The Federal Communications Commission on Thursday approved AT&T’s $1.9 billion purchase of wireless airwaves from Qualcomm. The approval provided a much-needed boost for the telecom giant, which this week suffered a rejection of its much bigger bid for T-Mobile.

In a 3 to 1 vote approving the deal, AT&T will acquire airwaves that it will use to bolster its high-speed mobile Internet network, known as its fourth-generation LTE network. AT&T is in a dash to keep up with competitor Verizon Wireless, which has built out its network more quickly and also has been on a spectrum-buying spree to keep up with the Internet demands being created by new smartphones and tablets.

The commission cited the companies’ argument that the airwaves weren’t going to be used by Qualcomm, therefore a sale wouldn’t reduce competition.

But Democrat Michael J. Copps, the only commissioner who voted against the deal, said the transaction would give Verizon and AT&T, the top two carriers, too much dominance. And he said that conditions attached to the deal were too weak.

“I could be persuaded, with the right set of pro-consumer conditions, to concur in the transaction,” said Copps, who is scheduled to retire at the end of the year. “While much of the competitive analysis in today’s order is strong, the conditions the Commission does attach strike me as falling short of advancing the public interest demand.”

The increase in airwaves falls far short of what AT&T was trying to acquire from its $39 billion bid for T-Mobile. Federal antitrust officials blocked that deal.

AT&T said that even with the Qualcomm airwaves, it will continue to hunt for spectrum so it can continue to build more robust networks to avoid the dropped calls and slow downloads it experienced when it began to carry its first real smartphone — Apple’s iPhone.

Rural carriers had argued against allowing AT&T to store the spectrum for a rainy day. And they wanted rules attached to the deal that would prevent AT&T from striking exclusive deals with consumer electronics makers, as it did with Apple for more than three years.

The FCC rejected those requests. But it did require AT&T to allow competitors to roam on its network.

Some consumer groups said regulators should allow smaller competitors a chance at scarce airwaves.

“AT&T obviously wants more spectrum for itself, and less for potential competitors, but it doesn’t need this spectrum to improve its own offerings,” said Matt Wood, policy director of the public interest group Free Press.

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