I was going to suggest grenades...

...but then I thought about it some more.

Seriously, birds eyes respond to movement. That's why a hawk can see a mouse moving on a field over 100 yards away. If the mouse were still, the hawk would never notice it or even see it.

What you want to do is use something like a scarecrow, but one that will move in the wind. As long as the scare crow "flies" or appears to move in the wind without any means of support, the pidgeons will realize that it's big enough to feed on them, and probably leave the area. I would contact some of the exterminators in your area to see what's available in the form of a wind toy that looks like a hawk, eagle or other large bird. I know that one of the churches in Winnipeg has large plaster eagles on it's steeple to keep birds away, but I expect it doesn't work well because it doesn't move. Even a bird brain would soon figure out that something that doesn't move can't chase it down and eat it.