<s>
Phase-shift	B-General_Concept
keying	I-General_Concept
(	O
PSK	O
)	O
is	O
a	O
digital	B-General_Concept
modulation	B-Application
process	O
which	O
conveys	O
data	B-General_Concept
by	O
changing	O
(	O
modulating	O
)	O
the	O
phase	O
of	O
a	O
constant	O
frequency	O
reference	O
signal	O
(	O
the	O
carrier	O
wave	O
)	O
.	O
</s>
<s>
The	O
modulation	B-Application
is	O
accomplished	O
by	O
varying	O
the	O
sine	O
and	O
cosine	O
inputs	O
at	O
a	O
precise	O
time	O
.	O
</s>
<s>
It	O
is	O
widely	O
used	O
for	O
wireless	B-Architecture
LANs	I-Architecture
,	O
RFID	B-Application
and	O
Bluetooth	B-Protocol
communication	O
.	O
</s>
<s>
Any	O
digital	B-General_Concept
modulation	B-Application
scheme	O
uses	O
a	O
finite	O
number	O
of	O
distinct	O
signals	O
to	O
represent	O
digital	B-General_Concept
data	I-General_Concept
.	O
</s>
<s>
The	O
demodulator	B-Device
,	O
which	O
is	O
designed	O
specifically	O
for	O
the	O
symbol-set	O
used	O
by	O
the	O
modulator	B-Application
,	O
determines	O
the	O
phase	O
of	O
the	O
received	O
signal	O
and	O
maps	O
it	O
back	O
to	O
the	O
symbol	O
it	O
represents	O
,	O
thus	O
recovering	O
the	O
original	O
data	B-General_Concept
.	O
</s>
<s>
CPSK	O
requires	O
a	O
complicated	O
demodulator	B-Device
,	O
because	O
it	O
must	O
extract	O
the	O
reference	O
wave	O
from	O
the	O
received	O
signal	O
and	O
keep	O
track	O
of	O
it	O
,	O
to	O
compare	O
each	O
sample	O
to	O
.	O
</s>
<s>
Because	O
the	O
symbols	O
are	O
encoded	O
in	O
the	O
difference	O
in	O
phase	O
between	O
successive	O
samples	O
,	O
this	O
is	O
called	O
differential	B-General_Concept
phase-shift	I-General_Concept
keying	I-General_Concept
(	O
DPSK	B-General_Concept
)	O
.	O
</s>
<s>
DPSK	B-General_Concept
can	O
be	O
significantly	O
simpler	O
to	O
implement	O
than	O
ordinary	O
PSK	O
,	O
as	O
it	O
is	O
a	O
'	O
non-coherent	O
'	O
scheme	O
,	O
i.e.	O
</s>
<s>
there	O
is	O
no	O
need	O
for	O
the	O
demodulator	B-Device
to	O
keep	O
track	O
of	O
a	O
reference	O
wave	O
.	O
</s>
<s>
A	O
trade-off	O
is	O
that	O
it	O
has	O
more	O
demodulation	B-Device
errors	O
.	O
</s>
<s>
There	O
are	O
three	O
major	O
classes	O
of	O
digital	B-General_Concept
modulation	B-Application
techniques	O
used	O
for	O
transmission	O
of	O
digitally	O
represented	O
data	B-General_Concept
:	O
</s>
<s>
All	O
convey	O
data	B-General_Concept
by	O
changing	O
some	O
aspect	O
of	O
a	O
base	O
signal	O
,	O
the	O
carrier	O
wave	O
(	O
usually	O
a	O
sinusoid	O
)	O
,	O
in	O
response	O
to	O
a	O
data	B-General_Concept
signal	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
PSK	O
,	O
the	O
phase	O
is	O
changed	O
to	O
represent	O
the	O
data	B-General_Concept
signal	O
.	O
</s>
<s>
A	O
convenient	O
method	O
to	O
represent	O
PSK	O
schemes	O
is	O
