I don't believe that alt makes a difference to the 12 miles radius.
IMO, I don't see the need for the "cone". If the enemy is above 500 AGL, the bar-dar shows and then the dot(s) will show on dot-dar within the 12 mile radius. Plenty of time to react, and as Curly stated ... If your country is unwilling to defend it, then your deserve to lose it.
Rather than the antenna, how about just the radar itself? Usually in the center of the field, its small, and you will most likely die at the hands of the laser-ack, trying to kill it right off the bat.