I have received quite a few responses from readers saying something to the effect: “just wait until XG Technology deploys their VOIP network, and that will prove their claims once and for all”. I guess these readers have completely missed the point I was trying to make. So let me try one more time.

All of my xMax related posts addressed a single fundamental issue: the claim that *xMax can operate using far less transmit power than conventional communication systems.* (Based on the published claims “far less” means orders of magnitude less, not “a little bit less”). This is a crucial claim, because it it were true (which it isn’t), xMax would have a much larger range than a conventional system if they both used the same power, or it could operate with far less power in the same range. All of my xMax related posting were aimed at explaining why this one specific claim is false.

The fact that this claim is false does not mean that it is not possible to deploy an xMax based VOIP network. It only means that one could use a conventional physical layer to do the same deployment, and that an xMax physical layer does not offer an advantage. Thus, a deployment of xMax does not prove the claim that “xMax can operate using far less transmit power than conventional communication systems”. It only proves that xMax works, which I have no reason to doubt, and said so repeatedly. So do many other conventional communication systems! Unless one performs a careful one-to-one comparison of xMax with another system, the mere fact that xMax is deployed has little if any bearing on the validity of the claim.

There are simple, direct, and conclusive ways to prove or falsify the xMax claim, and I have discussed this in the earlier post “xMax performance claims can be easily tested. Why aren’t they?”. All that is needed is to have an independent entity measure the BER vs. EbN0 curve for xMax and publish it on the xG website ….

To conclude: Yes – xMax works, and if they did a good job implementing the overall system, they should be able to deploy it. No – xMax can not and will not “operate using far less transmit power than conventional communication systems.”

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I wish to address the above remarks about xMax transmitted power levels being “far less” than conventional levels. In fact, they are. Here’s why:

Remember that xMax receivers don’t require data bits that are thousands or hundreds of thousands of carrier cycle periods in duration, (nt). Only one r.f. cycle is needed to define an xMax data bit; (n = 1).

Power is energy expended per second. Given equal field strengths, data rates and carrier frequencies, an xMax signal will thus consume (n) times less power than the conventional signal.

David

Unfortunately what you are saying is simply wrong. It is certainly true that if you use a single cycle instead of all n cycles your average power is reduced by a factor of n. But that is not the point. You need to compare the power required to give the same

performancein the two cases.The performance of a digital communication receiver depends on the

energyper bit, not thepower.This is why Eb/N0 plays such a key role in determining the performance of a communication systems, where Eb is theenergy per bit. Thus, if you compare two communication systems: one which uses a waveform consisting of a single cycle and one which uses a waveform consisting of n cycles, then the two waveforms must have the same energy to get the same bit-error-rate (BER). What that means is that the first system will require a peak power which isn times largerthan that of the second system to give equal performance. If instead of peak power you look at average power, the average power must be thesamein order to get the same performance (BER).The story which Bobier and company repeatedly tell about somehow saving power by using a single cycle is based on a fundamental and persistent misunderstanding of how digital communication systems work. Please see my post on “xMax and waveform communication” which addresses this issue. Bobier’s patents show yet another fundamental misunderstanding related to the Fourier transform of single cycle signals, but that is a topic for a separate discussion.

Jim

Perhaps the following will clear any misunderstanding.

All noise in the universe is CW in nature, whther manmade or natural. In the xMax system, all such CW noise is rejected or filtered out. This is not taken into account in the Eb/No ratio and, further, to my knowledge at least, no one had tested performance of such a single-cycle comm system until xMax appeared.

In such testing, my 15 July observation about average power held true. As long as the peak “power” (energy) of an xMax cycle equals that of each cycle in a conventional system, performances are indistinguishable.

The result is as I stated: xMax energy per second (power) can be reduced by the (n) factor without degradation of recovered intelligence.

David

Again, I am sorry, but you seem to be harboring some misconception. Regarding CW, which stands for continuous wave, this is an electromagnetic wave of constant amplitude and frequency. Thermal noise is very definitely not CW. It is wideband and you can think of it as consisting of an infinite number of sinusoids with random frequencies, amplitudes and phases. The notion that thermal noise can be rejected or filtered out completely by a “clever” filter is nonsense. How much noise is left at the output of a linear filter is very well understood. This is usually taught in an undergraduate course on “random signals and systems”. Bobier’s claim that his Wavelet Pass Filter somehow eliminates noise is based on a lack of knowledge of basic facts about the nature of receiver noise and the effect of linear time-invariant filtering.

Regarding your comment “As long as the peak “power” (energy) of an xMax cycle equals that of each cycle in a conventional system, performances are indistinguishable” – I am sorry, but this is simply wrong. Performance depends on Eb/N0, where Eb is energy (not power), and where N0 is noise power spectral density, which is the same for xMax as for anyone else on the planet.

Jim

You delve into semantics. Of course thermal noise is as you describe. But isn’t it easier to say “CW” than to say “an infinite number of sinusoids with random frequencies, amplitudes and phases”? In other words, each of those infinite number is CW in nature if it persists longer than some arbitrary but agreed upon time interval. In the present context, that interval almost certainly is always much greater than one cycle’s period.

Aside from this, I stand behind my statements regarding noise. “How much noise is left at the output of a linear filter is very well understood” is right but only if a linear filter is used.

xMax development required a deeply fundamental and rigorous retraining of thought processes. Time and again conventional thinking ensnared xMax developers. I urge you to envision the difficulties overcome.

Newtonian mechanics can be developed from Relativity but the reverse is not true.

I now beg off further participation in this blog. It’s too energy intensive. Perhaps the advice I’ve seen others give you is best. Just wait a bit and see for yourself. Going too far out on a limb can be an embarrassing undertaking.

David.

Dave, maybe this can help. Noise is unpredictable by nature. We can measure its statistics such as average power per unit bandwidth, but when you sample it you get completely random numbers. If noise wasn’t random, then it would be easy to subtract from the signal and our problems would be over.

Data is also unpredictable; if we know in advance what the sender is going to say, then there’s no need to send it!

So the unpredictable signal must compete with the unpredictable noise. If the signal isn’t strong enough, there’s just no way to know if we’re seeing a real message or just an unlucky bit of noise masquerading as one. It doesn’t matter how smart you are or how much computer power you have; you just can’t extract information that’s not there.

In 1948, Claude Shannon figured out just how much noise a signal can tolerate before it becomes impossible, even in theory, to reliably recover its information. He found an absolute limit to how many bits/sec you can reliably send with a given power, bandwidth and noise level. That’s the famous Shannon Limit, and for infinite bandwidth it is an Eb/N0 ratio equal to the natural logarithm of 2, or -1.6 decibels. Lots of smart people have gone over Shannon’s proof and a few gave proofs of their own with the same result as Shannon.

It’s important to understand that this is a mathematical proof, not a physical theory, so there is NO chance that the Shannon limit will ever be overcome with faster computers or more clever modulation or coding schemes. If you’re at capacity and it’s not fast enough, you have no choice but to change to one with a higher Shannon limit.