Sprint's new "LTE Plus" network is super fast, but it may not be able to reach your house. So Sprint is working on plans to put tiny cell sites on or near your house, according to CTO John Saw.

"It's all about getting the signal closer to the customer," Saw told me in an interview last week.

LTE Plus is the culmination of a long network struggle for Sprint, which involved buying Nextel and Clearwire, having to rip out and at least partially shut down three networks to merge them, and ending up with a gigantic swathe of 2.5GHz LTE, which can be really fast but doesn't go far from towers or penetrate walls easily.

What Sprint calls "LTE Plus" is really just LTE on wide channels of its high-band airwaves using a technique called 2x carrier aggregation, which creates a virtual lane that's twice as wide as what any of the other carriers are offering.

The new network has been spreading across the country and finally launched in New York two months ago, after Sprint got court permission to shut down the old Clearwire WiMAX network, which used the same airwaves.

Our partners Ookla Speedtest.net showed Sprint's mean LTE speeds as relatively steady from May 2015 to January 2016, when they suddenly shot up. Between January and March, mean download speeds rose from 11.64 to 15Mbps—still the slowest of the four major carriers, but better than before.

Head to Denver, though, where Speedtest.net showed a major jump in speeds in July 2015, and you'll find Sprint in second place, ahead of AT&T and Verizon. In Houston, Sprint's LTE speeds are ahead of T-Mobile and Verizon after a dramatic jump between August and November 2015, according to Speedtest. All in all, LTE Plus is now in 191 markets, Sprint said.

Now the trick is to get LTE Plus into buildings, which can rebuff the 2.5GHz waves. Part of that is about strapping small cell sites to light poles rather than putting them on rooftops. But part of it may also be about letting individual subscribers host their own sites, possibly connected to their wired home Internet networks.

"We have developed indoor solutions with 2.5 in them, and I don't want to talk more about what we're doing, because it's too early. It's easy to put 2.5 in a Wi-Fi hotspot ... [but] we're going to be a lot smarter than giving away free routers," he said.

To use LTE Plus, you need one of 14 phones Sprint sells; basically, this year or last year's Samsung, LG, HTC or Apple flagships.

We'll give you a real verdict on how well Sprint's upgrade is performing in our annual Fastest Mobile Networks tests, which go on the road in 30 major U.S. cities during May and will be published in June.

Back In the Home Internet Game?

LTE Plus has tremendous capacity, but Sprint isn't going to use it to deliver home Internet the way Clearwire did, Saw said. That doesn't mean Sprint is forever out of the home Internet game—just that it may be a future game.

"We have a lot of priorities at Sprint, and one of them is making sure we focus on our main customers, who are mobile. But one of the first few applications for 5G is going to be fixed wireless," Saw said. ("Fixed wireless" is another term for home Internet, because most homes don't move.)

So yeah, what is that 5G, anyway? All of the carriers are now saying they're leaders in 5G. In Saw's view, 5G is a "dense network using high-band spectrum," which conveniently places Sprint as a leader, as one can see its 2.5GHz band as the very lowest band of that high-band spectrum.

"2.5 is going to be the low-band, beachfront spectrum of 5G," Saw said. "Ten years ago, everybody laughed at us, but I think it's come full circle, and everybody now recognizes the value of high-band spectrum for 5G."