Sprint Nextel Corp., the third-largest U.S. wireless carrier, agreed to buy Midwestern airwaves and customers from U.S. Cellular Corp. for $480 million.

The spectrum is in the so-called PCS band and spans parts of Illinois, Indiana, Michigan, Missouri and Ohio, Sprint said today in a statement. The Overland Park, Kansas-based company plans to use the airwaves to bolster its wireless coverage as it rolls out a new network based on a technology called long-term evolution, or LTE.

Sprint, which received $3.1 billion in cash last month as part of a $20 billion investment from Softbank Corp., is putting some of that money to work in a network expansion race against competitors including Verizon Wireless and AT&T Inc.

“Acquiring this spectrum will significantly increase Sprint’s network capacity and improve the customer experience in several important Midwest markets including Chicago and St. Louis,” Sprint Chief Executive Officer Dan Hesse said in the statement.

Under the deal, which is expected to be completed in mid-2013, Sprint will pay cash and assume liabilities.

Sprint fell 1.1 percent to $5.67 at 10:05 a.m. in New York. The stock had more than doubled this year through yesterday.