xG Technology's xMax

For several years, a Florida company called xG Technology, Inc (traded as XGT.L on the Alternative Investment Market of the London Stock Exchange) has been talking up a digital radio communications technology that they variously call "xMax" or "xG Flash Signal". They variously claim it can transmit high speed digital data with very low power and/or almost no spectrum.

This sounds a lot like Harold Walker's clearly unworkable VMSK, so the obvious question arises: is this the same thing?

First of all, xG appears to be an independent effort by Joseph A. Bobier. Harold Walker says he knows Bobier and has worked cooperatively with him in the past, but Bobier's work on xMax appears to be independent. Walker is not mentioned on the xG website, and Bobier has not responded to my emails asking for comment. It has been very hard to tell just what xMax is or even in what way it is supposedly better than existing technologies because xG has been so tight-lipped and vague. But some recently granted patents and their website can provide some insights. And while I'm still analyzing them, my initial impression is that it doesn't look good at all. Considering that xG Technology's current market capitalization is in the range of US $1.5 billion, this is more than a little distressing to me.

The Technology Page on xG's website says the following:

xG Flash Signal uses breakthrough single cycle modulation to deliver longer range and lower power RF communications. Single cycle modulation is implemented when individual sinusoidal cycles of RF energy are modulated to represent one or more bits of data.

This proprietary modulation method differs from conventional approaches where tens to hundreds of thousands of RF cycles are required to convey a single bit of information. With each additional cycle representing more RF power, getting the job done with fewer cycles translates into more power efficient RF transmissions.

One clear conclusion can be drawn from this paragraph: whoever wrote it doesn't have a clue about digital radio communications. For six decades we've known that there is an absolute lower limit on the RF energy required to send a bit of data over a noisy radio channel. Every competent radio engineer is familiar with this limit, and the state of the art is already very close to it.

While many opportunities for innovation remain in the digital wireless field, a breakthrough in required RF power due to a new modulation scheme is not one of them.

Once again, some theoretical background

(To skip forward to how this relates to xMax, click here).

The foundation for modern digital radio communications was laid almost single-handedly in 1948 by the late Claude Shannon. It is hard to overstate the importance of his paper A Mathematical Theory of Communication. Among several other remarkable and fundamental insights, Shannon proved that it is possible to communicate without error (or with an arbitrarily low error rate) on a noisy channel as long as just one requirement is met: the special ratio Eb/N0 must be greater than ln(2), the natural logarithm of 2. Numerically, that is about 0.693, or -1.6 decibels (dB) in electrical engineering terms. This number is now known naturally enough as the Shannon bound. This is a theoretical limit; any real receiver will always do worse.

What is Eb/N0? Basically, it's closely related to the signal-to-noise_ratio, or SNR. It seems obvious that you can't receive a signal unless it's stronger than the noise, and this is almost true. Spelled out, Eb/N0 is the ratio, at the receiver, of the signal energy per bit to the noise power spectral density. What does that mean?

The received energy per bit is, simply enough, the signal power at the receiver in watts divided by the data rate in bits/sec. Power is energy per unit time, so the energy per bit times the number of bits per second gives the signal power. An important note: here a bit refers to a user data bit, not the encoded bits from an error correction code or a symbol from a modulator. Bits are what the end users send and receive.

The noise power spectral density N0 takes a little more explanation. Shannon assumes that the channel is impaired by additive white Gaussian noise (AWGN). Not every channel is AWGN, but it's a good assumption because AWGN is common in nature; it is essentially the "waterfall" noise you hear or the "snow" that you see when you tune to a radio or TV channel without a signal. "White" noise consists of all frequencies in equal amounts just as white light consists of all frequencies (colors) of light. So the intensity of AWGN can be specified with a single number: the noise power, in watts, per hertz of bandwidth. That's N0. (Note that we're using the word "bandwidth" in its original communications sense as "a range of frequencies" and not in its newer and rather inaccurate computer networking sense as "a data rate". When we mean data rate, we'll say data rate, not "bandwidth".)

An interesting thing about Eb/N0 is that it's a dimensionless ratio. Energy is measured in watt-seconds, also known as joules, while N0 is measured in watts per hertz. But a hertz is a reciprocal second, so "watts per hertz" is the same as watt-seconds or joules. This makes the ratio Eb/N0 a dimensionless quantity, as it would have to be to be represented in decibels.

