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Discussion Groups | Comp.DSP | Fourier Transform (spectrum) of QPSK and BPSK?

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Fourier Transform (spectrum) of QPSK and BPSK? - radio913@aol.com - 2006-11-12 03:48:00

Hi All,

        Does anyone have a mathematical derivation
 of the expected spectrum of a QPSK signal, given a
known symbol rate (which is 1/2 the data rate for QPSK)?

        The signal i am measuring doesn't have any
 sideband carrier suppression at all, which is supposed
to be a figure of merit for phase and amplitude imbalance
of your IQ mixer (how orthogonal or in-quadrature the I and Q
channels are).

         The bottom line is I'm trying to measure phase
and amplitude imbalance with just a spectrum analyzer,
without having to buy an expensive VSA which can display
the constellation, and give me EVM, etc.

          Thanks for any REAL help (which is Info from someone
who isn't pretending to know more than they actually do!). 


Slick


Re: Fourier Transform (spectrum) of QPSK and BPSK? - 2006-11-12 04:39:00

r...@aol.com wrote:
> Hi All,
>
>         Does anyone have a mathematical derivation
>  of the expected spectrum of a QPSK signal, given a
> known symbol rate (which is 1/2 the data rate for QPSK)?
>
>         The signal i am measuring doesn't have any
>  sideband carrier suppression at all, which is supposed
> to be a figure of merit for phase and amplitude imbalance
> of your IQ mixer (how orthogonal or in-quadrature the I and Q
> channels are).
>
>          The bottom line is I'm trying to measure phase
> and amplitude imbalance with just a spectrum analyzer,
> without having to buy an expensive VSA which can display
> the constellation, and give me EVM, etc.
>
>           Thanks for any REAL help (which is Info from someone
> who isn't pretending to know more than they actually do!).
>
>
> Slick

It will be harder to discern the imbalances from a QPSK SA display than
with an ordinary tone. Try changing the modulation to a complex
exponential: sin(wt) + j*cos(wt). You get a three-tone display on the
SA. From left to right, the components are: opposite sideband
(undesired), carrier (undesired), and desired signal. You can directly
measure the levels in dBc of the undesired components. I'm not sure if
you can relate them back mathematically to imbalances in the modulator,
but what you can do is tweak the modulator until they are minimized.

John


Re: Fourier Transform (spectrum) of QPSK and BPSK? - Randy Yates - 2006-11-12 09:36:00

"r...@aol.com" <r...@aol.com> writes:

> Hi All,
>
>         Does anyone have a mathematical derivation
>  of the expected spectrum of a QPSK signal, given a
> known symbol rate (which is 1/2 the data rate for QPSK)?

From [proakiscomm], the spectrum expression for any linear modulation
(such as QPSK) is

  Phi(f) = (1/T) * | G(f) |^2 * Phi_ii(f),

where G(f) is the Fourier transform of the transmit pulse shape g(t)
and Phi_ii(f) is the power spectral density of the information
sequence I(n). T is the symbol period.

So without knowing your pulse shape, we can't really give you a
specific spectrum.

--Randy

@BOOK{proakiscomm,
  title = "{Digital Communications}",
  author = "John~G.~Proakis",
  publisher = "McGraw-Hill",
  edition = "fourth",
  year = "2001"}
-- 
%  Randy Yates                  % "Though you ride on the wheels of tomorrow,
%% Fuquay-Varina, NC            %  you still wander the fields of your
%%% 919-577-9882                %  sorrow."
%%%% <y...@ieee.org>           % '21st Century Man', *Time*, ELO
http://home.earthlink.net/~yatescr


Re: Fourier Transform (spectrum) of QPSK and BPSK? - Vladimir Vassilevsky - 2006-11-12 14:18:00

r...@aol.com wrote:

>         Does anyone have a mathematical derivation
>  of the expected spectrum of a QPSK signal, given a
> known symbol rate (which is 1/2 the data rate for QPSK)?

If the data is random, then the spectum is the Fourier transform of a 
single pulse. A textbook like Proakis or Sklar should have that.


> 
>         The signal i am measuring doesn't have any
>  sideband carrier suppression at all,  which is supposed
> to be a figure of merit for phase and amplitude imbalance
> of your IQ mixer (how orthogonal or in-quadrature the I and Q
> channels are).
> 
>          The bottom line is I'm trying to measure phase
> and amplitude imbalance with just a spectrum analyzer,
> without having to buy an expensive VSA which can display
> the constellation, and give me EVM, etc.

1. Run 01 10 01 10 01 10 ... and 11 00 11 00 ... patterns to measure the 
carrier suppression in I and Q channels. There should be no peak at the 
carrier frequency.

2. Run 00 01 11 10 00 01 11 10 .... pattern to measure the 
amplitude/phase balance between I and Q. There should be a symmetrical 
spectrum shifted up from the center frequency.

> 
>           Thanks for any REAL help (which is Info from someone
> who isn't pretending to know more than they actually do!). 

Your majesty's "Thank you" means soo much. You don't have to thank me, 
$100 will be just all right.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com


Re: Fourier Transform (spectrum) of QPSK and BPSK? - radio913@aol.com - 2006-11-12 15:21:00



Re: Fourier Transform (spectrum) of QPSK and BPSK? - Rune Allnor - 2006-11-12 15:21:00

r...@aol.com skrev:
> Hi All,

>           Thanks for any REAL help (which is Info from someone
> who isn't pretending to know more than they actually do!).

Do you have any particular person in mind? If not, how do you
tell the difference between pretenders and others?

Rune


Re: Fourier Transform (spectrum) of QPSK and BPSK? - radio913@aol.com - 2006-11-12 15:41:00



Re: Fourier Transform (spectrum) of QPSK and BPSK? - radio913@aol.com - 2006-11-12 16:54:00



Re: Fourier Transform (spectrum) of QPSK and BPSK? - Rune Allnor - 2006-11-12 17:23:00

r...@aol.com skrev:
> On Nov 12, 12:21?pm, "Rune Allnor" <all...@tele.ntnu.no> wrote:
> > radio...@aol.com skrev:
> >
> > > Hi All,
> > > ? ? ? ? ? Thanks for any REAL help (which is Info from someone
> > > who isn't pretending to know more than they actually do!).Do you have any particular person in mind? If not, how do you
> > tell the difference between pretenders and others?
> >
>
>       I had YOU in mind, judging from your other
> posts!

Well, that's usenet for you; you get exactly what you pay for.
As others already hinted at, you might be better off contacting
people whose knowledge you acknowledge, and pay them.

Rune


Re: Fourier Transform (spectrum) of QPSK and BPSK? - Randy Yates - 2006-11-12 18:36:00



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