xMax and waveform communications

The XG Technology web page states that “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.” While a detailed description of the “breakthrough single cycle modulation” is not available, examination of some of the related patents by J. Bobier (such as (i) “missing cycle based carrier modulation”, Patent no. 6968014, dated 11/22/05; (ii) “suppressed cycle based carrier modulation using amplitude modulation” Patent no. 6901246, Dated 5/31/05; (iii) “tri-state integer cycle modulation”, Patent no. 7003047, dated 2/21/06) is quite revealing. To understand what is revealed we need to present a bit of communication theory, so here goes.

All digital communication systems involve waveform communication, that is to say, the information to be transmitted is encoded in a set of waveforms. Let us say that you want to transmit bits. If the bit value is `0′ you transmit one waveform, and if its value is `1′ you transmit a second waveform. Different modulation techniques use different waveforms. The two waveforms may have different shapes (e.g. orthogonal modulation, FSK), or the same shape but different amplitudes and phases (QAM, PAM, PSK). At the receiver the communication signal is passed through one or more matched filters. The function of the matched filter is to reduce the noise and to discriminate between the transmitted waveforms (if they have different shapes). It is well established that in the presence of Gaussian noise, the optimal receiver (i.e. the receiver which has the best possible performance) will use matched filters.

Now here is the interesting part for our discussion. The performance of the communication system does not depend on the actual shape of the waveforms used, only on some high level properties. Specifically, their energy (power times duration), bandwidth, and the correlation or “angle” between two waveforms. For example, if you use a given waveform (for `0′) and the negative of that waveform (for `1′) we say that there is a 180 degree “angle” between the two waveforms. If you use orthogonal waveforms (e.g. two sinusoids with appropriately chosen frequencies) we say that there is a 90 degree “angle” between the two waveforms. These three parameters: energy, bandwidth and “angle”, are all we need to know about the waveforms. If you look in standard textbooks on communications, even relatively old ones such as the book by Wozencraft and Jacobs (later of Qualcomm fame) “Principles of Communication Engineering” 1965 , you find that this observation is made early in the book and the shape of the waveforms then “disappear” from further discussion. This is important because there are an infinite number of waveforms which have the same energy, bandwidth and angle, but because they all have the same receiver structure and  performance there is no need to discuss them separately.

Conventional communication systems have chosen particular sets of waveforms which were easy and cheap to implement. For example, a BPSK system uses a part of a sinusoidal waveform whose phase is 0 or 180 degress depending on the value of the transmitted bit. However, there is nothing to prevent someone from using completely different unconventional waveforms – after all there is an infinite set to select from! Of course the performance of the system which uses the new waveform will be the same as that of systems using other waveforms with the same energy, bandwidth, and “angle”.

Bobier’s patents propose a particular class of such unconventional waveforms. The different patents present variations on the basic theme of modulating a single cycle at a time, instead of a large group of cycles. How novel are these waveforms is unclear, but that is not really important here. The statements made in these patents reveal a lack of understanding of the fundamental equivalence of communication techniques which use very different waveforms with the same energy, bandwidth and “angle”. The inventor seems completely unaware that there are an infinite number of such waveforms yielding the same performance, and that he has chosen just one of them. My conjecture is that this misunderstanding has to do with the inventor’s lack of mathematical background (however, not having met or talked with the inventor this is only a conjecture). The language of mathematics is needed to abstract the problem so that one can see and understand the essential equivalence of practical engineering implementations which look very different in their details, but are just different faces of the same coin. In my consulting activities I have seen this problem more then once where otherwise creative and highly competent engineers were unable to understand important concepts which required this level of abstraction.

So what should we conclude from this about xMax? There is no reason to doubt that is uses an “unconventional” waveform (although it seems closely related to the VMSK idea) , and that it does work. At the same time there should be no doubt that its performance can not be better than that of “conventional” well established communication techniques. The claim that a new modulation technique (i.e. a new waveform or set of waveforms) can provide large performance gains is certainly false, and shows some basic misunderstanding of well known and well established principles of communications.


5 responses to “xMax and waveform communications

  1. Good article!

    Your discusson also shows why Harold Walker’s VMSK is so extremely
    power-inefficient. The VMSK ‘1’ and ‘0’ waveforms are nearly
    identical, differing only in the very center of each bit. Bobier’s
    “Missing Cycle Modulation” (MCM) has the same problem: only one RF
    cycle out of the many in each bit actually carries information. Most
    of the transmitted bit energy can’t help the receiver distinguish
    between 0’s and 1’s, so it’s simply wasted.

    So not only can’t MCM do better than conventional waveforms, it
    actually does MUCH worse. That may be why xG seems to have abandoned
    it in favor of a new “carrierless” design.

    Many modulation methods include a *little* unmodulated transmitter
    power to help the receiver find and track the incoming signal. For
    example, ATSC digital TV has a “pilot” that takes 7% of the transmitter
    power. But VMSK, MCM and other so-called “ultra narrowband” (UNB)
    techniques go completely overboard and put almost all of their power
    into an unmodulated spectral line that conveys no information. Only a
    tiny fraction of power goes into the data, which ironically is
    extremely WIDE band, not narrowband.

  2. In my post I implicitly assumed that xMax got rid of the carrier. Otherwise it will be very power inefficient. Once you take out the carrier, you are left with a waveform communication system which uses some non-standard waveform. There is nothing wrong with that. However, changing the waveform simply can not offer a performance advantage over other more conventional choices. This point seems to elude both Walker and Bobier. This is absolutely obvious if you study any of the standard texts on communication theory and have the mathematical background necessary to think of these waveforms as vectors in “waveform space”. Also the notion that you need a “special filter” at the receiver shows that they do not understand the notion of an optimal receiver, and the fact that in the presence of white Gaussian noise the optimal receiver is a matched filter. This also is explained in standard texts in communication.

  3. You are quite right — changing the waveform cannot gain an advantage over conventional techniques. But choosing the wrong waveform can make things much worse. The matched filter is always the optimum receiver for any given waveform, but it cannot overcome a poor choice of waveform.

  4. All of these techniques seem to put much trust into the wrong assumption that it’s possible to “slightly” mark the carrier to convey information. Again, I really wonder if VMSK, xG and whatelse are based on pre-Shannon comms theory :-S

  5. JimDeGries@gmail.com

    As far as I can tell they are largely based on a misunderstanding of the frequency domain representation of signals. This misunderstanding is related to a lack of good knowledge of the Fourier transform and its properties.

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