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Shannon's specter

In 1948, while working at Bell Labs, Claude Shannon published a paper that laid the groundwork of information theory. In that paper, Shannon formulated the basic model of transmitter, receiver and transmission channel that has driven communications engineering to date. But in the same study, Shannon also set out to define a fundamental limit to the amount of information that could be transmitted over such a link.

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He theorized that the amount of error-free data that could be transmitted over a channel of any given bandwidth was limited by noise. While more and more efficient technologies can be developed to push more data into a channel, there is a ceiling at which any gains of capacity would essentially be canceled out by noise. That fundamental limit became known as Shannon's Law.

While Shannon's Law existed as an ultimate barrier, it never posed a problem for telecom engineers for most of the century. Bell Labs and other technology firms innovated well within the theoretical confines of the law, but within the last decade, that law has started carrying more weight — particularly in wireless. Since Shannon's Law applies to a particular channel of spectrum, wireline carriers have been able to add more channels by laying bigger pipes or more of them. Wireless technologies, however, are limited to the spectrum available in a given location. With the advent of 3G and 4G technologies, the wireless industry is finally starting to run up against the barrier of Shannon's Law.

“We've been up against Shannon's Law from a theoretical point of view for the last ten years,” said Alex Reznik, principle engineer for InterDigital. “The technology has just been catching up.”

A look at the new orthogonal frequency division multiplexing (OFDM) technologies that form the basis of 4G serves as an example. While the industry highlights the gains in speeds that long-term evolution (LTE), ultra mobile broadband (UMB) and WiMAX will bring, those capacity gains are primarily due to wider channels, not greater spectral efficiency — i.e. 4G lays bigger pipes rather than increasing the amount of data flowing through the same-sized pipe.

In fact, many of the innovations in cellular technology have been methods used to actually decrease noise in the channel in order to push the theoretical speeds further up the curve of Shannon's Law (the lower the interference, the higher the capacity gains) or to expand the number of channels available. The name cellular itself carries the implication of dividing spectrum into discrete cells that can utilize the same spectrum independently of other cells. Interference cancellation and forward error correction technologies can clean the transmission further.

Spectrum reuse and radio resource management techniques are designed to optimize the spectrum available for maximum efficiency. Those techniques have led to EV-DO's tremendous gains over CDMA 1X and Revison A's gains over EV-DO. They've allowed GSM vendors to exponentially increase data speeds of UMTS in all of the iterations of high-speed packet access (HSPA). But all those techniques have been related to the efficiency of the transmission working within the parameter's of Shannon's Law; they haven't increased the theoretical capacities that CDMA and OFDM have run up against, said Bill Krenick, wireless advanced architectures manager for terminals in Texas Instruments' semiconductor group,

“We can only be so efficient,” Krenick said. “Once we get close to Shannon's law, we can't pack any more information into any given hertz.”

The result is that vendors have started playing down the net gains of spectral efficiency that future technologies will bring. While touting such capacity gains was the fashion during the migration from analog to digital and from digital to 3G, a look at the theoretical capacities of 3G versus 4G technology shows that is no longer possible. The last evolutionary step of UMTS HSPA technology, HSPA+, promises theoretical downlink capacity of 42 Mb/s and 11 Mb/s on the uplink. The next 4G technology based on OFDM, LTE, promises downlink speeds of 100 Mb/s and uplink speeds of 50 Mb/s, an increase of more than double on the downstream — but requiring double the amount of spectrum.

Applying Shannon's Law to those theoretical speeds paints a clear picture. Just assuming thermal background noise and no other interference, producing a signal-to-noise ratio of 20 decibels, Shannon's law would set a limit of about 6 bits/sec per Hertz of error-free information capacity that no point-to-point transmission could ever exceed, said Tom Quirke, director of product marketing for Motorola. Taking LTE's targets of 100 Mb/s on the downlink over a 20 MHz channel, the 4G technology already has a theoretical spectral efficiency of 5 bits/sec per Hertz, Quirke said — and that's assuming optimal conditions that rarely exist outside a lab.

Moving beyond the thermal noise that pervades any place that registers a temperature, there are loads of interference from other users, from the cell site and from neighboring cell sites. Networks are inescapably noisy creatures, and all that interference lowers the signal-to-noise, dropping both the theoretical and real-world capacity available over any channel, Quirke said.

“Noise is like a hiss,” Quirke said. “Without noise, you could essentially have an infinite amount of information over even a finite amount of spectrum.” Even with all the interference cancellation techniques known to science, a certain degree of noise will be ever-present, he said. “That thermal noise is always there.”

So if the wireless industry has reached the theoretical limit of how fast networks can go, what's next? Where does the industry innovate from here? In reality, much of that innovation has already started. Instead of squeezing more bits into individual frequencies, engineers are now looking toward creating more frequencies for use. Receive diversity technologies like multiple input/multiple output (MIMO) smart antenna technologies send the same information from two or more separate transmitters to an equal number of receivers, cutting down on the information loss of a single transmission. Beamforming technologies look to steer a radio link toward a specific user, allowing signals that would normally interfere to emit from the same transmitter.

But a lot of what engineers are investigating now is how to use bigger chunks of spectrum. CDMA technologies are limited by small channel sizes, but OFDM, which splits a channel into numerous tiny subchannels, allows a network to transmit in broad swathes of spectrum. OFDM technologies are targeting 20 MHz channels now, Motorola's Quirke said, but as the wireless industry strives to deliver wireline broadband speeds, it will have to find even bigger swathes.

“A lot of what the industry will be doing is trying to find that big chunk of spectrum,” Quirke said. “You'll need more than a 100 MHz if you ever truly want to get into Gigabit speeds.”

Utilizing such large sections of spectrum may cause far more political and regulatory difficulties than scientific ones, though. Any 100 MHz chunk can have hundreds of individual licensees and dozens of differing designated uses. Although wireless carriers tend to relentlessly use their spectrum, squeezing every drop of capacity imaginable, the same can't be said for the numerous TV broadcast, educational, government and military bands that populate the airwaves. TI's Krenick said that RF engineers are exploring the idea of cognitive radio, which identifies on the fly spectrum in other bands that is not being used and allocates those resources for a cellular network.

Spread spectrum and cognitive radio, however, face their own set of limitations. Just as information can only move through the pipe so quickly due to Shannon's law, the pipe can only be made so big, as its size is limited by available spectrum. The same goes for newer techniques like MIMO. They may lower that signal-to-noise ratio, moving the transmission further up the capacity curve laid out by Shannon's law, but still can never exceed it. There's only so much more capacity that can be squeezed out by these techniques, and the cost of implementing them will outweigh the modest gains in capacity they achieve, InterDigital's Reznik said.

We're hitting a throughput wall in communications networks, but the industry is already thinking of ways to break through it, Reznik said. Shannon's Law applies to a single radio link between a transmitter and a receiver. The key is to create multiple radio links; each link itself is limited by Shannon's law, but taken collectively, they could exceed it, he said.

InterDigital and other technologists envision a cooperative multi-link network where a handset communicates with multiple base stations, special relay routers and possibly even other handsets. In such a network, everything is a transmitter, and everything is a receiver, establishing multiple links with multiple devices. And while each of those individual radio links would have a limited capacity, information would be coming from multiple directions, compounding the overall capacity allotted to any given user on the network, Reznik said. The concept of a distributed network is still entirely theoretical, but faced with the bounds of Shannon's Law, it is one that is starting to gain credence.

“I don't see it as completely unreasonable to see a distributed architecture in the next ten years,” Reznik said. “The standards bodies are already taking the first timid steps.”

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© 2014 Penton Media Inc.

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