on	O
a	O
constellation	B-Application
diagram	I-Application
.	O
</s>
<s>
In	O
PSK	O
,	O
the	O
constellation	B-Application
points	I-Application
chosen	O
are	O
usually	O
positioned	O
with	O
uniform	O
angular	O
spacing	O
around	O
a	O
circle	O
.	O
</s>
<s>
Two	O
common	O
examples	O
are	O
"	O
binary	O
phase-shift	B-General_Concept
keying	I-General_Concept
"	O
(	O
BPSK	O
)	O
which	O
uses	O
two	O
phases	O
,	O
and	O
"	O
quadrature	O
phase-shift	B-General_Concept
keying	I-General_Concept
"	O
(	O
QPSK	O
)	O
which	O
uses	O
four	O
phases	O
,	O
although	O
any	O
number	O
of	O
phases	O
may	O
be	O
used	O
.	O
</s>
<s>
Since	O
the	O
data	B-General_Concept
to	O
be	O
conveyed	O
are	O
usually	O
binary	O
,	O
the	O
PSK	O
scheme	O
is	O
usually	O
designed	O
with	O
the	O
number	O
of	O
constellation	B-Application
points	I-Application
being	O
a	O
power	O
of	O
two	O
.	O
</s>
<s>
BPSK	O
(	O
also	O
sometimes	O
called	O
PRK	O
,	O
phase	O
reversal	O
keying	O
,	O
or	O
2PSK	O
)	O
is	O
the	O
simplest	O
form	O
of	O
phase	B-General_Concept
shift	I-General_Concept
keying	I-General_Concept
(	O
PSK	O
)	O
.	O
</s>
<s>
It	O
does	O
not	O
particularly	O
matter	O
exactly	O
where	O
the	O
constellation	B-Application
points	I-Application
are	O
positioned	O
,	O
and	O
in	O
this	O
figure	O
they	O
are	O
shown	O
on	O
the	O
real	O
axis	O
,	O
at	O
0°	O
and	O
180°	O
.	O
</s>
<s>
Therefore	O
,	O
it	O
handles	O
the	O
highest	O
noise	O
level	O
or	O
distortion	O
before	O
the	O
demodulator	B-Device
reaches	O
an	O
incorrect	O
decision	O
.	O
</s>
<s>
It	O
is	O
,	O
however	O
,	O
only	O
able	O
to	O
modulate	O
at	O
1bit/symbol	O
(	O
as	O
seen	O
in	O
the	O
figure	O
)	O
and	O
so	O
is	O
unsuitable	O
for	O
high	O
data-rate	O
applications	O
.	O
</s>
<s>
Yet	O
there	O
is	O
the	O
possibility	O
of	O
extending	O
this	O
bit/symbol	O
,	O
given	O
the	O
modulators	B-Application
symbol	O
encryption	O
/	O
decryption	O
logic	O
system	O
.	O
</s>
<s>
In	O
the	O
presence	O
of	O
an	O
arbitrary	O
phase-shift	O
introduced	O
by	O
the	O
communications	O
channel	O
,	O
the	O
demodulator	B-Device
(	O
see	O
,	O
e.g.	O
</s>
<s>
As	O
a	O
result	O
,	O
the	O
data	B-General_Concept
is	O
often	O
differentially	O
encoded	O
prior	O
to	O
modulation	B-Application
.	O
</s>
<s>
BPSK	O
is	O
functionally	O
equivalent	O
to	O
2-QAM	B-Device
modulation	B-Application
.	O
</s>
<s>
In	O
the	O
specific	O
form	O
,	O
binary	O
data	B-General_Concept
is	O
often	O
conveyed	O
with	O
the	O
following	O
signals	O
:	O
</s>
<s>
The	O
topmost	O
signal	O
is	O
a	O
BPSK-modulated	O
cosine	O
wave	O
that	O
the	O
BPSK	O
modulator	B-Application
would	O
produce	O
.	O
</s>
<s>
After	O
modulation	B-Application
,	O
the	O
base	O
band	O
signal	O
will	O
be	O
moved	O
to	O
the	O
high	O
frequency	O
