You may want to use a transformer to connect the antenna to the coax.
^^Seconded!
I recently hooked an outdoor skywire to the center conductor of an old cable TV (rg59) run that makes ingress into my listening room to a female F-connector wall plate. How lucky!
That was a great first step. It brought in a huge signal, but also some huge noise. It turns out the noise the shield is supposed to protect against still needs to go somewhere, and most likely it is directly (DC-) coupled to your receiver and your antenna.
I wound a 1:1 isolation transformer on a binocular ferrite core, and clipped the primary to the antenna/ground terminals on my receiver, and the secondary to the center conductor/shield of the cable. Now the coax shield cannot pass common-mode directly into the receiver. It seems to have cut the noise down (but maybe it's just that psychological trick we use to make ourselves feel better.) However, that common mode still has a path to the antenna.
To defeat this, there is another refinement I intend to make: another 1:1 isolation transformer for the antenna side with the antenna and an Earth ground (currently the wire just terminates to the center conductor of the cable and has no ground) working against center conductor and shield. This leaves the coax "floating" so that common-mode cannot directly flow onto the antenna or into the receiver.
A final refinement involves grounding the shield to its own Earth ground (NOT the antenna's Earth Ground!) to give the common mode current a sink.
I got these ideas from
http://www.hifidelity.com/w3eee/ under "reducing noise."
My understanding is that this also provides some spark protection to one's receiver's frontend.
Amidon sells all the ferrite and wire you need to do this if you are interested, OP.