Sources of Radio Noise

The most important sources of radio noise are the thermal vibrations of the receiver's own atoms and objects seen by its antenna. The thermal noise power density emitted by an object is

N0 = kT, where

k = Boltzmann constant, 1.38*10-23 J/K
T = absolute temperature in kelvins

So at a temperature of 300 kelvins (26.85 C or 80.33 F),

N0 = kT
= 1.38*10-23 J/K * 300 K
= 4.14*10-21 W/Hz (-203.83 dBJ)
The noise power in a bandwidth B is
N = N0B
So the total noise power from an object at 300 K in a bandwidth of 1 MHz is
N = N0B
= 4.14*10-21 * 1*106
= 4.14*10-15 = 4.14 femtowatts = -143.83 dBW
That's an incredibly small power, but it is nonetheless a critical limiting factor in most radio systems.

Eb/N0 is closely related to signal-to-noise_ratio, or S/N. The relationship is

Eb/N0 = (S/N) * (B/R), where

S = signal power, watts
N = noise power, watts
B = signal bandwidth, hertz
R = bit rate, bits/sec

Eb/N0 equals S/N only when the signal occupies one hertz of bandwidth (B) for every bit per second of data rate (R). When the signal is wider than the data rate, the Eb/N0 is greater than the S/N. When the data rate is greater than the bandwidth, the Eb/N0 is less than the S/N. The ratio R/B is known as the spectral efficiency.

Some older textbooks refer to Eb/N0 as the "SNR per bit". This term fell out of use and Eb/N0 became the preferred figure of merit for digital communications for a simple reason: it's independent of signal bandwidth. Although bandwidth seems like a simple concept, it can be remarkably tricky to measure or even define. It has several different definitions, and while they give similar results on many signals, some unusual signals can have very different bandwidths depending on which definition is chosen. (The "ultra narrow band" delusion is entirely about concocting pathological signals that are "narrow band" only by an incorrect and irrelevant definition of the term).

A signal can also be deliberately widened in bandwidth to make it more resistant to interference. This is spread spectrum, a technique with military origins that's the basis of CDMA digital cellular, some forms of WiFi and many cordless phones. Spreading reduces the required S/N by the amount that the signal is widened, making it even harder to compare different kinds of modems. So it's much easier all around to instead use Eb/N0 as a figure of merit that doesn't depend at all on a definition of bandwidth or whether the signal is spread.

The Shannon bound of -1.6 dB is for infinite bandwidth, the most favorable case. (It's a little counterintuitive that using more bandwidth should let you use less power since the total received noise power increases with bandwidth. But it's true.) If your bandwidth is limited, then the minimum Eb/N0 is greater. If you are strictly limited to one hertz of bandwidth per bit per second of data rate, then the Eb/N0 must be at least 0 dB. As your bandwidth becomes even more constrained, the minimum Eb/N0 rises exponentially. That's why telephone modems require good connections, and it is why so-called "ultra narrow band" schemes like VMSK are completely unworkable.

The most important things to understand about the Shannon bound is that it comes from a mathematical proof, and that it is universal. Shannon proved, and countless others have verified his proof, that you cannot communicate without error when Eb/N0 is worse than the Shannon bound for the particular data rate and channel bandwidth. This applies to every modulation and coding scheme, whether or not it has yet been invented. No matter how clever you are, and no matter how much computer power you have, you cannot exceed the Shannon limit and communicate without error. Period.

Shannon and xMax

With this theoretical background, we can see the big problem with xG's claims about using fewer RF cycles per bit. Each RF cycle carries some amount of energy, and if a certain number of cycles are needed to build up enough energy in each bit to permit it to be detected, then you simply cannot do with less. Efficiencies can often be improved, but you can no more exceed the Shannon bound than you can build an engine that exceeds 100% efficiency. It doesn't matter how clever Joseph Bobier's design may be, it simply can't be done.

xG's statement implies you can also reduce the number of RF cycles needed to transmit a bit by increasing the transmitted energy in each RF cycle. This is true, but it completely defeats the claimed benefit of reducing the energy consumed per data bit.

