Jerry Avins wrote:
> Vladimir Vassilevsky wrote: >> >> >> John Hadstate wrote: >> >>> On Jun 3, 8:41 pm, Steve Underwood <ste...@dis.org> wrote: >>> >> >>>> You are throwing away information about the noise. How will that allow >>>> you to track through the noise in an optimal way? That has to be a loss >>>> over a scheme which leaves the noise intact, and tracks through it. >>>> >>> >>> >>> Excuse me. Are you a complete idiot? >>> By definition, noise carries no information. >>> What, exactly, is your problem? >> >> No, the idiot is not Steve. >> >> (S + N)^2 = S^2 + 2xSxN + N^2 >> ^^^ ^^^^^^^^^^^ >> Signal Noise > > The cross term disappears for orthogonal signals. Noise is usually > orthogonal to everything else. Powers add, not voltages.
An orthogonal signal will not affect the signal of interest. For example, the orthogonal sine and cos terms of a QPSK signal have no effect on each other, unless some signal degradation blurs them. Noise is uncorrelated with the signal of interest, but it is not orthogonal to it. If it were, the size of the noise would have no impact on our ability to see the signal. We would be able to recover the signal buried in any amount of noise.
>> (S + N)^4 = S^4 + 4xS^3xN + 4xN^3xS + 6xS^2xN^2 + N^4 >> ^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >> Signal Noise
Regards, Steve
> > > John Hadstate wrote: > >> On Jun 3, 8:41 pm, Steve Underwood <ste...@dis.org> wrote: >> > >>> You are throwing away information about the noise. How will that allow >>> you to track through the noise in an optimal way? That has to be a loss >>> over a scheme which leaves the noise intact, and tracks through it. >>> >> >> >> Excuse me. Are you a complete idiot? >> By definition, noise carries no information. >> What, exactly, is your problem? > > No, the idiot is not Steve. > > (S + N)^2 = S^2 + 2xSxN + N^2 > ^^^ ^^^^^^^^^^^ > Signal Noise
The cross term disappears for orthogonal signals. Noise is usually orthogonal to everything else. Powers add, not voltages.
> (S + N)^4 = S^4 + 4xS^3xN + 4xN^3xS + 6xS^2xN^2 + N^4 > ^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ > Signal Noise
Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
On Jun 4, 12:12&#2013266080;pm, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
wrote:
> John Hadstate wrote: > > On Jun 3, 8:41 pm, Steve Underwood <ste...@dis.org> wrote: > > >>You are throwing away information about the noise. How will that allow > >>you to track through the noise in an optimal way? That has to be a loss > >>over a scheme which leaves the noise intact, and tracks through it. > > > Excuse me. &#2013266080;Are you a complete idiot? > > By definition, noise carries no information. > > What, exactly, is your problem? > > No, the idiot is not Steve. > > (S + N)^2 = S^2 &#2013266080; + 2xSxN + N^2 > &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080;^^^ &#2013266080; &#2013266080; ^^^^^^^^^^^ > &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; Signal &#2013266080; &#2013266080;Noise > > (S + N)^4 = S^4 + 4xS^3xN + 4xN^3xS + 6xS^2xN^2 + N^4 > &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080;^^^^ &#2013266080;^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ > &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080; &#2013266080;Signal &#2013266080; &#2013266080;Noise >
??? There is no dispute that squaring, etc. throws away noise (in the sense that it can't be exactly recovered through an inverse process). So what is your point with the above equations? The noise is there, but scattered around in sidebands of the original signal. This is a good thing. I am not squaring the squared signal to produce a fourth- power signal. I am squaring a filtered squared signal to produce a fourth-power signal that is then filtered again. Thus, your equations don't represent what is really going on in the front-end of my loop anyway. I suggest you break out the spectrum analyzer and look for yourself.
On Jun 4, 11:32&#2013266080;am, Eric Jacobsen <eric.jacob...@ieee.org> wrote:
> On Wed, 4 Jun 2008 08:09:26 -0700 (PDT), John Hadstate > > <jh113...@hotmail.com> wrote:
> >By definition, noise carries no information. > > >What, exactly, is your problem? > > I think his problem may be that he actually attempted to help you with > something. &#2013266080; You tend to make that difficult for people. >
I suspect we have a difference of opinion over whether he or you or VV were actually trying to help anyone. It sounded a lot more like "grandstanding" than an offer to help. If you recall, I gave up looking for help on this subject weeks (months?) ago when it was obviously not forthcoming from you or anyone else. (VV, to his credit, did offer a couple of keywords that led me down a different search path and did eventually yield useful information.) My post regarding my QPSK demodulator algorithm was not in the nature of a request for help. It merely documented a procedure that I found that works to solve a moderately difficult problem.

> On Jun 3, 8:41 pm, Steve Underwood <ste...@dis.org> wrote: >
>>You are throwing away information about the noise. How will that allow >>you to track through the noise in an optimal way? That has to be a loss >>over a scheme which leaves the noise intact, and tracks through it. >> > > > Excuse me. Are you a complete idiot? > By definition, noise carries no information. > What, exactly, is your problem?
