On this particular aircraft, the upper antenna was recently replaced after a brief history of failures. Two processors had been installed, but the failure repeated after only a couple of days of the processor(s) being replaced.
I suspect (without seeing the removed antenna) that one of the four elements had shorted out in the antenna itself. This short was taking out (frying) the transceiver in each of the two previous processors. After a third processor was installed, the system has been operating normally.
A previous discussion of a directional antenna fault on a MD-11 can be found here