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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 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
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Stoney Reply
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Adin Reply
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biomolecules are e building blocks of every organics and inorganic materials.
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Damian Reply
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Introduction about quantum dots in nanotechnology
Praveena Reply
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Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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Damian Reply
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Akash Reply
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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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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