Hello,
I posted this to the Systema forum at
http://www.russianmartialart.com/forum, but I thought I'd cross-post
it here as well. It is a list of exercises in response to someone's
request for drills to increase awareness to have an "almost
supernatural ability to sense an attack from behind."

Here are a few drills from our classes that may be helpful in
developing awareness, though not to the extent of the supernatural. I
believe this kind of awareness is perfectly naturally and attainable
for any human being.

Allow your partner to approach you with a knife from behind, so that
you cannot see him, and press the knife into your back. Practice
turning to avoid the knife before it makes contact. At first, you
will probably turn after the knife makes contact, being unable to see
it, your body will rely on the sense of touch instead. But eventually
the gap between your the knife's touch and your movement will lessen.
With practice, your body will learn to "see" the approaching knife
and turn before contact is made. This is not supernatural, just a
kind of sensitivity that can be developed. I saw this exercise
demonstrated on one of Vlad's videos, I think it was "Fundamentals of
Knife Disarming." We've practiced this in our class, and I found that
after a few tries, the body starts to listen to non-visual cues, even
if the mind is not conscious of noticing these things. The sound of
my partner approaching, then stopping, the variance in his breathing
as the knife is thrust, the feeling of even a mock attack with a
practice weapon in one's immediate vicinity is quite different than
without such a presence. I think it was also on Fundamentals of Knife
Disarming where Vlad explained that humanity has such a long history
of violence with metal weapons, that our bodies are able to sense
when threatened with a blade.

more sensitivity work with knives, from an old training journal:

Working with knives in close quarters: We stood side by side with our
partners, shoulders touching, and then one person attacked the other
with the knife. Edgar explained to us that you have to feel the
attack first, with your shoulder or your arm, rather than waiting for
the knife to arrive in your personal space. An important part of
Systema--maybe all martial arts, but I've never studied another--is
to feel the attack before it happens, using perception and
sensitivity, and move before the knife is pressed against you. Of
course this isn't always possible, and that's why we also work on
freeing from holds, grabs, and chokes, but whenever you can, move
before you end up in such a vulnerable situation. We also did this
exercise side-by-side facing in opposite directions, and with our
eyes closed. Then we tried the same thing back-to-back, which is a
lot more difficult. You have no choice but the feel the attack, as
you cannot see what's coming. Closing the eyes actually didn't make a
big difference with the back-to-back exercise because your perception
is most dependent on feeling, not vision. Then we did the same
exercises in chairs, side-by-side, and side-by-side facing opposite
directions.

Our frequent guest teacher Denis D. often had us do an exercise I
call "Statues." Your partner attacks you in any way they please,
taking one or two steps towards you, you move to avoid, and then they
freeze. Once they are frozen, you work on finding the tension,
starting from the top of the body, and moving your hands downward, to
find the place where the structure of your partner's body can be
collapsed.

A sensitivity exercise we often do in our class is to stand facing
your partner with your hands on his shoulders with a feather-light
touch. Step in one direction and allow your body's movement to move
your partner. Step again and make sure to keep your partner within
your sphere of influence, as if you are rolling a barrel. But make
sure to use the least possible force to faciliate his movement. You
can push or pull, place your hands on his shoulders or anywhere else,
just try to keep your touch feather-light and make sure to step
rather than just use your arms to move them. The person being moved
should also yield to the least possible pressure. I think the person
being moved has an even greater opportunity to practice sensitivity
than the one doing the moving, but it is excellent practice for both.
Whether it's a gentle push or a hard strike or kick, you want to
cultivate your body's instinct to move out of the way rather
than "contesting for space." At the same time, you don't want to
encourage your body to fear contact and begin to move too soon or too
fast. When your partner pushes or pulls you, just allow yourself to
be moved at the same speed as if your movement is only an extension
of your partner's. In this way, avoidance in Systema can be so subtle
and seamless that an attacker will not realize he has not made
contact as fully as he had anticipated.

Martin Wheeler showed us a sensitivity exercise to "feel the drift"
of your partner:

To illustrate how we are never standing still, our partners stood
motionless and we lightly touched their arms to feel the "drift".
Then Martin asked us to push them in the direction of the drift. It
takes a lot of sensitivity to detect this small motion of the body.
The idea is not to just shove them in one direction, but to feel
which way they are drifting naturally and push them in the same
direction. Martin showed us how you can even do this without touching
the person, he demonstrated on several people, pushing them in the
direction of their drift when he was standing behind them several
inches away.

another old training journal about finding the tension:

Martin demonstrated finding the tension of the person drawing the
gun. The weapon creates tension in the hand and arm and you can
follow this to the torso. He had us try to find the tension while our
partner drew, and push the tense spot to move our partner's arm. This
was very illuminating work. I find it difficult to find the tension
without patting my partner all over. I was working with Edgar and he
told me to just take my time. It takes sensitivity to learn to feel
this tension rather than trying to see it, as it can be too subtle to
be perceived visually.

As the previous posters suggest, crowd work, and working with your
eyes closed, are good practice. Also if you are interested in
developing sensitivity and awareness, you might want to check out the
Beyond the Physical tape.

Good luck and *Vsego nailuchshego* (best wishes),
Rachel