On 11/26/2010 07:43 AM, kiran2urs wrote:
> Hi,
>
> I have a few basic doubts in the QPSK modulation&  drawing of
> constellation,
>
> 1) For the QPSK modulation complex signal is required (or) real signal is
> enough?

There seems to be a lot of confusion on this subject lately.  Radio 
signals are entirely real -- there are no imaginary numbers in this real 
world of ours*.  Imaginary numbers are handy for radio applications. 
They're handy because they are an exact mathematical stand-in for 
representing radio signals in quadrature, even going so far as to have 
formal mathematical ties to the Fourier transform.

So if you have a (real) radio signal

x(t) = a(t) * cos(w * t) + b(t) * sin(w * t),

then you can _represent_ it as

x_m(t) = a(t) + i * b(t) (where i = sqrt(-1)), and say that

x(t) = (x_m(t) * e^(i * w * t) + (x_m(t))' * e^(-i * w * t))/2,

where (x_m(t))' is the complex conjugate of x_m(t).

Furthermore, you can perform a quadrature downconversion on x(t) that 
gives you two channels that _act_ like a real and an imaginary part, and 
upon which you can perform arithmetic that is _behaviorally_ exactly 
_like_ complex arithmetic.

I emphasize the words "represent", "act", "behaviorally" and "like" 
because your never, ever actually have imaginary quantities floating 
around -- this is the real world.  Even inside a computer algorithm, all 
numbers are real.  We can only simulate complex arithmetic, and in this 
case keep in mind that we're doing _quadrature_ arithmetic, which is 
like complex arithmetic in all the details, but is still different.

> 2) In the drawing of constellation x-axis is the real value ,y-axis is
> imaginary

That is the typical way of doing it, yes.

> &  how the angle is represented in the constellation?

I'm not sure what you mean.  Angle is angle.

> 3) If the QPSK signal is the complex signal,which formula will suits for
> the representation of 1 st quadrant symbol
>
> cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t + (pi/4))
>
> (or)
>
> cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t - (pi/4))

Neither.  In complex representation a signal that's centered in the 1st 
quadrant would be something like 1 + i.  In real radio terms this would be

cos(w * t) + sin(w * t).

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html

>Hi,
>
>I have a few basic doubts in the QPSK modulation & drawing of
>constellation,
>
>1) For the QPSK modulation complex signal is required (or) real signal is
>enough?
>

Ans: Complex

>2) In the drawing of constellation x-axis is the real value ,y-axis is
>imaginary & how the angle is represented in the constellation?
>

Ans: 45 Deg

>3) If the QPSK signal is the complex signal,which formula will suits for
>the representation of 1 st quadrant symbol
>
>cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t + (pi/4))
>
>(or)
>
>cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t - (pi/4))
>

Ans:  http://en.wikipedia.org/wiki/Phase-shift_keying

Hi,

I have a few basic doubts in the QPSK modulation & drawing of
constellation,

1) For the QPSK modulation complex signal is required (or) real signal is
enough?

2) In the drawing of constellation x-axis is the real value ,y-axis is
imaginary & how the angle is represented in the constellation?

3) If the QPSK signal is the complex signal,which formula will suits for
the representation of 1 st quadrant symbol

cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t + (pi/4))

(or)

cos(2*pi*Fc*t + (pi/4)) + sqrt(-1)*sin(2*pi*Fc*t - (pi/4))

Please explain these basic questions 

Thanking u in advance

Regards,
KIRAN KUMAR