Effective Isotropic Radiated Power - that's a key characteristic when determining the signal strength from a given transmitter. It's derived from the geometry of the antenna as related to the bandwidth and the transmitted power.

A well designed antenna has a gain ratio, sort of an amplification factor based on the radiated pattern. A simple 1/4 wavelength dipole antenna is the baseline for comparison, so it has no gain. As you go from omnidirectional antennas like a dipole to more directional antennas, you get the gain factor.

To visualize this, picture a flashlight bulb without the reflector in a dark room. The light is radiated in all directions and is rather dim. Put a mirror behind the light and half of the energy is reflected, making the light appear brighter. Put a parabolic reflector behind the bulb and the radiated pattern is much more directional, giving the appearance of a much brighter bulb. The more directional the reflector, the brighter the bulb appears.

If you remember the old rooftop TV antennas, you've seen an example of a Yagi style antenna. Yagi antennas use a series of reflectors and director elements to narrow the beamwidth and increase the gain. They're typically capable of gains on the order of 20-30 dB, or amplications of 100 to 1000. A good dish antenna can easily exceed 60 dB (amplication factor of 1 million) and the best antennas like the ones on the Deep Space Network can do a lot better than that. The penalty for these high gains is narrower and narrower beamwidth. The antennas we used to control satellites (the Air Force Satellite Control Network) typically had gains on the order of 60-63 dB (1 to 2 million) and beamwidths of approximately 0.1 degree. For communicating with satellites out at geosynch, the transmitter power was typically 1 kilowatt, so the EIRP was on the order of 1-2 gigawatts.

Out at geosynch, our satellites used folded dipole antennas for TT&C. There was one on the front and one on the back of the satellite, and they were designed to allow communications even if the satellite were tumbling (omnidirectional antenna pattern). Even with all that EIRP, the received signal strengths with those dinkly little antennas was on the order of -80 dBm.

Pioneer does only radiate a few watts of power and is billions of miles away, but it is using a good parabolic antenna, one with a gain probably on the order of 50-60 dB. To transmit to Earth, it has to have good pointing accuracy. However, to receive that incredibly weak signal, you need the incredible capabilities of the DSN, and even they're having a tough time of it.

A radar from Earth would have a tough time picking out something as tiny as a Mars lander. Radars typically have good parabolic antennas, but only a minute percentage of the energy received by the target is reflected back in the direction of the transmitting antenna. That weak signal has to travel all the way back to the receiver. Instead of contending with the inverse square law, radars are stuck with an inverse fourth power relation because the signals have to travel both ways. It's just a really tough proposition.

If you read the really good writeup of a proposed amateur satellite for Mars, you'll see just how difficult it is to get a signal back from there, much less the difficulty of getting signals there and back.