So xG's claims simply don't make any sense.

xG's Florida tests

xG announced that in November 2005 they demonstrated xMax in Ft. Lauderdale, Florida using what they implied were unprecedented low transmitter powers. A closer look at those numbers tells a different story.

According to xG, 35 milliwatts were used to transmit a 3.67 Mb/s signal over a distance of 18 miles on the 902 MHz "ISM" band. Other reports said they used 50 mW from a 204-meter tall transmission tower with 6.5 dBi of gain on the transmitting antenna and a 8 dBi directional receive antenna.

Florida is a very flat state, so we can easily compute the range to the horizon from the top of this tower as

range = R cos-1(R/(R+h)), where

R = radius of the earth
h = tower height, same units

Plugging in R = 6378 km and h = 0.204 km,
= 6378 cos-1(6378/(6378+0.204))
= 6378 cos-1(.99996801607)
= 51 km

The operating distance in the demo was 18 miles or 28.8 km, well within line of sight range of this tower. The atmosphere is transparent at 902 MHz, so the signal loss with distance is purely geometric: the receiving antenna simply captures a smaller fraction of the transmitted energy.

This is the inverse square law, and radio engineers routinely incorporate it and other well-understood physical properties of radio wave propagation into link budgets so they can predict the performance of communication systems even before they're built. So we'll do a link budget with xG's numbers.

The first component in the link budget is the inverse square path loss, computed as

path_loss(dB) = 20*log10(4*π*D/λ)
where D is the distance and λ is the wavelength in the same units. 18 miles is 28,968 meters and the wavelength of 915 MHz (the center of the 902-928 MHz band) is 0.3279 meters. Plugging in these numbers gives us:
20*log10(4*π*28968/0.3279) = 120.9 dB

This is the "loss" between two isotropic antennas that radiate equally in all directions. Such antennas don't actually exist, but they're a useful reference. Real antennas achieve gains by focusing the power in a desired direction at the expense of others. Antenna gains are usually cited in dBi, decibels with respect to an ideal isotropic antenna. According to this article, the transmitter used an omnidirectional antenna with a gain of 6.5 dBi and a directional receive antenna with 8 dBi gain. Both figures seem reasonable, so we'll add them to the link budget.

The transmitted power is said in one place to be 35 milliwatts; in another, 50 mW. We'll use the smaller figure to be conservative, so that's -14.56 dBW, or decibels referenced to 1 watt. Therefore the received power would be:

P(rx) = P(tx) - path_loss + tx_gain + rx_gain
= -14.56 dBW - 120.9 dB + 6.5 dBi + 8 dBi
= -120.96 dBW
The data rate is stated to be 3.67 Mb/s, or 65.65 dB-Hz (decibels referenced to one Hz). So the received energy per bit, Eb, is:
Eb = P(rx) - 10*log10(bit_rate)
= -120.96 dBW - 10*log10(3.67*106)
= -120.96 dBW - 65.65 dB-Hz
= -186.61 dBJ, decibels referenced to one joule

Now we need to compute N0, the received power spectral density. The receiving equipment is not specified, but we can make an educated guess about its performance. White Gaussian noise is radiated by every object not at absolute zero temperature by the random thermal vibrations of its molecules. If the object is hot enough, it visibly glows; this is how the sun and incandescent light bulbs produce their heat and light. At room temperature the radiated power is very small, but highly significant in communications systems. It can be calculated as N0 = k*T, where k is the Boltzmann constant, 1.38*10-23 J/K or -228.6 dBJ/K, and T is the absolute temperature in kelvins. With reasonably state-of-the-art receiver technology it is not hard to make an amplifier at 915 MHz that produces considerably less noise than that radiated by the earth and picked up by the antenna. So we can assume the system noise temperature is merely the temperature of the earth, about 300 kelvins (24.8 dBK, decibels referenced to one kelvin). This makes:

