Question to RF Experts regarding direct conversion receivers

Hi all,

Does anyone knows what the output of direct conversion receiver when I am transmitting the same information in the I/Q paths and between the receiver and transmitter I have finite frequency offset?
i.e., the transmitted signal is:

Sout=I*cos(w0t)+I*sin(w0t)

for example, If my information is I= sin(w1t)+sin(w2t)
Then, the receiver output will be:

Sreceiver=[I*sin(w0t)+I*cos(w0t)]*cos[(w0+dw)t]
where I=sin(w1t)+sin(w2t)
Has anyone here tried this experiement or encoutered the results over this issue?

Best Regards,

cos(w0t)+sin(w0t)=sqrt(2)cos(w0t-pi/4)

The signal is just amplitude modulated with extra 45 degree phase shift and sqrt(2) amplitude gain.