Their are many reasons for hearing one side of a 
conversation.  Mostly it has to do with the signal being to near to 
you, and skiping 100 miles over your head.  The signal might be to 
far away or you might have covering band noise as well.
Radials increase the radiation efenciency  of an antenna that is only 
fed from the positive output of a radio.  They therefore help both 
verticals and long wires.  Antennas tuned as half waves do not need 
radials.  In a perfect ideal plane, you would have 120 radials 
resonent for each desired band of operating frequencies.  Theese 
would cover a 360 radias around your antenna.  Anything less is a 
compramize.  So as you can see, compramizes are okay, since verticals 
work, and if you have that kind of space, you probably aren't puting 
up verticals anyway.  You might be puting up phased towers, like 
broadcast stations for example.
If your fence is metal, ground your vertical to that.  It'll work.