A little knowledge is a dangerous thing

A reader wrote to me a rather angry message about my critical technical evaluation of xMax. He chastised me for ignoring the fact that xMax is able to reduce the received noise and interference by many orders of magnitude more than conventional systems, thanks to the Wavelet Pass Filter (WPF) which Bobier describes in several patents, especially in “Integer Cycle Event Detection using Wavelet Pass Filter System and Method“. He also pointed me to various articles such as “Going Beyond Interruptible Usage” which say:

“The Wavelet Pass Filter is the key to xMax. This device, which provides significant signal processing gain, allows the receiver to recover the weak information-bearing signal found amidst the narrowband interference and noise from legacy and neighboring users in the adjacent sidebands.”

In another article we read that:

““We’re talking about a 25 to 45 decibel advantage in an industry where 2 decibels is worth killing for,” Bobier said. “And you don’t have to throw a lot of spectrum or power at [producing a broadband signal], if you can get rid of the noise.” By virtually eliminating the typical noise floor, xMax enables the power levels for its information-bearing signal to be as much as 100,000 times below the FCC’s current regulated power limit for out-of-band emissions, which is designed to prevent systems from interfering with each other. In fact, xMax’s power levels are 10,000 times below the FCC’s power limits for ultrawideband (UWB) transmissions, according to xG officials.”

In other words, says the reader, xMax has this clever filter which virtually eliminates noise and interference. That is why it can operate with much less power. So there!

I have to confess right here and now that I did indeed ignore this claim of superior noise and interference reduction. I did so because this claim, like many other technical statements in the xMax literature and patents, is wrong and is based on ignorance of basic principles of signal processing and communications. So let me take a deep breath, get something cold to drink and maybe an aspirin or two, and try to explain briefly.

A communication system is required to detect a known signal (waveform) in the presence of thermal noise and interference. Let us ignore for the moment interference and discuss the noise. Thermal noise is known to be represented very accurately as a white Gaussian random process. The theory of detecting a known signal in white Gaussian noise is treated in standard textbooks dealing with detection or communication. The optimal detector, i.e. the detector which gives the smallest bit error rate, is known to use a matched filter whose output is used to determine whether a 0 or a 1 was transmitted. The signal-to-noise ratio (SNR) at the output of the matched filter is higher than the SNR at the output of any other filter. In other words, no other filter has a better performance than the matched filter.

Not surprisingly, all conventional communication systems use matched filters in their receivers. The only communication system I have seen which does not use a matched filter is xMax, which uses instead the WPF, which according to its description is not a matched filter. Consequently, the SNR at the output of WPF can only be worse than the corresponding SNR at the output of a matched filter. There is no doubt that the noise reduction capability of the WPF is not better, and is in fact worse than that of the matched filter used in conventional communication systems.

Next let us consider what happens in the presence of interference. Interference can be wideband or narrowband. Wideband interference acts pretty much like white Gaussian noise and therefore the matched filter is still the optimal solution. Narrowband interference has a different character and needs to be treated separately. Conventional communication systems use a variety of techniques to deal with such interference. Spread spectrum techniques (such as CDMA) convert the narrowband interference into wideband noise at the receiver, so we again can use the optimal matched filter. In multi-carrier systems such as OFDM the narrowband interference effects only one (or a few) of the frequency bins. The effect of this interference is eliminated by coding across the frequency bins. To summarize: conventional communication systems are already designed to optimally handle the effects of interference. The sub-optimal WPF offers an interference mitigation capability which is inferior to that of filters used in modern communication systems.

To conclude: the claim that the WPF can somehow reduce noise and interference more than the reduction which takes place in existing highly optimized communication systems is  false. Any competent communication engineer should recognize this claim as making no technical sense.

I really wish that the author of the WPF patents would have taken a few basic courses in signals and systems, analog/digital signal processing, and communications. Or at the very least, that he would talk and listen to some people who do have this knowledge. This would have saved me a lot of typing. A little knowledge is indeed a dangerous thing.

As a side comment, the patent “Integer Cycle Event Detection using Wavelet Pass Filter System and Method” which describes the WPF in excruciating detail reveals a lack of knowledge of well known filter design techniques. This long document has numerous technical mis-statements whose description would require a separate post.

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3 responses to “A little knowledge is a dangerous thing

  1. I read your article with interest because a lot of the things surrounding the Xg company and technology are highly suspicious. However, your article was weak, inconclusive and does not provide evidence that xMax doesn’t work. It merely showed that it does not follow the conventional wisdom. Xg have not convinced me that it works, but you have not convinced me that it doesn’t. I suppose the proof will be in real life implementations.

  2. JimDeGries@gmail.com

    The “conventional wisdom” on which I based my comments is the well developed theory of signals and systems, filter design, and digital communication. This is standard material taught to electrical engineering students. This knowledge can be applied to analyze and evaluate the performance of any communication system, including xMax. In any case, if you read my post you should know that I never said that xMax does not work. I consistently said the opposite: it should work, but its performance can not be better than that of existing communication techniques. Therefore the performance claims made about xMax are entirely false. This can be established conclusively without waiting for the xMax deployment, by any competent communication engineer who analyzes the patents and the publicly available information.

  3. Paul, it’s important to understand that much of the “conventional wisdom” in communications consists of mathematical theorems. The Shannon Channel Capacity Theorem is the most famous, but there are many more: the matched filter theorem, the Fourier transforms, etc.

    Unlike a theory in physics, which is always subject in principle to being overturned or modified by additional empirical data, a mathematical theorem remains true forever as long as its assumptions are valid. And the assumptions underlying the Shannon theorem are *very* broad and general.

    The mathematics of communication make it very clear that xMax cannot provide the “vast” reductions in power that were originally claimed. The BER-vs-Eb/N0 curve only confirms that xMax is no better than conventional techniques. There is simply no need to wait to make this conclusion.

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