If you're already in a basement, you may be in good shape to start with. Do you have a good copper ground available? (Copper drain pipe, bored spike into the ground?)

What kind of Radio RF, btw? AM or FM? It makes a difference.... AM tends to "hug" the ground as it propogates, while FM is bounced up into the air. (Overly short explanation, but you get the idea...)

I'd start with JUST your power amp feeding the speakers, with your input gain set to OFF. Make SURE you disconnect everything else physically, and raise the input to nominal working level (that you're normally using with your mixer.) See where you are there. Radio RF? No Radio RF? (If none, continue from here....)

Then add the console, but with NOTHING physically connected to it. (NOTHING!) Your only connections should be your mixer's outputs to your amps' inputs. (Still none? Keeping going....)

Then begin (one at a time) adding all of your outboard gear - everything from CD players to processors, etc. If you're using rack-mounted gear, watch out for gear that is and isn't grounded to the rack rails. Don't quit at the first suspect piece of gear: You may also have to physically remove rack gear and try it one at a time if you find multiple cases of RF coming in from several pieces of gear.

Last thing in the chain that you'll add are mic cables and mics. Most balanced XLR stuff should NOT add radio inference on their own. Unless you're really REALLY close to an antennae (or antenna farm), you should be able to track down the defective gear or cable this way, and either remove, isolate or repair it.

If you can't find any one piece of gear, or have multiple instances of RF, you may have to consult a pro for trickier things like copper mesh and single point grounding to a big copper plate to the ground, and you may have to add some magnetic beads to the legs of various input gear, or even lift some grounds, but that's probably more radical than necessary. HOPEFULLY!

Good luck; I'd love to hear what you found.......

Good suggestions above. Sounds like it's probably an AM station. What you might want to look for are "farite" traps. You may have seen them connected around your computer monitor cable and/or other ancillary devices where RF interference looms. These are frequently available at computer/network supply centers and can be placed around many of your input and output cabling. You could also be suffering from ground loop. Make sure your mixer, is grounded. Try lifting the grounds from your other input output devices with a commonly available cheater plug from your local hardware store. Don't do this in your bare feet or on a wet floor! If interfaced with your computer, computers do not have transformers in their power supplies and are a regular source of problems when interfaced with other pieces of audio equipment.