band	O
by	O
multiplying	O
.	O
</s>
<s>
Sometimes	O
this	O
is	O
known	O
as	O
quadriphase	B-General_Concept
PSK	O
,	O
4-PSK	B-General_Concept
,	O
or	O
4-QAM	B-Device
.	O
</s>
<s>
(	O
Although	O
the	O
root	O
concepts	O
of	O
QPSK	O
and	O
4-QAM	B-Device
are	O
different	O
,	O
the	O
resulting	O
modulated	B-Application
radio	O
waves	O
are	O
exactly	O
the	O
same	O
.	O
)	O
</s>
<s>
QPSK	O
uses	O
four	O
points	O
on	O
the	O
constellation	B-Application
diagram	I-Application
,	O
equispaced	O
around	O
a	O
circle	O
.	O
</s>
<s>
With	O
four	O
phases	O
,	O
QPSK	O
can	O
encode	O
two	O
bits	O
per	O
symbol	O
,	O
shown	O
in	O
the	O
diagram	O
with	O
Gray	B-Device
coding	I-Device
to	O
minimize	O
the	O
bit	O
error	O
rate	O
(	O
BER	O
)	O
sometimes	O
misperceived	O
as	O
twice	O
the	O
BER	O
of	O
BPSK	O
.	O
</s>
<s>
The	O
mathematical	O
analysis	O
shows	O
that	O
QPSK	O
can	O
be	O
used	O
either	O
to	O
double	O
the	O
data	B-General_Concept
rate	O
compared	O
with	O
a	O
BPSK	O
system	O
while	O
maintaining	O
the	O
same	O
bandwidth	B-Algorithm
of	O
the	O
signal	O
,	O
or	O
to	O
maintain	O
the	O
data-rate	O
of	O
BPSK	O
but	O
halving	O
the	O
bandwidth	B-Algorithm
needed	O
.	O
</s>
<s>
Given	O
that	O
radio	O
communication	O
channels	O
are	O
allocated	O
by	O
agencies	O
such	O
as	O
the	O
Federal	O
Communications	O
Commission	O
giving	O
a	O
prescribed	O
(	O
maximum	O
)	O
bandwidth	B-Algorithm
,	O
the	O
advantage	O
of	O
QPSK	O
over	O
BPSK	O
becomes	O
evident	O
:	O
QPSK	O
transmits	O
twice	O
the	O
data	B-General_Concept
rate	O
in	O
a	O
given	O
bandwidth	B-Algorithm
compared	O
to	O
BPSK	O
-	O
at	O
the	O
same	O
BER	O
.	O
</s>
<s>
Writing	O
the	O
symbols	O
in	O
the	O
constellation	B-Application
diagram	I-Application
in	O
terms	O
of	O
the	O
sine	O
and	O
cosine	O
waves	O
used	O
to	O
transmit	O
them	O
:	O
</s>
<s>
Note	O
that	O
the	O
signal-space	O
points	O
for	O
BPSK	O
do	O
not	O
need	O
to	O
split	O
the	O
symbol	O
(	O
bit	O
)	O
energy	O
over	O
the	O
two	O
carriers	O
in	O
the	O
scheme	O
shown	O
in	O
the	O
BPSK	O
constellation	B-Application
diagram	I-Application
.	O
</s>
<s>
Although	O
QPSK	O
can	O
be	O
viewed	O
as	O
a	O
quaternary	O
modulation	B-Application
,	O
it	O
is	O
easier	O
to	O
see	O
it	O
as	O
two	O
independently	O
modulated	B-Application
quadrature	O
carriers	O
.	O
</s>
<s>
The	O
modulated	B-Application
signal	O
is	O
shown	O
below	O
for	O
a	O
short	O
segment	O
of	O
a	O
random	O
binary	O
data-stream	O
.	O
</s>
<s>
The	O
binary	O
data	B-General_Concept
that	O
is	O
conveyed	O
by	O
this	O
waveform	O
is	O
:	O
11000110	O
.	O
</s>
<s>
Offset	O
quadrature	O
phase-shift	B-General_Concept
keying	I-General_Concept
(	O
OQPSK	O
)	O
is	O
a	O
variant	O
of	O
phase-shift	B-General_Concept
keying	I-General_Concept
