>Randy Yates <yates@ieee.org> writes:
>> [...]
>> However, note that this introduces a 2 * pi / M phase ambiguity, since
>> if
>>
>>   phi = m * 2 * pi / M,
>>
>> then
>>
>>   M * phi = m * 2 * pi
>>           == 0.
>
>Let me rewrite this:
>
>if
>
>  phi = m * 2 * pi / M + theta,
>
>then
>
>  M * phi = m * 2 * pi + M * theta
>          == M * theta.
>--
>Randy Yates                      % "Bird, on the wing,
>Digital Signal Labs              %   goes floating by
>mailto://yates@ieee.org          %   but there's a teardrop in his
eye..."
>http://www.digitalsignallabs.com % 'One Summer Dream', *Face The Music*,
ELO
>

Thanks a lot Randy for such detailed and good explanation. I am clear
now.

Randy Yates <yates@ieee.org> writes:
> [...]
> However, note that this introduces a 2 * pi / M phase ambiguity, since
> if
>
>   phi = m * 2 * pi / M,
>
> then
>
>   M * phi = m * 2 * pi
>           == 0.

Let me rewrite this:

if

phi = m * 2 * pi / M + theta,

then

M * phi = m * 2 * pi + M * theta
== M * theta.
--
Randy Yates                      % "Bird, on the wing,
Digital Signal Labs              %   goes floating by
mailto://yates@ieee.org          %   but there's a teardrop in his eye..."
http://www.digitalsignallabs.com % 'One Summer Dream', *Face The Music*, ELO

"Ali A Nasir" <aliarshad46@hotmail.com> writes:

>>>   I have the information about the constellation that I am using but
> not
>>>allowed to use any training or preamble ( since its blind recovery ).
>>Let
>>>us say I am using pi/4 QPSK
>>>
>>
>>pi/4 QPSK constellation is the same as 8PSK. Possible to use blind
>>phase/frequency offset estimator based on 8-th power.
>>
>>Or you need only the removal of phase ambiguity?
>>
>>
>
>
>      I need the removal of small carrier frequency offset in addition to
> constant phase offset. Can you please explain the offset estimator based on
> 8th power ?

Ali,

If you have an M-ary PSK signal, the possible phases are

r[n] = exp(i * m[n] * 2 * pi / M + phi),   m[n] \in {0, 1, ..., M-1},

where phi is some unknown phase. Thus

(r[n])^M = exp(i * m[n] * 2 * pi + M * phi)
= exp(i * M * phi)

This is the basis of the Mth-power technique for carrier recovery.

However, note that this introduces a 2 * pi / M phase ambiguity, since
if

phi = m * 2 * pi / M,

then

M * phi = m * 2 * pi
== 0.

> Any paper or book reference ? Will that be blind estimator ?

Yes, it's a blind estimator in that it doesn't require any special
source symbol sequence.
--
Randy Yates                      % "Midnight, on the water...
Digital Signal Labs              %  I saw...  the ocean's daughter."
mailto://yates@ieee.org          % 'Can't Get It Out Of My Head'
http://www.digitalsignallabs.com % *El Dorado*, Electric Light Orchestra

>     I need the removal of small carrier frequency offset in addition to
>constant phase offset. Can you please explain the offset estimator based
on
>8th power ? Any paper or book reference ? Will that be blind estimator ?
>
>Regards,
>Ali
>

http://electronix.ru/forum/index.php?showtopic=23652

>
>
>Alexander Petrov wrote:
>
>> pi/4 QPSK constellation is the same as 8PSK. Possible to use blind
>> phase/frequency offset estimator based on 8-th power.
>
>You would be better off by considering the two subsequent symbols and
>the 4th power.
>
>
>DSP and Mixed Signal Design Consultant
>http://www.abvolt.com
>

so that I could better understand how to implement the blind phase and
frequcency offset estimation considering two subsequent symbols and fourth
power ?