No, the idiot is not Steve. (S + N)^2 = S^2 + 2xSxN + N^2 ^^^ ^^^^^^^^^^^ Signal Noise (S + N)^4 = S^4 + 4xS^3xN + 4xN^3xS + 6xS^2xN^2 + N^4 ^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Signal Noise Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
On Jun 4, 11:30&#2013266080;am, Eric Jacobsen <eric.jacob...@ieee.org> wrote:
> On Wed, 4 Jun 2008 08:17:15 -0700 (PDT), John Hadstate > > > <jh113...@hotmail.com> wrote: > >Yes, I've no doubt that you can. &#2013266080;The point is that I don't need any > >"added tricks". &#2013266080;My implentation locks-up and tracks in a very > >straightforward way, just as predicted by theory, and in an > >environment with a really crappy S/N ratio that is subject to all > >kinds of operator errors. > > I think what you've described constitutes a lot more "added tricks", > and added implementation expense as well, than what I was talking > about.
"A lot more added tricks?" If you compare the block diagram of my implementation with that of a Costas Loop, you won't find a lot more blocks, and quite a few of the blocks are identical. Implementation expense? We are both talking about software, right? Tell me about implementation expense in a software package, please. If I had found this method in the first place, I could have saved some development time, but at least I learned about a half-dozen or so "conventional" approaches that are too brittle for my application. My software doesn't have the luxury of a nice static environment where all the signal parameters are known in advance and you have nice long training sequences to lock up on. If it did, we'd cast it in NAND gates and forget about it.
> > And have you tested it at low SNR yet? &#2013266080; Or with modulations higher > than QPSK?
I have no need to generalize to solutions above 4PSK (and I wouldn't suggest this approach for doing so). The lowest SNR I tested in development was on a recording of a signal that showed a time-varying (S+N)/N from about 3 to about 10 dB. with fractional percentages of variation in the carrier frequency (carrier frequencies were in the low audio range). By the way, just before I left for work this morning, I uncovered one of the PDFs that I used as a reference while hatching this scheme. The PDF describes "my" scheme almost perfectly, the main difference being that they used a complicated system of switches to accomodate both BPSK and QPSK, as well as some other modulation types. So much for novelty!
On Wed, 4 Jun 2008 08:09:26 -0700 (PDT), John Hadstate
<jh113355@hotmail.com> wrote:

>On Jun 3, 8:41&#2013266080;pm, Steve Underwood <ste...@dis.org> wrote: >> John E. Hadstate wrote: >> >> > "Steve Underwood" <ste...@dis.org> wrote in message >> >news:g221qr\$773\$1@nnews.pacific.net.hk... >> >> Eric Jacobsen wrote: >> >>> Are you suggesting the 4th order nonlinearity is not less resistant to >> >>> noise or distortion or multipath, etc.? &#2013266080; Usually that's the achilles >> >>> heel of such an approach, so if you have evidence otherwise it'd be >> >>> very interesting to see. &#2013266080; Performing the phase unwrap as you just >> >>> described when the reference is noisy (due to the nonlinearities) >> >>> would be expected to degrade in noise or distortion. >> >> >> I'd make a more general point. Squaring throws away information. Its a >> >> non-reversible operation, so it has to throw information every time it >> >> is used. Are you really really sure that lost information is of no >> >> consequence downstream in the processing? If not, it might not be a >> >> good idea to be so cavalier with it. >> >> > The information is only being thrown away in the part of the system >> > where it interferes with the lock-up needed to regenerate the carrier. &#2013266080; >> > The incoming signal goes to two places: to the two squaring blocks and >> > filters that lead to the product mixer for the 4x PLL, and to the 1x >> > product mixer that eventually results in the demodulation of the dibits. >> >> > And yes, I'm very sure that the lost information is not only not needed, >> > it's not wanted. &#2013266080;The end result of all this is that the 4x PLL has a >> > much wider pull-in range in the presence of noise than does the Costas >> > Loop, it locks up quicker (given the proper choice of time constants and >> > gain) and it holds-in better. &#2013266080;But don't take my word for it. &#2013266080;Try it >> > for yourself. >> >> You are throwing away information about the noise. How will that allow >> you to track through the noise in an optimal way? That has to be a loss >> over a scheme which leaves the noise intact, and tracks through it. >> > >Excuse me. Are you a complete idiot? > >By definition, noise carries no information. > >What, exactly, is your problem?
I think his problem may be that he actually attempted to help you with something. You tend to make that difficult for people. Leaving the noise "intact" is better than amplifying it, which is what the nonlinearities essentially do. Eric Jacobsen Minister of Algorithms Abineau Communications http://www.ericjacobsen.org Blog: http://www.dsprelated.com/blogs-1/hf/Eric_Jacobsen.php