Re: [Discuss-gnuradio] Re: new to GNU radio

[Tom Rondeau]

jiqun qi wrote:
> Hey,
>
> In fact, the mapped complex symbol will go into two parts, that is,
> the real part and the image part will modulate the cos(w_c * t) and
> sin(w_c * t), separately.
> E.g., complex symbol is denoted, y = a+jb = r*cos(theta) + j*r*sin(theta);
>   

I would just stick with this representation. Remember, it's called 
_phase_ shift keying. All of the information is stored in the phase of 
the signal. You can use the representation above:

y = r*cos(theta) + jr*sin(theta)

Or the complex baseband formula (remember Euler):
y = r*exp(j*theta)

For BPSK, a 1 (or 0) is when theta is 0;  a 0 (or 1) is when theta is 
pi. The mapping is completely arbitrary as long as both TX and RX sides 
know it.

For QPSK, theta can be 0, pi/2, pi, or 3pi/2 (0, 90, 180, 270 degrees).

This is all in complex baseband. We then "modulate" onto the carrier 
frequency later using a quadrature upconverter. I've seen this confusion 
over the word modulate plenty of times in the past; modulate technically 
means to multiply a signal with a carrier (see your local Fourier 
transform table which will often list the Fourier transform of 
x(t)cos(wt) as modulation; Carlson I know does, but unfortunately 
Oppenheim and Haykin sitting in front of me don't use labels for their 
pairs).

Does this make sense now? Basically, we do our "modulation" in complex 
baseband and then "modulate" it to a carrier. In GNU Radio the carrier 
upconversion is done in the USRP.

Follow George's suggestion of looking in digital/benchmark_loopback.py, 
which takes an MPSK modulator and demodulator block through a simulated 
channel. We currently support DBPSK, DQPSK, and D8PSK. We use 
differentially encoded formats to make it a bit easier on the receiver. 
For non-differential modulations, you need to be able to make a decision 
on the absolute phase of the signal before you can demodulate it.

I also wish I had my slides finished on the basics of narrowband 
communications using GNU Radio examples. It gives nice diagrams to show 
all of these principles.

Tom



> so, a*cos(w_c * t) - b*sin(w_c *t)
> = r*cos(theta)*cos(w_c * t) - j*r*sin(theta)*sin(w_c * t)
> = r*cos(w_c * t + theta)
>
> This is the final transmitted real signals, where w_c is the carrier
> frequency, shown in Gnu radio as well.
>
>
>   
> > i understood in QPSK how the bits get mapped to constellation space.
> >     
> > One doubt still persists.QPSK modulation theory tells us that we need to
> > change the phase of the carrier depending upon the incoming data
> > bits..i.e what we see mapped to the constellation space is the modulated
> > data.
> > I cannot see a carrier frequency specified anywhere in bqpsk.y..Where do
> > i specify the carrier frequency for my transmission...this part is still
> > a bit hazy...
> > I can see the incoming bits getting mapped to constellation space not
> > the modulated data..M i missing something here?
> >