Too many people depend on their Radars, when I play some of the playlists without one I just steam roll everyone, I've never really played FPS with always on radar, used to play a lot of Hard core mode in CoD. I instead just use my wits, I know where my team is, I know where the enemy will spawn, choke points are the same most of the time, people tend to hide in the same corners and so on.
Radar is super helpful with getting into position, if I notice someone rushing they either have a shotgun or a panic super, so I can make sure I get a decent line of sight to get them down before there close enough. If someone is not moving, then there camping around a corner with a shotgun, I try to get an angle where I could see them running away, throw a nade and see what happens.
Using headphones is also very important, you can hear someone go invisible, you can hear someone fire of shots for their last round sniper, you can hear someone pop a super. Using that along with your map knowledge and radar means I can hear a blade dance, make sure I have a decent line of sight and try snipe them. If its a golden gun, I look for cover where I can see a choke point and weave in/out trying to get them to waste their shots while I also try snipe them.