Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » Principles of Digital Communications » Carrier Phase Modulation

Navigation

Table of Contents

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.
 

Carrier Phase Modulation

Module by: Behnaam Aazhang. E-mail the author

Summary: A description of phase shift keying in which information is conveyed through the phase of the modulated signal.

Phase Shift Keying (PSK)

Information is impressed on the phase of the carrier. As data changes from symbol period to symbol period, the phase shifts.

∀m,m∈12…M: s m ⁢t=A⁢ P T ⁢t⁢cos2⁢π⁢ f c ⁢t+2⁢π⁢(m−1)M m m 1 2 … M s m t A P T t 2 f c t 2 m 1 M
(1)

Example 1

Binary s 1 ⁢t s 1 t or s 2 ⁢t s 2 t

Representing the Signals

An orthonormal basis to represent the signals is

ψ 1 ⁢t=1 E s ⁢A⁢ P T ⁢t⁢cos2⁢π⁢ f c ⁢t ψ 1 t 1 E s A P T t 2 f c t
(2)
ψ 2 ⁢t=-1 E s ⁢A⁢ P T ⁢t⁢sin2⁢π⁢ f c ⁢t ψ 2 t -1 E s A P T t 2 f c t
(3)

The signal

S m ⁢t=A⁢ P T ⁢t⁢cos2⁢π⁢ f c ⁢t+2⁢π⁢(m−1)M S m t A P T t 2 f c t 2 m 1 M
(4)
S m ⁢t=A⁢cos2⁢π⁢(m−1)M⁢ P T ⁢t⁢cos2⁢π⁢ f c ⁢t−A⁢sin2⁢π⁢(m−1)M⁢ P T ⁢t⁢sin2⁢π⁢ f c ⁢t S m t A 2 m 1 M P T t 2 f c t A 2 m 1 M P T t 2 f c t
(5)

The signal energy

E s =∫−∞∞A2⁢ P T 2t⁢cos22⁢π⁢ f c ⁢t+2⁢π⁢(m−1)Mdt=∫0TA2⁢(12+12⁢cos4⁢π⁢ f c ⁢t+4⁢π⁢(m−1)M)dt E s t A 2 P T t 2 2 f c t 2 m 1 M 2 t 0 T A 2 1 2 1 2 4 f c t 4 m 1 M
(6)
E s =A2⁢T2+12⁢A2⁢∫0Tcos4⁢π⁢ f c ⁢t+4⁢π⁢(m−1)Mdt≃A2⁢T2 E s A 2 T 2 1 2 A 2 t 0 T 4 f c t 4 m 1 M A 2 T 2
(7)
(Note that in the above equation, the integral in the last step before the aproximation is very small.) Therefore,
ψ 1 ⁢t=2T⁢ P T ⁢t⁢cos2⁢π⁢ f c ⁢t ψ 1 t 2 T P T t 2 f c t
(8)
ψ 2 ⁢t=(−2T)⁢ P T ⁢t⁢sin2⁢π⁢ f c ⁢t ψ 2 t 2 T P T t 2 f c t
(9)

In general,

∀m,m∈12…M: s m ⁢t=A⁢ P T ⁢t⁢cos2⁢π⁢ f c ⁢t+2⁢π⁢(m−1)M m m 1 2 … M s m t A P T t 2 f c t 2 m 1 M
(10)
and ψ 1 ⁢t ψ 1 t
ψ 1 ⁢t=2T⁢ P T ⁢t⁢cos2⁢π⁢ f c ⁢t ψ 1 t 2 T P T t 2 f c t
(11)
ψ 2 ⁢t=2T⁢ P T ⁢t⁢sin2⁢π⁢ f c ⁢t ψ 2 t 2 T P T t 2 f c t
(12)
s m = E s ⁢cos2⁢π⁢(m−1)M E s ⁢sin2⁢π⁢(m−1)M s m E s 2 m 1 M E s 2 m 1 M
(13)

Example 2

x t ′ =-1i⁢A⁢cos−(2⁢π⁢ f c ⁢ t ′ )+2⁢π⁢ f c ⁢τ x t ′ -1 i A 2 f c t ′ 2 f c τ θ ′
(23)
x t =-1i⁢A⁢cos2⁢π⁢ f c ⁢t−(2⁢π⁢ f c ⁢ τ ′ −2⁢π⁢ f c ⁢τ+ θ ′ ) x t -1 i A 2 f c t 2 f c τ ′ 2 f c τ θ ′
(24)

Local oscillator should match to phase θθ.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

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

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

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

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

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? 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

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