N0 = 10log10(1.38*10-23) + 10log10(T)
= -228.6 dBJ/K + 24.8 dB-K = -203.8 dBJ
So we finally have:
Eb/N0 = Eb(dBJ) - N0(dBJ)
= -186.61 dBJ - (-203.8 dBJ) = +17.2 dB
This is obviously well above the Shannon bound of -1.6 dB. If the transmitter power was 50 mW rather than 35 mW, the Eb/N0 would have been another 1.55 dB higher, or 18.74 dB. Either way, this is a pretty strong signal. One of the least efficient of the conventional binary digital modulation schemes, noncoherent Frequency Shift Keying or FSK, can achieve a bit error rate of 10-6 (one error in a million bits) with an Eb/N0 of only 14 dB without the error correction that is now a standard element of nearly every modern digital radio system. Eb/N0 ratios below 3 dB were achieved in the 1970s on the Pioneer and Voyager spacecraft. One of the codes originally developed for Voyager is a standard part of IEEE 802.11a and 802.11g WiFi, although somewhat higher Eb/N0 ratios are needed, especially at the higher speeds, to conserve bandwidth. Newer coding systems developed in the 1990s can come within fractions of a dB of the Shannon bound, and these are already appearing in operational systems.

xMax vs WiFi

I compare xMax to WiFi in greater detail here, but the published specifications for one make of 802.11g WiFi transceiver provide a useful benchmark.

As calculated above, the received signal power at the xMax receiver was -120.91 dBW or -90.91 dBm. The Ruckus Wireless 802.11g transceiver specifies a receiver sensitivity of only -96 dBm at 6 Mb/s. That's 5 dB less power for almost twice the data rate (6 Mb/s vs 3.7 Mb/s), or 7.1 dB less power for WiFi compared to xMax at the same speed. Note that this comparison does not require any estimates, while the Eb/N0 calculation above required that we estimate the noise temperature of the receiving system. This is because receiver sensitivity figures combine the effects of system noise and demodulator/decoder Eb/N0.

It is possible that the xMax demo operated with link margin, meaning that it could have worked on a weaker signal than the one used. But one can reasonably presume that if this were the case, xG would have lowered the signal level and eliminated the margin to make its demo seem more impressive. In any event, xG Technology is the one claiming to have a new and vastly more power-efficient modulation method so it is entirely up to them to prove it.

The xMax demo may impress those who haven't done the calculations and are unaware of how little power it actually takes to transmit digital data over a benign line-of-sight path. But the same demonstrated performance could have been easily achieved with just about any conventional digital modulation scheme, including an off-the-shelf WiFi transceiver, and some of these schemes already come very close to the theoretical limits.

Broadcast stations use such powerful transmitters because they cannot assume line of sight paths; large margins are required to reliably overcome obstacles, fading, reflections and interference throughout their entire service areas.

This is not to say there can't be any more big developments in digital radio communications; far from it! But they will not come as fundamental modulation breakthroughs from xG Technologies or anyone else. Opportunities still abound in frequency reuse, the basis of modern cellular phones; cooperative ad-hoc networking; improved spectrum sharing; better adaptivity to changing or hostile radio link conditions; improved interference mitigation; multiple-in, multiple-out (MIMO) antenna arrays; improvements in RF hardware that will let us make better use of the underutilized higher frequency bands, and in other ways. But not from breakthroughs in modulation, because there won't be any more.

By way of analogy, dialup modems reached their theoretical limits years ago, but Internet access speeds continue to rise thanks to cable modems, fiber deployments, radio networking, and DSL. It is foolish to try to beat fundamental physical limits when you have workable alternatives!


From my analysis it seems that xG's xMax technology is nothing special. Despite xG's implications to the contrary, no spectacular results have been demonstrated, certainly nothing that would call into question the fundamental principles of communication theory that have been firmly established for six decades. And a reading of xG's published claims and patents belie a surprising lack of awareness of these principles. Prospective investors should be very wary.

See also:

  • A review of Bobier's TriState Integer Cycle Modulation, added 16 May 2007
  • comments on MiCOM lab test of xMax, added 4 June 2007
  • comments on Prof. Stu Schwartz's evaluation of xMax added 6 June 2007
  • an analysis of xG's claims that xMax requires 3,000,000 times less power than WiFi, revised 29 June 2007
  • Prof. Ben Friedlander's blog on xMax and other wireless fantasies, added 21 June 2007
  • Comments on Patent Application 20040196910 from an engineer who wishes to remain anonymous, added 17 June 2007.
  • Phil Karn, revised 1 March 2015