NEW YORK — AT&T Inc. has gone on a shopping spree for wireless spectrum, striking three separate deals that should let it increase its capacity for wireless broadband.

The Dallas-based phone company said Thursday that it has agreed to buy NextWave Wireless Inc., a troubled company that’s mainly a holder of spectrum rights, for $600 million, most of which will go toward paying off NextWave debt.

AT&T also revealed it has agreed to buy spectrum from Comcast Corp. and Horizon Wi-Com, a small Miami-based company that tried to start up its own wireless broadband network. AT&T did not reveal what it was paying. Comcast has given up on plans to start a wireless network and is selling most of its spectrum to Verizon Wireless.

The deals all involved spectrum in one particular band. Put together, they would provide near-nationwide coverage and a substantial boost to AT&T’s capacity.