modulation	B-Application
using	O
four	O
different	O
values	O
of	O
the	O
phase	O
to	O
transmit	O
.	O
</s>
<s>
It	O
is	O
sometimes	O
called	O
staggered	O
quadrature	O
phase-shift	B-General_Concept
keying	I-General_Concept
(	O
SQPSK	O
)	O
.	O
</s>
<s>
In	O
the	O
constellation	B-Application
diagram	I-Application
shown	O
on	O
the	O
right	O
,	O
it	O
can	O
be	O
seen	O
that	O
this	O
will	O
limit	O
the	O
phase-shift	O
to	O
no	O
more	O
than	O
90°	O
at	O
a	O
time	O
.	O
</s>
<s>
The	O
modulated	B-Application
signal	O
is	O
shown	O
below	O
for	O
a	O
short	O
segment	O
of	O
a	O
random	O
binary	O
data-stream	O
.	O
</s>
<s>
The	O
license-free	O
shaped-offset	O
QPSK	O
(	O
SOQPSK	O
)	O
is	O
interoperable	O
with	O
Feher-patented	O
QPSK	O
(	O
FQPSK	O
)	O
,	O
in	O
the	O
sense	O
that	O
an	O
integrate-and-dump	O
offset	O
QPSK	O
detector	O
produces	O
the	O
same	O
output	O
no	O
matter	O
which	O
kind	O
of	O
transmitter	O
is	O
used	O
.	O
</s>
<s>
These	O
modulations	B-Application
carefully	O
shape	O
the	O
I	O
and	O
Q	O
waveforms	O
such	O
that	O
they	O
change	O
very	O
smoothly	O
,	O
and	O
the	O
signal	O
stays	O
constant-amplitude	O
even	O
during	O
signal	O
transitions	O
.	O
</s>
<s>
SOQPSK	O
modulation	B-Application
can	O
be	O
represented	O
as	O
the	O
hybrid	O
of	O
QPSK	O
and	O
MSK	B-Device
:	O
SOQPSK	O
has	O
the	O
same	O
signal	B-Application
constellation	I-Application
as	O
QPSK	O
,	O
however	O
the	O
phase	O
of	O
SOQPSK	O
is	O
always	O
stationary	O
.	O
</s>
<s>
The	O
standard	O
description	O
of	O
SOQPSK-TG	O
involves	O
ternary	B-Protocol
symbols	I-Protocol
.	O
</s>
<s>
SOQPSK	O
is	O
one	O
of	O
the	O
most	O
spread	O
modulation	B-Application
schemes	O
in	O
application	O
to	O
LEO	O
satellite	O
communications	O
.	O
</s>
<s>
One	O
property	O
this	O
modulation	B-Application
scheme	O
possesses	O
is	O
that	O
if	O
the	O
modulated	B-Application
signal	O
is	O
represented	O
in	O
the	O
complex	O
domain	O
,	O
transitions	O
between	O
symbols	O
never	O
pass	O
through	O
0	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
-QPSK	O
lends	O
itself	O
to	O
easy	O
demodulation	B-Device
and	O
has	O
been	O
adopted	O
for	O
use	O
in	O
,	O
for	O
example	O
,	O
TDMA	O
cellular	O
telephone	O
systems	O
.	O
</s>
<s>
The	O
modulated	B-Application
signal	O
is	O
shown	O
below	O
for	O
a	O
short	O
segment	O
of	O
a	O
random	O
binary	O
data-stream	O
.	O
</s>
<s>
Dual-polarization	O
quadrature	B-General_Concept
phase	I-General_Concept
shift	I-General_Concept
keying	I-General_Concept
(	O
DPQPSK	O
)	O
or	O
dual-polarization	O
QPSK	O
-	O
involves	O
the	O
polarization	O
multiplexing	O
of	O
two	O
different	O
QPSK	O
signals	O
,	O
thus	O
improving	O
the	O
spectral	B-Protocol
efficiency	I-Protocol
by	O
a	O
factor	O
