Skip to content Skip to navigation

Connexions

You are here: Home » Content » Homework 6 of Elec 430

Navigation

Recently Viewed

This feature requires Javascript to be enabled.

Homework 6 of Elec 430

Module by: Behnaam Aazhang. E-mail the author

User rating (How does the rating system work?)
Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

:
(0 ratings)

Summary: (Blank Abstract)

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

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 t−1 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 0≤t≤T 0 t T where P T t=1if0≤t≤T0otherwise P T t 1 0 t T 0

Figure 1
Figure 1 (Fig1.png)

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 τ∈ℝ τ . Consider the following receiver structure

Figure 2
(a) (b)
r t = s m t+ N t r t s m t N t
Figure 2(b) (Fig2.png)
  • 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 ∈2AA-A-2A a n 2 A A A 2 A . The transmitted signal is

X t =∑n=14 a n st−nT 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

Give Feedback:

E-mail the module author | Rate module ( How does the rating system work?)

Rating system

Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

(0 ratings)

Download:

Module PDF

Add module to:

My Favorites (?)

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

| A lens (?)

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions 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 Connexions 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