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#: 73521 S17/TAPR NNC/DSP 07-Apr-88 16:43:49 Sb: #73502-#HF Modems, Part 2 Fm: Barry McLarnon VE3JF 71470,3651 To: Phil Karn, KA9Q 73210,1526 (X) Developing a realistic software model of the HF channel is a toughie... I know guys who worked on it for years. Even though there are plenty of guidelines available on what parameters to use, the models always have shortcomings, like leaving out impulsive noise and interference. There's just no substitute for on-the-air testing, although we do have a black box in our lab where I work that comes fairly close. It's a DSP tapped delay line channel simulator in which the tap weights can be set dynamically according to a measurement of the time-varying impulse response of an actual channel. The measurement is done by transmitting a pseudorandom probe signal over an HF link and recording the received signal on an instrumentation recorder. The recorder then can be played back into the simulator, which analyzes the signal and sets its tap weights to reproduce the impulse response in the path of the modem signal under test. This does a nice job of reproducing the fading and multipath under repeatable conditions for comparative tests, but it doesn't reproduce the non-Gaussian noise and QRM. The nice thing about DSP modems is that we can try a few different approaches on the air without messing with a bunch of different hardware. Re framing structures for HF: we definitely see eye-to-eye on this one. Dump HDLC and adopt a robust frame sync strategy? Right On! We should have a selective-repeat ARQ datalink protocol too. The new framing structure will allow us to use coding and signal processing to drag those packets out of the noise. For more food for thought, dig up the following article: D. Chase, "Code combining - a maximum-likelihood decoding approach for combining an arbitrary number of noisy packets", IEEE Trans. Commun., vol. COM-33, p. 385, May 1985. I see Franklin also mentioned Chase - he is the guru of soft-decision decoding of block codes. Franklin, are you at liberty to disclose some details of the work you did in this area? 73, Barry *** There are replies: 73531, 73600 *** More *** #: 73531 S17/TAPR NNC/DSP 07-Apr-88 23:21:33 Sb: #73521-HF Modems, Part 2 Fm: Franklin Antonio, N6NKF 76337,1365 To: Barry McLarnon VE3JF 71470,3651 (X) Your question strikes at the heart of the issue i've been struggling with for the past few months. An awful lot of the work i've done in this area has been done for, well i guess i should call it "work". If work and hobby were less related, i'd be having a much easier time with these issues. I have to figure this out for myself. I would imagine you may have some of the same conflicts? How do you deal with it? Re Chase / Golay, etc... Two years ago, i wrote a chase-algorithm [24,12] Golay decoder routine. I did it as part of "work", and as a result, cannot make it available to the amateur effort. Seems a shame at one level, but of course i cannot violate the trust of my co-workers. Whole reason i gotgot interested in ham radio again a couple of years ago was to do technical stuff like this, and now i find it difficult because of its similarity to work. Sigh. *** More *** #: 73600 S17/TAPR NNC/DSP 09-Apr-88 10:17:27 Sb: #73521-HF Modems, Part 2 Fm: David Toth VE3GYQ 72255,152 To: Barry McLarnon VE3JF 71470,3651 (X) I have a test model ready to go whenever you guys want. It's called the HF Packet Network, and we can get ALL the guys to test the code (20+ stations per freq x 2 frequencies i.e. 14.109 and 10.149) ... I know it is not as convenient as a simulation, but it is real and can be controlled. Just a useless offer <grin> Dave *** More *** #: 73533 S17/TAPR NNC/DSP 07-Apr-88 23:30:33 Sb: Queries Fm: Franklin Antonio, N6NKF 76337,1365 To: Lyle Johnson, WA7GXD 76246,565 (X) I received the promised return phone call from Beth Harwood of Analog Devices today. She claims to have checked with engineering re possible effects of clocking the 7569 at 6.25 MHz. The answer is that "it won't work" "it will miss codes" "it will probably work ok at 5.5 MHz". I thanked her for the return call, but did not inquire further. Her number is: 617-935-5565 X-2628. On related issue... seems there are new cmos A/D & D/A announcements every day. Just saw in ECN announcement from Linear Technology for LTC1092. 