QUESTION:
I can understand how we can receive and transmit adequately from Earth to
Pathfinder, given the power of our transmitters and gain of our antennae,
but how does Pathfinder communicate with Earth? It seems to me it would be
difficult for a small probe on the surface of mars to receive and transmit
with enough gain to establish a robust data connection. Do you use a very
low bandwidth?

I remember reading during one of the Voyager fly-bys that strength of the
radio signal received by DSN dishes from Voyagers I and II was something
like 1.0 x E-6 watts. How strong (or weak) is the signal coming from Mars
Pathfinder once it has landed?

ANSWER from David Dubov:
The one quantity that most people overestimate is the amount of man-made and
natural noise that exists at microwave communication frequencies. We use
very sensitive low noise microwave receivers and large antennas here on
Earth to receive the signal from Mars Pathfinder. At the 8 gigahertz radio
frequency that Mars Pathfinder uses to talk back to Earth, the ratio of
signal power to noise power is 6000 to 1, or about 37 decibels. This allows
us to receive data from the spacecraft 190 million kilometers away at a
modest data rate of 1 or 2 kilobits per second. Compare that to your
computer modem which probably operates at 14.4 or 28.8 kilobits per second!

The radio signal strength from the Mars Pathfinder high gain antenna on the
July 4, 1997 landing day will be -146 dBm (decibels referenced to a
milliwatt) or 2.5e-18 watts as received at our Deep Space Network 34 meter
diameter antenna on Earth.