Hi Roee,
you forgot that there is a delay between sending and receiving, and
that the receiver LO is not at the same phase as the transmitter LO.
So in your receiver I(t) and Q(t), you don't mix with a cos(w0*t)
and a -sin(w0*t), but with cos(w0*t+tau) and a -sin(w0*t+tau),
respectively, with tau being the resulting timing offset.
In the result, the overall signal stays the same, but has a
different phase, ie. a rotation in the complex plane, which means
that Q(t) is no longer necessarily 0.
I recommend replacing the separate I and Q by the Re{} and Im{} of
the complex receive signal. In that manner, you can understand
mixing as a multiplication by e^{-j w0 t} instead of two
multiplications with cos and -sin; that makes the math a lot
shorter, and hence easier to comprehend. However, that is just my
taste in math.
Best regards,
Marcus
On 17.11.2015 09:46, Roee Bar wrote:
Yes, the images came ok.
Using your original example of transmitting
I(t)=cos(wm*t), Q(t)=sin(wm*t), let’s take I(t)=cos(wm*t) and
Q(t)=0:
sout(t) = cos(wm*t)*cos(wo*t) - 0*sin(wo*t) = 1/2 *
[ cos(wm*t-wo*t) + cos(wm*t+wo*t) ]
At the receiver (sorry if the derivation is too
explicit):
I(t) = sout(t) * cos(wo*t) = 1/2 * [
cos(wm*t-wo*t) + cos(wm*t+wo*t) ] * cos(wo*t) = 1/4 * [
cos(wm*t) + cos(wm*t - 2*w0) + cos(wm*t + wo*t) + cos(wm*t) ] =
1/2 * cos(wm*t) + 1/4 * [cos(wm*t - 2*w0) + cos(wm*t + 2*wo*t)]
Q(t) = sout(t) * -sin(wo*t) = 1/2 * [
cos(wm*t-wo*t) + cos(wm*t+wo*t) ] * -sin(wo*t) = 1/4 * [
-sin(wm*t) + sin(wm*t - 2*wo*t) - sin(wm*t + 2*wo*t) + sin(wm*t)
] = 1/4 * [ sin(wm*t - 2*wo*t) - sin(wm*t + 2*wo*y) ]
After the low pass filter, which removes 2*wo+wm and
2*w0-wm components, we end up with:
I(t) = 1/2 * cos(wm*t)
Q(t) = 0
But in the USRP I don’t get Q(t)=0…
Thanks,
Roee
I'm referring to the receiver. It's
essentially two receivers in parallel, one mixing down
with the local oscillator (cosine) and the other mixing
down with the same local oscillator, but phase shifted -90
degrees (sine). This is how it generates two components
for the input signal. Of course, you can only input a real
signal, but the receiver can generate both the I and Q
components in the 'dual' receiver mode. This is similar to
how a vector network analyzer (VNA) operates.
Did the images I sent on the first e-mail
come through ok? They were pretty basic, but show the
layout of the transmitter and receiver.
-Trip
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