10 bit A/D, with sample & hold. 8-pin dip. Serial interface (yuk). 20uS conversion time, $10.15 in 100 quantity. Good news is it's >8 bits for reasonable price and small board area. But, gee... serial interface? I'm not pushing this chip.. i just saw the blurb & thought i'd pass it on. #: 73538 S17/TAPR NNC/DSP 08-Apr-88 01:11:21 Sb: AD7569 Fm: Lyle Johnson, WA7GXD 76246,565 To: Franklin Antonio Franklin, Well, I'll plan on letting it self-clock then using its internal oscillator. The down side is the "jitter" we'll see in conversion times, especially if we let the end of conversion trigger the D/A load (which we therefore won't!). I appreciate the information. I gave Dan and Eric and Chuck the last 150k or so from here and expect some feedback from them soon. Onward! Lyle #: 73607 S17/TAPR NNC/DSP 09-Apr-88 11:44:10 Sb: TMP320C15 Fm: Lyle Johnson, WA7GXD 76246,565 To: Tom Clark Tom, I gave Cris the TMP320C15 processor yesterday. She should have sent it out, so you will probably receive it by the middle of next week. I have no way of checking to see if it will work at 25 MHz or not, so... I also note that the old GI (I think they call themselves MicroSemi now) just announced a 32 MHz version of the 320C10. If we can get by without the additional memory of the '15, we can drop our cycle times to 125 nSec rather than 160 nSec and save a few dollars in the process. I suspect the memory is more valuable than the speed, but thought I'd mention it. Lyle #: 73617 S17/TAPR NNC/DSP 09-Apr-88 16:09:13 Sb: #73050-HF Modems Fm: Franklin Antonio, N6NKF 76337,1365 To: Barry McLarnon VE3JF 71470,3651 (X) Barry, i saw some comments go by a while back re peak-to-average power ratio for sum of sinusoids. Seem to remember it was a msg from you to Tom C. The msg must have scrolled off the end of the universe, as i cannot find it now. Seem to remember that you gave a formula. Is this in the literature anyplace? If not, could you repeat the formula? #: 73689 S17/TAPR NNC/DSP 11-Apr-88 01:09:37 Sb: #73561-Dayton Hotel Fm: Tom Clark W3IWI 71260,3640 To: Franklin Antonio, N6NKF 76337,1365 I've been trying to follow the heuristic discussions on the HF schemes and I'm getting a bit confused in the terminology. My problem is that I come from a different signal processing world (radio astronomy, replete with its own jargon pertaining mainly to signals that >>ARE<< noise, plus SETI). I have a modest proposal for those of us who have some ideas, but feel we are saying the same thing with a biorthogonal set of semantics (perhaps even from a parallel universe!). Bob M, Phil K, Franklin A, and Tom C will be at Dayton. Barry M >>>SHOULD<<< come (I'll twist his pointy little head if he doesn't, & I know Dr. Death has offered him a ride). Therefore, whatsay we plan to get together for a few hours and discuss the ideas INCLUDING defining each of our own set of terminology! ;-) 73, Tom #: 73690 S17/TAPR NNC/DSP 11-Apr-88 01:09:51 Sb: #73607-TMP320C15 Fm: Tom Clark W3IWI 71260,3640 To: Lyle Johnson, WA7GXD 76246,565 (X) Thanks Lyle. I'll look forward to seeing it. FYI -- for the 'travelling circus' at Dayton I'll be bringing an XT clone (the old Mitsubishi that ran the IWI BBS for a couple of years). I have access (from work) to one of the new transmission LCD devices that allows a CGA screen (in monochrome) to be displayed with a viewgraf machine. That way the entire audience can really see the screen (for a change). [Phil -- how do you want to demo NET? that machine could either be used on a SLIP link or I could drop an ethernet board into it]. #: 73693 S17/TAPR NNC/DSP 11-Apr-88 01:10:17 Sb: Meese Fm: Tom Clark W3IWI 71260,3640 To: N6NKF Franklin -- tried to run your spectrum code at home where I have a VGA video (running EGA mode) plus a Mouse Systems serial mouse. The mouse is installed with the driver that is supposed to make it look like a Microsoft mouse. It doesn't work. No cursor appears, I can't move up & down the scroll bar. Pressing the buttons does non-reproducable things. What am I doing wrong? 