The chronology is roughly as follows:
The Sheffield was one of several ships on picket duty, preventing
anyone from sneaking up on the fleet. It had all transmitters
(including radar) off because it was communicating with a satellite.
Two Argentinan planes were detected by another ship's radar. They
first appeared a few miles out because they had previously been flying
too low to be detected. The planes briefly activated their radars,
then turned around and went home.
Two minutes later a lookout on the Sheffield saw the missile's flare
approaching. Four seconds later, the missile hit. The ship eventually
sank, since salvage efforts were hindered by uncontrollable fires.
What actually happened is that the planes popped up so that the could
acquire targets on their radars, then launched Exocet missiles and
left. (The Exocet is an example of a "Fire and Forget" weapon. Moral
or not, they work.) The British didn't recognize that they had been
attacked, since they believed that the Argentinans didn't know how to
use their Exocet missiles.
It is irrelevent that the Sheffield had its radar off, since the
missile skims just above the water, making it virtually undetectable
by radar. For most of the flight, it proceeds by internal guidance,
emitting no telltale radar signals. About 20 seconds before the end
of the flight, it turns on a terminal homing radar which guides it
directly to the target. The Sheffield was equipped with an ESM
receiver, whose main purpose is to detect hostile radar transmissions.
The ESM receiver can be preset to sound an alarm when any of a small
number of characteristic radar signals are received. Evidently the
Exocet homing radar was not among these presets, since there would
have been a warning 20 sec before impact. In any case, the ESM
receiver didn't "think the missile was friendly", it just hadn't been
told it was hostile. It should be noted that British ships which were
actually present in the Falklands were equipped with a shipboard
version of the Exocet.
If the failure was as deduced above, then the ESM receiver behaved
exactly as designed. It is also hard to conceive of a design change
which would have changed the outcome. The ESM receiver had no range
information, and thus was incapable of concluding "anything coming
toward me is hostile", even supposing the probably rather feeble
computer in the ESM receiver were cable of such intelligence.
In any case, it is basically irrelevant that the ESM receiver didn't
do what it might have done, since by 20 seconds before impact it was
too late. The Sheffield had no "active kill" capability effective
against a missile. Its anti-aircraft guns were incapable of shooting
down a tiny target skimming the water at near the speed of sound.
It is also poossible to cause a missile to miss by jamming its radar,
but the Sheffield's jamming equipment was old and oriented toward
jamming russian radars, rather than smart western radars which
wheren't even designed when the Sheffield was built. The Exocet has a
large bag of tricks for defeating jammers, such as homing in on the
jamming signal.
In fact, the only effective defense against the Exocet which was
available was chaff: a rocket dispersed cloud of metalized plastic
threads which confuses radars. To be effective, chaff must be
dispersed as soon as possible, preferably before the attack starts.
After the Sheffield, the British were familiar with the Argentinan
attack tactics, and could launch chaff as soon as they detected the
aircraft on their radars. This defense was mostly effective.
Ultimately the only significant mistake was the belief that the
Argentinans wouldn't use Exocet missiles. If this possibility was
seriously analysed, then the original attack might have been
recognized. The British were wrong, and ended up learning the hard
way. Surprise conclusion: mistakes can be deadly; mistakes in war are
usually deadly.
The Risks Digest Volume 3: Issue 67