 , a 4 a 4 are transmitted where a n 2AAA(2A) a n 2 A A A 2 A . The transmitted signal is

X t =n=14 a n stnT X t n 1 4 a n s t n T
(3)
where st s t is a rectangular pulse of duration TT and height of 1. Assume that we have a channel with impulse response gt g t which is a rectangular pulse of duration TT and height 1, with white Gaussian noise with S N f= N 0 2 S N f N 0 2 for all f f.

• a) Draw a typical sample path (realization) of X t X t and of the received signal r t r t (do not forget to add a bit of noise!)
• b) Assume that the receiver knows gt g t . Design a matched filter for this transmission system.
• c) Draw a typical sample path of Y t Y t , the output of the matched filter (do not forget to add a bit of noise!)
• d) Find an expression (or draw) unT u n T where ut=s*g* h opt t u t s g h opt t .

## Problem 3

Proakis and Salehi, problem 7.35

## Problem 4

Proakis and Salehi, problem 7.39

## 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.

PDF | EPUB (?)

### What is an EPUB file?

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

#### 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?

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?

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