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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 1 2 M s m t A P T t 2 f c t 2 m 1 M

Representing the signals

An orthonormal basis to represent the signals is

1 t 1 E s A P T t 2 f c t
2 t -1 E s A P T t 2 f c t

The signal

S m t A P T t 2 f c t 2 m 1 M
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

The signal energy

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
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
(Note that in the above equation, the integral in the last step before the aproximation is very small.)Therefore,
1 t 2 T P T t 2 f c t
2 t 2 T P T t 2 f c t

In general,

m m 1 2 M s m t A P T t 2 f c t 2 m 1 M
and 1 t
1 t 2 T P T t 2 f c t
2 t 2 T P T t 2 f c t
s m E s 2 m 1 M E s 2 m 1 M

Demodulation and detection

r t s m t N t for some m 1 2 M

We must note that due to phase offset of the oscillator at the transmitter, phase jitter or phase changes occur because of propagation delay.

r t A P T t 2 f c t 2 m 1 M N t

For binary PSK, the modulation is antipodal, and the optimum receiver in AWGN has average bit-error probability

P e Q 2 E s N 0 Q A T N 0
The receiverwhere
r t A P T t 2 f c t N t
The statistics
r 1 t 0 T r t 2 f c t t 0 T A 2 f c t 2 f c t t 0 T 2 f c t N t
r 1 A 2 t 0 T 4 f c t 1
r 1 A 2 T t 0 T A 2 4 f c t 1 A T 2 1
where 1 t 0 T N t c t is zero mean Gaussian with variance 2 N 0 T 4 .


P e Q 2 A T 2 2 2 N 0 T 4 Q A T N 0
which is not a function of and depends strongly on phase accuracy.
P e Q 2 E s N 0
The above result implies that the amplitude of the local oscillator in the correlator structure does not play a role inthe performance of the correlation receiver. However, the accuracy of the phase does indeed play a major role. Thispoint can be seen in the following example:

x t -1 i A 2 f c t 2 f c
x t -1 i A 2 f c t 2 f c 2 f c

Local oscillator should match to phase .

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Questions & Answers

what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
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industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Digital communication systems. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10134/1.3
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