AT&T Inc. (NYSE: T), the largest U.S. telephone company, has agreed to buy NextWave Wireless Inc. in a deal worth as much as $600 million in cash, giving it more airwave capacity to provide mobile Internet services.

The phone giant didn’t stop there, making two other deals for even more spectrum.

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

AT&T also revealed Thursday that it has agreed to buy spectrum from Comcast Corp., the cable company, and Horizon Wi-Com, a small Miami-based company that tried to start up its own wireless broadband network. In those cases, the company didn’t reveal what it was paying.

Comcast has given up on its own plans to start a wireless network, and is selling most of its spectrum to Verizon Wireless.

Analyst John Hodulik at UBS said he expects that AT&T is paying a total of less than $1 billion for the three deals.

The three 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. AT&T said it will begin to deploy the spectrum in three years.

However, the radio bands lie close to frequencies that are used for satellite communications, and interference concerns have prevented them from being used. AT&T has asked the Federal Communications Commission to approve a solution that it says would prevent interference.

Mobile-phone carriers are racing to add more airwaves as they roll out new services and congestion grows on current networks. NextWave holds licenses for Wireless Communication Services, or WCS, which would start being used for mobile Internet access for the first time under a plan by AT&T and Sirius XM Radio Inc. The Federal Communications Commission is weighing the proposal, submitted in June.

“WCS spectrum was first auctioned in 1997, but has not been utilized for mobile Internet usage due to technical rules designed to avoid possible interference to satellite radio users in adjacent spectrum bands,” Dallas-based AT&T said today in the statement. The Sirius proposal “effectively creates much-needed new spectrum capacity.”

AT&T has been on the hunt for more wireless spectrum, a hunt that led it to agree to buy T-Mobile USA last year for $39 billion. That deal fell through on antitrust grounds.

The $600 million for NextWave includes $25 million for its shares, and an additional $25 million if certain conditions are met. That sent the shares, which trade over the counter, jumping from 25 cents at Wednesday’s close to $1.29 Thursday.

The deal doesn’t include all of NextWave’s spectrum. Some Canadian and U.S. holdings will be placed into a new holding company, to be owned by its debtholders.

In its latest regulatory filing, NextWave listed the value of its spectrum holdings at $434 million and its debt at $1.1 billion.

NextWave has had a difficult life. It was spun out from Qualcomm Inc. in 1995. The next year, it bid $4.74 billion to buy the rights to 95 spectrum licenses from the government, big enough to cover nearly 94 million people. But the company couldn’t make its payments and filed for bankruptcy protection.

The FCC took back and re-auctioned the licenses, but NextWave argued that bankruptcy law protected it from seizure of its assets. It took the fight all the way to the Supreme Court, which sided with it. The company emerged from bankruptcy in 2005, a year after it reached a settlement with the FCC.

NextWave sold some of the licenses from the 1996 auction to Verizon Wireless, AT&T Inc., and MetroPCS Communications Inc. It returned others to the FCC.

NextWave’s current spectrum holdings derive from another FCC auction in 2005 and from acquisitions from other companies. It spent $500 million on the license, it said in 2008. It was then also developing wireless network equipment, but those operations have folded or been sold off since then. The shares were delisted from the Nasdaq in 2010 because they failed to meet the minimum $1 value.

(The AP and Bloomberg contributed to this report.)