Regards

Regards,
Ali

>>   I have the information about the constellation that I am using but
not
>>allowed to use any training or preamble ( since its blind recovery ).
>Let
>>us say I am using pi/4 QPSK
>>
>
>pi/4 QPSK constellation is the same as 8PSK. Possible to use blind
>phase/frequency offset estimator based on 8-th power.
>
>Or you need only the removal of phase ambiguity?
>
>

I need the removal of small carrier frequency offset in addition to
constant phase offset. Can you please explain the offset estimator based on
8th power ? Any paper or book reference ? Will that be blind estimator ?

Regards,
Ali


Alexander Petrov wrote:

> pi/4 QPSK constellation is the same as 8PSK. Possible to use blind
> phase/frequency offset estimator based on 8-th power.

You would be better off by considering the two subsequent symbols and
the 4th power.

DSP and Mixed Signal Design Consultant
http://www.abvolt.com

>   I have the information about the constellation that I am using but not
>allowed to use any training or preamble ( since its blind recovery ).
Let
>us say I am using pi/4 QPSK
>

pi/4 QPSK constellation is the same as 8PSK. Possible to use blind
phase/frequency offset estimator based on 8-th power.

Or you need only the removal of phase ambiguity?


On Aug 16, 7:07&#2013266080;am, "Ali A Nasir" <aliarsha...@hotmail.com> wrote:
> >On Aug 15, 10:35=A0am, Eric Jacobsen <eric.jacob...@ieee.org> wrote:
> >> On 8/13/2009 11:40 PM, Ali A Nasir wrote:
> >[snip]
> >> > =A0 =A0 =A0 Thanks for your guidance, Could you please explain some
> thi=
> >> > FEC lock indicator. Is it Frequency Error Correction sort of thing
> used=
> > in
> >> > Frequency Locked Loops ?
>
> >> No. =A0 There are techniques to tell whether some FEC decoders are
> workin=
> >g
> >> on valid data or not. =A0 This is sometimes done in Viterbi decoders
> by
> >> observing the frequency of register renormalization. =A0 Similarly a
> >> Reed-Solomon decoder generates a syndrome which can be used to tell
> >> whether the codeword was valid or not.
>
> >> The idea, then, is that if the FEC is indicating that it has acquired
> a
> >> valid data stream then the phase ambiguity of the constellation must
> be
> >> correct.
>
> >> --
> >> Eric Jacobsen
> >> Minister of Algorithms
> >> Abineau Communicationshttp://www.abineau.com
>
> >Another thing to consider is the use of rotationally-invariant
> >trellis code. &#2013266080;But the OP said no preamble. &#2013266080;Can you use
> >a code?
>
> >Julius
>
> &#2013266080; &#2013266080; Yup Julius, I can use encoding but no initial preamble or training. So
> you think that rotationally invariant trellis codes or reed solomon coding
> can help in this regard ?

It will have the same problem as with any convolutional code without
proper start and ending points.  You have to at least agree on which
one is the first symbol, right?  So maybe it's not as bad a problem.

Julius

>On Aug 15, 10:35=A0am, Eric Jacobsen <eric.jacob...@ieee.org> wrote:
>> On 8/13/2009 11:40 PM, Ali A Nasir wrote:
>[snip]
>> > =A0 =A0 =A0 Thanks for your guidance, Could you please explain some
thi=
>> > FEC lock indicator. Is it Frequency Error Correction sort of thing
used=
> in
>> > Frequency Locked Loops ?
>>
>> No. =A0 There are techniques to tell whether some FEC decoders are
workin=
>g
>> on valid data or not. =A0 This is sometimes done in Viterbi decoders
by
>> observing the frequency of register renormalization. =A0 Similarly a
>> Reed-Solomon decoder generates a syndrome which can be used to tell
>> whether the codeword was valid or not.
>>
>> The idea, then, is that if the FEC is indicating that it has acquired
a
>> valid data stream then the phase ambiguity of the constellation must
be
>> correct.
>>
>> --
>> Eric Jacobsen
>> Minister of Algorithms
>> Abineau Communicationshttp://www.abineau.com
>
>Another thing to consider is the use of rotationally-invariant
>trellis code.  But the OP said no preamble.  Can you use
>a code?
>
>Julius
>

Yup Julius, I can use encoding but no initial preamble or training. So
you think that rotationally invariant trellis codes or reed solomon coding
can help in this regard ?