of	O
2	O
.	O
</s>
<s>
With	O
more	O
than	O
8	O
phases	O
,	O
the	O
error-rate	O
becomes	O
too	O
high	O
and	O
there	O
are	O
better	O
,	O
though	O
more	O
complex	O
,	O
modulations	B-Application
available	O
such	O
as	O
quadrature	B-Device
amplitude	I-Device
modulation	I-Device
(	O
QAM	B-Device
)	O
.	O
</s>
<s>
Although	O
any	O
number	O
of	O
phases	O
may	O
be	O
used	O
,	O
the	O
fact	O
that	O
the	O
constellation	O
must	O
usually	O
deal	O
with	O
binary	O
data	B-General_Concept
means	O
that	O
the	O
number	O
of	O
symbols	O
is	O
usually	O
a	O
power	O
of	O
2	O
to	O
allow	O
an	O
integer	O
number	O
of	O
bits	O
per	O
symbol	O
.	O
</s>
<s>
(	O
Using	O
Gray	B-Device
coding	I-Device
allows	O
us	O
to	O
approximate	O
the	O
Lee	O
distance	O
of	O
the	O
errors	O
as	O
the	O
Hamming	O
distance	O
of	O
the	O
errors	O
in	O
the	O
decoded	O
bitstream	O
,	O
which	O
is	O
easier	O
to	O
implement	O
in	O
hardware	O
.	O
)	O
</s>
<s>
It	O
is	O
seen	O
that	O
higher-order	B-Device
modulations	I-Device
exhibit	O
higher	O
error-rates	O
;	O
in	O
exchange	O
however	O
they	O
deliver	O
a	O
higher	O
raw	O
data-rate	O
.	O
</s>
<s>
Bounds	O
on	O
the	O
error	O
rates	O
of	O
various	O
digital	B-General_Concept
modulation	B-Application
schemes	O
can	O
be	O
computed	O
with	O
application	O
of	O
the	O
union	O
bound	O
to	O
the	O
signal	B-Application
constellation	I-Application
.	O
</s>
<s>
Bandwidth	B-Algorithm
(	O
or	O
spectral	O
)	O
efficiency	O
of	O
M-PSK	O
modulation	B-Application
schemes	O
increases	O
with	O
increasing	O
of	O
modulation	B-Application
order	O
M	O
(	O
unlike	O
,	O
for	O
example	O
,	O
M-FSK	B-Device
)	O
:	O
</s>
<s>
The	O
same	O
relationship	O
holds	O
true	O
for	O
M-QAM	B-Device
.	O
</s>
<s>
Differential	B-General_Concept
phase	I-General_Concept
shift	I-General_Concept
keying	I-General_Concept
(	O
DPSK	B-General_Concept
)	O
is	O
a	O
common	O
form	O
of	O
phase	B-Device
modulation	I-Device
that	O
conveys	O
data	B-General_Concept
by	O
changing	O
the	O
phase	O
of	O
the	O
carrier	O
wave	O
.	O
</s>
<s>
This	O
problem	O
can	O
be	O
overcome	O
by	O
using	O
the	O
data	B-General_Concept
to	O
change	O
rather	O
than	O
set	O
the	O
phase	O
.	O
</s>
<s>
Another	O
variant	O
of	O
DPSK	B-General_Concept
is	O
Symmetric	O
Differential	B-General_Concept
Phase	I-General_Concept
Shift	I-General_Concept
keying	I-General_Concept
,	O
SDPSK	O
,	O
where	O
encoding	O
would	O
be	O
+90°	O
for	O
a	O
"	O
1	O
"	O
and	O
−90°	O
for	O
a	O
"	O
0	O
"	O
.	O
</s>
<s>
In	O
differentially	O
encoded	O
QPSK	O
(	O
DQPSK	B-General_Concept
)	O
,	O
the	O
phase-shifts	O
are	O
0°	O
,	O
90°	O
,	O
180°	O
,	O
−90°	O
corresponding	O
to	O
data	B-General_Concept
"	O
00	O
"	O
,	O
"	O
01	O
"	O
,	O
"	O
11	O
"	O
,	O
"	O
10	O
"	O
.	O
</s>
<s>
The	O
