Joe;

 

Best practice is to ground wire shield at only one end.  Grounding both ends results in multiple ground paths, and the potential for “ground loops”; slight differences in ground potential.  I’m not sure about your concern about the antenna effect; whatever minute signals picked up simple go to ground.

Guys, I'm not an EE but I should mention (the obvious) that the INTENT of the shielded wire is to absorb the signals floating around and grounding them to prevent the inner wire from being subject to the same signals. (IE functioning somewhat like an antenna) It is true that ANY high aspect ratio tube can become a hollow cavity antenna. I did scanning electron microscope work where nailing down all the potential RF sources was very important.

 

Bill Jepson