73, Tom #: 73699 S17/TAPR NNC/DSP 11-Apr-88 10:11:52 Sb: #73531-HF Modems, Part 2 Fm: Barry McLarnon VE3JF 71470,3651 To: Franklin Antonio, N6NKF 76337,1365 It is a big problem, and I'm sure Bob and some of the others are wrestling with it as well. I guess, as you say, everyone has to work this out for himself... in other words, apply "situation ethics". My current situation is not too bad, as I work for a gov't research lab on unclassified projects, and much of our work becomes freely available in the open literature. On the other hand, we also transfer technology to private industry for commercial exploitation, so the material transferred becomes proprietary in those instances. I'd like to think there is a fine line we can walk, where we can make use of some of the "intellectual property" we've acquired from the work side, in the hobby side, without overstepping the bounds by using the details of actual implementations. When in doubt, I probably err on the side of the hobby... :-) *** More *** #: 73700 S17/TAPR NNC/DSP 11-Apr-88 10:12:25 Sb: #73617-HF Modems Fm: Barry McLarnon VE3JF 71470,3651 To: Franklin Antonio, N6NKF 76337,1365 I'll do better than that... I'll dust off that message and ship you a copy in its entirety. I've been archiving all of the DSP discussions here since about the beginning of February. It's now up to about 300K of text! A few more points that I left out of the original posting: - There is a perfectly good term for peak-to-average ratio which we should make use of, namely crest factor (no puns about preventing cavities, please!) - Since we are normally comparing multitone formats to a single tone, which itself has a 3 dB crest factor, we should subtract 3 dB from the multitone figures to get to get the true relative rating. - The reference for the data on crest factors of phase-controlled multitone signals is: S. Boyd, "Multitone signals with low crest factor", IEEE Trans. Circuits Syst., Vol. CAS-33, Oct. 1986, pp. 1018-1022. *** More *** #: 73701 S17/TAPR NNC/DSP 11-Apr-88 10:13:22 Sb: #73617-HF Modems Fm: Barry McLarnon VE3JF 71470,3651 To: Franklin Antonio, N6NKF 76337,1365 Tom, things aren't quite as bad as they seem, and we should not abandon all hope of using multitone modems. Here's why: Your estimate of the PAR is a little on the high side. When N equal-amplitude sinusoids are added together, the PAR of the resulting signal is nominally equal to 20*log[SQRT(2N)]. For N = 16, this works out to about 15 dB, and for N = 32, it is about 18 dB (I am ignoring for the moment, the varying number of simultaneous tones if OOK is used). Also: up to a point, you can clip the peaks of the waveform (before applying it to the SSB modulator) without doing any harm. The limit is reached when the "self-noise" from intermod products start to have a significant effect on the bit error rates. Commercial 16-tone modem systems are typically run at 3 to 5 dB higher average power than that dictated by the PAR. Here's an interesting footnote: The reason I referred to the PAR above as nominal is that it can be reduced if we put some constraints on the sinusoids. The first constraint is that the tone frequencies be equally spaced, which we want anyway. Now if we control the phases of the tones (easy with DSP!), we can reduce the PAR quite dramatically. The absolute worst choice is to start them all in phase - then we get no improvement