<< Chapter < Page Chapter >> Page >
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 .

Got questions? Get instant answers now!

Questions & Answers

a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
how did I we'll learn this
Noor Reply
f(x)= 2|x+5| find f(-6)
Prince Reply
f(n)= 2n + 1
Samantha Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Digital communication systems. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10134/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital communication systems' conversation and receive update notifications?