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If you're interested in topics like this, check out Paul Kennedy's "Engineers of Victory". It basically talks about how the road to victory in WWII were a number of operational and technological challenges that needed to be solved.

http://www.amazon.com/Engineers-Victory-Problem-Solvers-Turn...

And yet, they couldn't develop an anti-mortar radar in time for D-day.
If not, they were close behind, e.g. http://nigelef.tripod.com/tgtacqcb.htm#Radar

Wikipedia tells us why those were initially Anti-Aircraft (AA) radars: https://en.wikipedia.org/wiki/Counter-battery_radar#History

"The first radars were developed for anti-aircraft purposes just before World War II. These were soon followed by fire control radars for ships and coastal artillery batteries. The latter could observe the splashes of water from missing shots, enabling corrections to be plotted. Generally the shells could not be seen directly, as they were too small and rounded to make a strong return, and traveled too quickly for the mechanical antennas of the era to follow.

Radar operators in light anti-aircraft batteries close to the front line found they were able to track mortar bombs. This was likely helped by the fins of the bomb producing a partial corner cube that strongly reflected the signal. These accidental intercepts led to their dedicated use in this role, with special secondary instruments if necessary, and development of radars designed for mortar locating. Dedicated mortar-locating radars were common starting in the 1960s and were used until around 2000."