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 From: Tom Rondeau Subject: Re: [Discuss-gnuradio] Re: new to GNU radio Date: Wed, 05 Mar 2008 11:06:18 +0000 User-agent: Thunderbird 2.0.0.12 (Windows/20080213)

```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?
```
```

```