difference	O
encodes	O
the	O
data	B-General_Concept
as	O
described	O
above	O
.	O
</s>
<s>
Symmetric	O
differential	O
quadrature	B-General_Concept
phase	I-General_Concept
shift	I-General_Concept
keying	I-General_Concept
(	O
SDQPSK	O
)	O
is	O
like	O
DQPSK	B-General_Concept
,	O
but	O
encoding	O
is	O
symmetric	O
,	O
using	O
phase	O
shift	O
values	O
of	O
−135°	O
,	O
−45°	O
,	O
+45°	O
and	O
+135°	O
.	O
</s>
<s>
The	O
modulated	B-Application
signal	O
is	O
shown	O
below	O
for	O
both	O
DBPSK	B-General_Concept
and	O
DQPSK	B-General_Concept
as	O
described	O
above	O
.	O
</s>
<s>
One	O
of	O
the	O
most	O
popular	O
applications	O
of	O
DPSK	B-General_Concept
is	O
the	O
Bluetooth	B-Protocol
standard	O
where	O
-DQPSK	O
and	O
8-DPSK	O
were	O
implemented	O
.	O
</s>
<s>
For	O
a	O
signal	O
that	O
has	O
been	O
differentially	O
encoded	O
,	O
there	O
is	O
an	O
obvious	O
alternative	O
method	O
of	O
demodulation	B-Device
.	O
</s>
<s>
Instead	O
of	O
demodulating	O
as	O
usual	O
and	O
ignoring	O
carrier-phase	O
ambiguity	O
,	O
the	O
phase	O
between	O
two	O
successive	O
received	O
symbols	O
is	O
compared	O
and	O
used	O
to	O
determine	O
what	O
the	O
data	B-General_Concept
must	O
have	O
been	O
.	O
</s>
<s>
When	O
differential	O
encoding	O
is	O
used	O
in	O
this	O
manner	O
,	O
the	O
scheme	O
is	O
known	O
as	O
differential	B-General_Concept
phase-shift	I-General_Concept
keying	I-General_Concept
(	O
DPSK	B-General_Concept
)	O
.	O
</s>
<s>
Note	O
that	O
this	O
is	O
subtly	O
different	O
from	O
just	O
differentially	O
encoded	O
PSK	O
since	O
,	O
upon	O
reception	O
,	O
the	O
received	O
symbols	O
are	O
not	O
decoded	O
one-by-one	O
to	O
constellation	B-Application
points	I-Application
but	O
are	O
instead	O
compared	O
directly	O
to	O
one	O
another	O
.	O
</s>
<s>
In	O
the	O
absence	O
of	O
noise	O
,	O
the	O
phase	O
of	O
this	O
is	O
,	O
the	O
phase-shift	O
between	O
the	O
two	O
received	O
signals	O
which	O
can	O
be	O
used	O
to	O
determine	O
the	O
data	B-General_Concept
transmitted	O
.	O
</s>
<s>
The	O
probability	O
of	O
error	O
for	O
DPSK	B-General_Concept
is	O
difficult	O
to	O
calculate	O
in	O
general	O
,	O
but	O
,	O
in	O
the	O
case	O
of	O
DBPSK	B-General_Concept
it	O
is	O
:	O
</s>
<s>
Using	O
DPSK	B-General_Concept
avoids	O
the	O
need	O
for	O
possibly	O
complex	O
carrier-recovery	O
schemes	O
to	O
provide	O
an	O
accurate	O
phase	O
estimate	O
and	O
can	O
be	O
an	O
attractive	O
alternative	O
to	O
ordinary	O
PSK	O
.	O
</s>
<s>
In	O
optical	O
communications	O
,	O
the	O
data	B-General_Concept
can	O
be	O
modulated	B-Application
onto	O
the	O
phase	O
of	O
a	O
laser	O
in	O
a	O
differential	O
way	O
.	O
</s>
<s>
The	O
modulation	B-Application
is	O
a	O
laser	O
which	O
emits	O
a	O
continuous	O
wave	O
,	O
and	O
