Re: [Discuss-gnuradio] Signal coming from the USRP to the computer

[John Andrews]

Thanks Patrick. I was concerned with the received signal path. Suppose, I have the receiver tuned to, let's say, GPS signal. What will the received signal look like. Considering the GPS message signal is m(t), then what would equation would best describe the received signal. 

If 'f_c' is the carrier frequency then the signal coming over the USB bus on to the computer for baseband processing will be,

inphase(t) = m(t) cos(phi)

quadrature(t) = m(t)sin(phi)

where, 'phi' is the instantaneous offset. Remember, phi here is a broad term which includes all kinds of offsets(frequency, phase etc).

On Tue, May 31, 2011 at 11:47 AM, Patrick Sisterhen <address@hidden> wrote:

I think a little more detailed precise answer to John's question might help:

John Andrews wrote:

> each complex sample that enters the
> USB bus is the following,
>
> x[i] = (inphase_component) + j (quadrature_component), and
> x[i] = m(t)cos( 2*pi*FREQ_OFFSET*t + PHI ) + jm(t)sin( 2*pi*FREQ_OFFSET*t +
> PHI ), where m(t), is the actual message signal, FREQ_OFFSET is the
> frequency offset, and PHI is the phase.
>
> Is that correct?

I think you're confusing the baseband and passband signals a little, and the equations aren't quite right.

The complex-baseband signal (your message) is the data that is transferred across the USB channel.
x[i] = (in-phase) + j*(quadrature)
       = (x_i) + j*(x_q)

These are samples of your message signal, after modulation (mapping to a complex QAM-constellation, for example), coding, pulse-shaping, etc.

The signal is up/down converted on the USRP device such that the transmitted RF signal is

r(t) = x_i*cos(2*pi*f_c) - (x_q)*sin(2*pi*f_c)

(where f_c is your RF carrier frequency, and I'm ignoring phase offsets and noise)

Notice the subtraction there (which comes from the trig identities) and that all the terms are real (it's a real passband signal).

Hope that helps a little.

Patrick Sisterhen
National Instruments
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