Direct conversion receiver

Hi,
If the signal transmitted at the transmitter is represented as,
x(t) = X_i(t)cos(2pifct) - X_q(t)sin(2pifct), where X_i(t) and
X_q(t)
are inphase and quadrature components of the message signal.

then, at the receiver does the following equation correctly represent
the
signal after downcoversion to baseband like in a "RFX2400 + USRP’ set
up.

inphase component of received signal = X_i(t)cos(2pif_offsett + phi )
+
noise_component
quadrature component of received signal = X_q(t)sin(2
pif_offsett +
phi) +
noise_component

where, ‘f_offset’ is the frequency offset present and ‘phi’ is the
received
signal phase.

Can someone suggest a good reference to direct conversion receivers?

Thanks.

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