a	O
Mach	O
–	O
Zehnder	O
modulator	B-Application
which	O
receives	O
electrical	O
binary	O
data	B-General_Concept
.	O
</s>
<s>
The	O
demodulator	B-Device
consists	O
of	O
a	O
delay	B-Device
line	I-Device
interferometer	I-Device
which	O
delays	O
one	O
bit	O
,	O
so	O
two	O
bits	O
can	O
be	O
compared	O
at	O
one	O
time	O
.	O
</s>
<s>
The	O
bit-error	O
rates	O
of	O
DBPSK	B-General_Concept
and	O
DQPSK	B-General_Concept
are	O
compared	O
to	O
their	O
non-differential	O
counterparts	O
in	O
the	O
graph	O
to	O
the	O
right	O
.	O
</s>
<s>
The	O
loss	O
for	O
using	O
DBPSK	B-General_Concept
is	O
small	O
enough	O
compared	O
to	O
the	O
complexity	O
reduction	O
that	O
it	O
is	O
often	O
used	O
in	O
communications	O
systems	O
that	O
would	O
otherwise	O
use	O
BPSK	O
.	O
</s>
<s>
For	O
DQPSK	B-General_Concept
though	O
,	O
the	O
loss	O
in	O
performance	O
compared	O
to	O
ordinary	O
QPSK	O
is	O
larger	O
and	O
the	O
system	O
designer	O
must	O
balance	O
this	O
against	O
the	O
reduction	O
in	O
complexity	O
.	O
</s>
<s>
At	O
the	O
time-slot	O
call	O
the	O
bit	O
to	O
be	O
modulated	B-Application
,	O
the	O
differentially	O
encoded	O
bit	O
and	O
the	O
resulting	O
modulated	B-Application
signal	O
.	O
</s>
<s>
Assume	O
that	O
the	O
constellation	B-Application
diagram	I-Application
positions	O
the	O
symbols	O
at	O
±1	O
(	O
which	O
is	O
BPSK	O
)	O
.	O
</s>
<s>
Differential	O
schemes	O
for	O
other	O
PSK	O
modulations	B-Application
may	O
be	O
devised	O
along	O
similar	O
lines	O
.	O
</s>
<s>
The	O
waveforms	O
for	O
DPSK	B-General_Concept
are	O
the	O
same	O
as	O
for	O
differentially	O
encoded	O
PSK	O
given	O
above	O
since	O
the	O
only	O
change	O
between	O
the	O
two	O
schemes	O
is	O
at	O
the	O
receiver	O
.	O
</s>
<s>
The	O
increase	O
in	O
required	O
to	O
overcome	O
differential	O
modulation	B-Application
in	O
coded	O
systems	O
,	O
however	O
,	O
is	O
larger	O
typically	O
about	O
3dB	O
.	O
</s>
<s>
Owing	O
to	O
PSK	O
's	O
simplicity	O
,	O
particularly	O
when	O
compared	O
with	O
its	O
competitor	O
quadrature	B-Device
amplitude	I-Device
modulation	I-Device
,	O
it	O
is	O
widely	O
used	O
in	O
existing	O
technologies	O
.	O
</s>
<s>
The	O
wireless	B-Architecture
LAN	I-Architecture
standard	O
,	O
IEEE	O
802.11b-1999	O
,	O
uses	O
a	O
variety	O
of	O
different	O
PSKs	O
depending	O
on	O
the	O
data	B-General_Concept
rate	O
required	O
.	O
</s>
<s>
At	O
the	O
basic	O
rate	O
of	O
1Mbit/s	O
,	O
it	O
uses	O
DBPSK	B-General_Concept
(	O
differential	O
BPSK	O
)	O
.	O
</s>
<s>
To	O
provide	O
the	O
extended	O
rate	O
of	O
2Mbit/s	O
,	O
DQPSK	B-General_Concept
is	O
used	O
.	O
</s>
<s>
In	O
reaching	O
5.5Mbit/s	O
and	O
the	O
full	O
rate	O
of	O
11Mbit/s	O
,	O
QPSK	O
is	O
employed	O
,	O
but	O
has	O
to	O
be	O
coupled	O
