AT&T has a problem in Chicago. The city was one of the first to be upgraded to the wireless carrier’s next-generation LTE (long-term evolution) network, which packs more data into a radio signal and offers much faster download speeds. But independent tests published this month showed that AT&T downloads in Chicago are less than half the speed of those on Verizon’s LTE network there. The reason? A lack of radio spectrum. AT&T’s radio licenses allow it to use only a 10-megahertz chunk of the airwaves for its LTE network in Chicago, compared with the 20 megahertz it has in other cities

AT&T faces the same problem in Los Angeles, and it’s just part of a challenge confronting the whole mobile communications industry: how to reconcile consumer expectations of forever faster, cheaper downloads on mobile Internet devices with limited room in the airwaves.

Networks are not in danger of running out of capacity just yet. Carriers have spent large sums buying up rights to the radio spectrum, and they’re being creative about ways to squeeze more out of what they already have. (Exact speeds vary, but an LTE connection is typically 10 times faster than one provided by a 3G network.) The federal government licenses spectrum space, and wireless carriers and other companies have for many years bought up and hoarded licenses, anticipating the need to expand.

But the largely unforeseen explosion in demand for wireless bandwidth, driven by the appearance of tablets and smart phones, has made it more urgent to ensure a supply for future use.  AT&T spokesman Mark Siegel says network traffic and the company’s spectrum portfolio affect the kind of service that users receive in different areas. “We will continue to invest and innovate to make the best, most efficient use of available spectrum across our network,” he says.

Chances are it will be able to fix the problem before too long. The company is sitting on unused spectrum acquired in 2006 that it eventually plans to use for LTE. It recently paid $1.9 billion to mobile chipmaker Qualcomm for wireless spectrum to serve important markets including San Francisco, New York, and Los Angeles. Verizon is simultaneously trying to sell off one chunk of spectrum it has owned for years and to buy another—one it thinks is better suited to LTE—from a consortium of cable companies. AT&T and T-Mobile both have plans to recycle some of their spectrum currently used for slower, 2G data connections, upgrading it to serve LTE connections so it can carry more data.

Carriers are increasingly looking for creative tactics that will relieve pressure on their networks. “Spectrum is certainly a limiting factor, but carriers are also constrained by a number of other things, too, particularly backhaul,” says Bill Moore of RootMetrics, which gathers data on cell-phone network bandwidth and other performance measures that are freely available online. Backhaul refers to the physical connections that link cell-phone towers to the Internet and phone networks. All carriers are working hard to upgrade their backhaul, replacing copper cable with high-capacity optical fiber.

Getting the necessary permissions to replace or install underground fiber is a slow process, says Bryan Darr, CEO of Mosaik Solutions, which collects data on wireless network coverage. That explains Verizon’s alliance with a consortium of major cable companies to connect their networks, announced late last year. “The cable operators have an awful lot of cable in the ground that’s capable of handling a lot of traffic,” says Darr. “They also know themselves that they need to be connected to the wireless industry because that’s where the future of content like TV is.”

A way to sidestep bottlenecks caused by constraints on spectrum and backhaul is to have smart phones and tablets make use of Wi-Fi as much as possible, says Darr. AT&T is investing heavily in that strategy by installing Wi-Fi hotspots in stadiums and busy city areas in Manhattan and San Francisco. Newer AT&T phones automatically switch to using Wi-Fi when in range, reducing the load on cell towers. “Once that can work more seamlessly for data and calls, it is going to be a huge help,” says Darr. This February AT&T reported that it had worked with other carriers, including China Mobile, on a successful trial of special Wi-Fi hotspots that can recognize an authorized device and take over its connection without dropping calls or interrupting downloads in progress.

Experts say that the major carriers are so far keeping pace with the demands of their customers. “Out of the four major national carriers, three are getting faster,” says Moore of RootMetrics; the fourth, Sprint, is due to introduce its first LTE networks this year, which should allow it to speed up too. He believes there is enough spectrum to go around but notes that carriers are caught in something of an arms race with their own customers. “All I see for now is that speeds go up,” says Moore, “and that will encourage consumer demands to go up as well.” Partly as a result, almost all wireless carriers phased out unlimited data plans last year. That means they can cap bandwidth use or charge more for it if they find demand for data outstripping their ability to supply it.