Sarah Tew/CNET

T-Mobile and Verizon Wireless have an increasingly complicated relationship.

The two companies are in the middle of closing a deal in which T-Mobile would get valuable wireless spectrum for $3.3 billion, a move that would aid its ability to offer coverage in rural and less populated regions of the country. Yet that isn't stopping T-Mobile from directing its sights at Verizon.

The latest attack: questioning the validity of Verizon's long-running campaign featuring coverage maps of all four carriers (of which Verizon, unsurprisingly, comes out looking far better than its competitors).

"I want to decimate that ad campaign from Verizon," T-Mobile Chief Technology Officer Neville Ray said to CNET in an interview Thursday.

T-Mobile is going about it in two ways. The first, most direct, route is through legal means. The company is arguing that the ads don't accurately reflect the full coverage of T-Mobile's network. By selectively choosing to only highlight LTE coverage, Verizon gives itself an advantage, Ray said. He added that the data, which is taken from T-Mobile's own site, is outdated.

"It's deceptive," he said. "That's the piece we're challenging."

He called the map campaign and focus on LTE markets covered a "deflection tactic," noting that Verizon has had its own issues with LTE coverage even as T-Mobile has laid claim to the nation's fastest LTE network.

Verizon Wireless

To be fair, Verizon's commercials clearly state that the maps are comparing LTE coverage. It's a campaign that's been utilized for a long time as well. The company wouldn't comment directly on the lawsuit.

"We prefer to compete in the marketplace, not in the courts. Our customers know what a true nationwide 4G LTE network experience feels like, map or not," said a Verizon representative.

But Ray argues that the map suggests that those few T-Mobile dots on the map represent all of the carrier's coverage, and excludes its 2G Edge network, as well as its HSPA+ coverage, which T-Mobile considers 4G.

That goes back to the years-long debate about whether HSPA+ is truly 4G or "faux G," although this argument has quieted down recently as everyone has moved to LTE.

Secondly, T-Mobile and Ray hope to combat that map by building out the network. Earlier Thursday, T-Mobile said it would upgrade its slower network by adding 4G LTE on top of its 2G Edge network. In addition, the company will use spectrum it is acquiring from Verizon to expand into new areas that it previously couldn't, because the spectrum it is getting has the ability to stretch over great distances.

Ray wouldn't discuss specific timing for the utilization of the 700MHz Verizon spectrum, but said that handsets compatible with the network will be released in the fourth quarter. He expects T-Mobile to close the deal with Verizon in the second quarter.

As for the 2G upgrade, Ray said he is working on upgrading the backhaul part of the network, or the ground lines connecting cell towers to the core network, with faster fiber-optic lines. T-Mobile also will be swapping out equipment and adding radios that will pick up both the 2G and 4G LTE network.

This is all a move to shore up T-Mobile's biggest weakness: its breadth of coverage. T-Mobile has largely focused on providing coverage in the biggest market, but it remains weak in rural and less populated areas -- parts where Verizon or AT&T do offer service.

"I'm not going to say we're going to fill out that map, but where it matters most to consumers, we're going to take care of it," he said.

T-Mobile has a goal to cover 250 million people by the end of the year, but Ray said he wants to push it to 280 million sometime next year.

"This time next year, we'll be in a far better place," Ray said.