Your antenna has two terminals. You will measure the received signal, or drive the transmitted signal, as a difference between these terminals. You need to be mindful of the kind of transmission line, and if this is a balanced or unbalanced system. But probably you'll couple to the antenna through a transformer so it won't matter.
Coax is an unbalanced transmission line. The shield is held at ground potential. By that, I mean there is no voltage difference between the shield and Earth, the tower, the antenna, etc.
Neglecting biasing, impedance matching, and other details, you might drive it like this:
simulate this circuit – Schematic created using CircuitLab
An issue is a dipole is a balanced antenna, so to feed it properly with coax you need a balun at the feedpoint.
Alternately you can use twin-lead and make it a balanced system all the way. That might look like this:
simulate this circuit
In this balanced system, at every stage there is a positive polarity and a negative polarity half of the circuit, symmetrical in voltage and impedance relative to ground. There is no ground connection at the input or the output.
In both cases, receiving looks the same except the receiving antenna is on the left, and the output is going to a demodulator.
This balanced system has a significant disadvantage: everything is twice as complicated. One way to convert between balanced and unbalanced is to feed a balanced signal into a center-tapped transformer. The center tap, being halfway between the balanced inputs, is at ground potential.
That is why a class-AB push-pull amplifier is a common final stage, looking (simplified) something like this:
simulate this circuit
For a working example, see the HPSDR Pennywhistle schematic.
The input and output transformers do some nice things for us:
- block the DC bias
- allow for impedance matching by adjusting the turns ratio
- provide galvanic isolation
Galvanic isolation is especially pertinent to your question. You'll notice there's no DC path from the amplifier to either the input or the output. So ground doesn't really matter: only the current through the transformer matters. So you can connect one end of either (or both) transformer to ground, or you can make a balanced connection and not connect ground at all.
Furthermore, consider that noise on ground is still noise. With the antenna isolated with a transformer you can avoid any possibility of ground loops which will pick up noise, and it's easier to isolate the ground reference for the receiver front-end from the digital noise, etc that might be present elsewhere.
For receive you probably do not need a class-AB amplifier. More likely you'll stick with the class-A amplifier in the first example. It's pretty common to isolate the input from the antenna with a simple transformer even if it's not strictly necessary. This allows for a balanced or unbalanced input and isolates the DC grounds between the antenna and the receiver.