with	O
complementary	B-Device
code	I-Device
keying	I-Device
.	O
</s>
<s>
The	O
higher-speed	O
wireless	B-Architecture
LAN	I-Architecture
standard	O
,	O
IEEE	O
802.11g-2003	O
,	O
has	O
eight	O
data	B-General_Concept
rates	O
:	O
6	O
,	O
9	O
,	O
12	O
,	O
18	O
,	O
24	O
,	O
36	O
,	O
48	O
and	O
54Mbit/s	O
.	O
</s>
<s>
The	O
6	O
and	O
9Mbit/s	O
modes	O
use	O
OFDM	B-Protocol
modulation	B-Application
where	O
each	O
sub-carrier	O
is	O
BPSK	O
modulated	B-Application
.	O
</s>
<s>
The	O
12	O
and	O
18Mbit/s	O
modes	O
use	O
OFDM	B-Protocol
with	O
QPSK	O
.	O
</s>
<s>
The	O
fastest	O
four	O
modes	O
use	O
OFDM	B-Protocol
with	O
forms	O
of	O
quadrature	B-Device
amplitude	I-Device
modulation	I-Device
.	O
</s>
<s>
Because	O
of	O
its	O
simplicity	O
,	O
BPSK	O
is	O
appropriate	O
for	O
low-cost	O
passive	O
transmitters	O
,	O
and	O
is	O
used	O
in	O
RFID	B-Application
standards	O
such	O
as	O
ISO/IEC	O
14443	O
which	O
has	O
been	O
adopted	O
for	O
biometric	O
passports	O
,	O
credit	O
cards	O
such	O
as	O
American	O
Express	O
's	O
ExpressPay	O
,	O
and	O
many	O
other	O
applications	O
.	O
</s>
<s>
Bluetooth	B-Protocol
2	I-Protocol
uses	O
-DQPSK	O
at	O
its	O
lower	O
rate	O
(	O
2Mbit/s	O
)	O
and	O
8-DPSK	O
at	O
its	O
higher	O
rate	O
(	O
3Mbit/s	O
)	O
when	O
the	O
link	O
between	O
the	O
two	O
devices	O
is	O
sufficiently	O
robust	O
.	O
</s>
<s>
Bluetooth	B-Protocol
1	I-Protocol
modulates	O
with	O
Gaussian	B-Device
minimum-shift	I-Device
keying	I-Device
,	O
a	O
binary	O
scheme	O
,	O
so	O
either	O
modulation	B-Application
choice	O
in	O
version	O
2	O
will	O
yield	O
a	O
higher	O
data	B-General_Concept
rate	O
.	O
</s>
<s>
A	O
similar	O
technology	O
,	O
IEEE	O
802.15.4	O
(	O
the	O
wireless	O
standard	O
used	O
by	O
Zigbee	B-Protocol
)	O
also	O
relies	O
on	O
PSK	O
using	O
two	O
frequency	O
bands	O
:	O
868	O
–	O
915MHz	O
with	O
BPSK	O
and	O
at	O
2.4GHz	O
with	O
OQPSK	O
.	O
</s>
<s>
High	O
definition	O
programming	O
is	O
delivered	O
almost	O
exclusively	O
in	O
8PSK	O
due	O
to	O
the	O
higher	O
bitrates	O
of	O
HD	O
video	O
and	O
the	O
high	O
cost	O
of	O
satellite	O
bandwidth	B-Algorithm
.	O
</s>
<s>
Historically	O
,	O
voice-band	O
synchronous	O
modems	B-Application
such	O
as	O
the	O
Bell	O
201	O
,	O
208	O
,	O
and	O
209	O
and	O
the	O
CCITT	O
V.26	O
,	O
V.27	O
,	O
V.29	O
,	O
V.32	O
,	O
and	O
V.34	O
used	O
PSK	O
.	O
</s>
<s>
The	O
mutual	O
information	O
of	O
PSK	O
can	O
be	O
evaluated	O
in	O
additive	O
Gaussian	O
noise	O
by	O
numerical	B-Algorithm
integration	I-Algorithm
of	O
its	O
definition	O
.	O
</s>
<s>
The	O
mutual	O
information	O
of	O
PSK	O
over	O
the	O
AWGN	O
channel	O
is	O
generally	O
farther	O
to	O
the	O
AWGN	O
channel	O
capacity	O
than	O
QAM	B-Device
modulation	B-Application
formats	O
.	O
</s>
