HL2: Stuck at Anticitizen One generator plaza standoff

As I recall, there's several supply boxes in the center. I would save these until you need them, due to them trying to give you what you need. In my experience, the boxes are also weighted towards magnum ammo and crossbow bolts, so don't be afraid to use them.

My general strategy is as follows:
For the initial waves, stay near the electro-walls and kill the soldiers as they are dropped off, with grenades and the SMG. When the white soldiers start appearing, switch to the Combine rifle as they drop that ammo (use the Gravity Gun for easy ammo pickups).
As soldiers start to approach from both directions, move to the center and crouch behind the little wall for cover during reloads. There's going to be a lot of enemies, so I use the magnum and crossbow at this point.
When Alyx says the core is exposed, blast it with the Gravity Gun and sprint past the gate. I believe soldiers will continue to spawn until you make it past the gate. Yes, you'll probably still be shot, so hopefully you've done well enough or saved some supply boxes to have enough health/energy at that point.

There's a couple instances of infinite enemies like this, or overwhelming. Usually they are pushing you to run/escape somewhere.