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.