You do need a spectrum license (or unlicensed spectrum) with WiMax. Further, even if you could operate a WiMax network in an unlicensed band, you will run into

You do need a spectrum license (or unlicensed spectrum) with WiMax. Further, even if you could operate a WiMax network in an unlicensed band, you will run into issues with: a) not all countries having the same unlicensed bands, and b) the need for consumer hardware (baseband radios) to support WiMax in the band(s) you need. You could potentially roll out WiMax in a 1500MHz band in some countries but very little hardware does (or will) support that.