I beleive that awareness is the most important part of self-defence.
I practise it with some of the guys from my dojo.
During training time and when not training, we try to sneak up and easily hit each other.
After some time you get very paranoid and react to everything that moves around you.

But as time passes, you learn how to control space around you and without being paranoid.

Any ideas of your own how to practise awareness?

That's definitely a good idea. My awareness could do with a bit of work, for sure. I'll ask some friends to attack me randomly in future. :-p

Most people that know me think that I am a very paranoid person. I never let anyone pass behind me without watching them or turning toward them. I only sit with my back against the wall in restaurants and such. The training you mentioned is similar to what we do in out dojang. I also like to put on a blindfold and have people randomely attack, thus hitting you while you don't "see it coming."

A few tips from the king of paranoia:
lock all doors asap in and out of the car/house

have keys in-hand before heading out to car

keep hands out of pockets when in public

don't be afraid to speak to anyone around you to feel them out

watch people

Don't walk closely around corners

park in the lighted areas

have a key or pen in-hand to use as a kubaton

Train to go from freindly conversation to full contact if needed

When attacked at random in the dojang, be sure that the attacker truly follows through with his reactions to whatever you do to defend yourself, thus making it realistic. Basically make this training as real as possible, not just attacking and then saying "well I would have punched you in the throat..." I think you know what I mean.

Just some humble advice from the top of my head. Just look, listen, feel and the rest will come.

Spend a day thinking like a preditor. Ask yourself who would be your victim and why.