at all. However, with the proper choice of just two different phases, 0 and pi, for each tone, the PAR can be made MUCH lower. For N = 32, the PAR can be reduced to 6 dB. And there is an even better algorithm that requires a different phase shift for each tone (which can be stored in a look-up table). It results in a PAR of 4.6 dB (!) for N = 32, and the PAR is <6 dB for ALL N. For large N, it produces a near-constant-envelope signal that bears a striking resemblance to a swept tone. The bad news is, if we start phase- or amplitude modulating the tones, we upset the applecart and the PAR starts heading back up. Everything is fine as long as we don't try and transmit any information! :-) 73, Barry #: 73713 S17/TAPR NNC/DSP 11-Apr-88 12:01:27 Sb: #73700-HF Modems Fm: Franklin Antonio, N6NKF 76337,1365 To: Barry McLarnon VE3JF 71470,3651 (X) Crest factor? Never heard of it. I think i've been computing the Colgate factor. I tend to think of signals in the two-dimensional model, and look at the length of the resulting vector. When it stays on the unit circle, as it does with a single tone, then peak=avg, and i call that a peak/avg ratio of 0db. I'll go look up that paper immediately. *** More *** #: 73731 S17/TAPR NNC/DSP 12-Apr-88 00:01:29 Sb: #73700-HF Modems Fm: Tom Clark W3IWI 71260,3640 To: Barry McLarnon VE3JF 71470,3651 (X) Barry -- pull me off a copy of the collected annals of DSPdom too for inclusion with the distribution disks Bob & I send out. On the next disks I hope to also have Phil's 'sounds' but I have to do some archive splitting. He FTPd me one 900kbyte long .ARC file! But some of the 'sounds' he included are either scatalogical or X-rated and probably shouldn't be circulated ;-) *** More *** #: 73740 S17/TAPR NNC/DSP 12-Apr-88 03:21:56 Sb: #73700-HF Modems Fm: Franklin Antonio, N6NKF 76337,1365 To: Barry McLarnon VE3JF 71470,3651 (X) I picked up a copy of the Boyd article, and the Ouderaa, Schoukens, Renneboog comments (Sept '87 IEEE-CAS). Now i see that your definition of "crest factor" is just 3db greater than my "peak/avg power". This article blew me away. The Shapiro-Rudin sequences are amazing. Just don't look like they'll do the trick, do they? Nonituitive. Problem is, i'm not clear on how to apply this to our benefit. They provide phases which will produce a reasonable crest factor IF YOU WANT ALL THE EQUALLY SPACED TONES IN SOME BAND. We want N out of M tones in some band. So suppose we have possible tones (evenly spaced) numbered 0, 1, 2, 3, 4, 5, 6, 7, 8. Now i want only tones 1, 3, 7 turned on. What are the correct phases of these three tones for low crest factor? Can i get the answer out of this paper? *** More *** #: 73732 S17/TAPR NNC/DSP 12-Apr-88 00:01:42 Sb: #73701-HF Modems Fm: Tom Clark W3IWI 71260,3640 To: Barry McLarnon VE3JF 71470,3651 (X) Thanks for the comments Barry. I have been meaning to do a simulation of multi-tone schemes with different spacings and initial phases. Franklin's Crest/Colgate comment hilights one of the reasons I think it would be splendid if we could meet in Dayton for discussons of orthogonal polynomials and related topics. Can you come? #: 73714 S17/TAPR NNC/DSP 11-Apr-88 12:04:55 Sb: #73699-HF Modems, Part 2 Fm: Franklin Antonio, N6NKF 76337,1365 To: Barry McLarnon VE3JF 71470,3651 (X) You say you've been archiving the DSP section? Paul Williamson, KB5MU, asked me whether an archive was available, and i didn't know the answer. Paul was admitted to the section a few days ago, and wanted to catch up on ancient history. Listening Paul? #: 73742 S17/TAPR NNC/DSP 12-Apr-88 04:33:03 Sb: #73689-Dayton Hotel Fm: Phil Karn, KA9Q 73210,1526 To: Tom Clark W3IWI 71260,3640 Yes! I think a late-nite bull session at Dayton, ideally in Tom Clark's hotel room, would be a perfect way to get the creative DSP juices flowing. Tom can provide the liquid stimulants as he always does. :-) Tom -- re TCP/IP demo -- I'll have my NEC laptop, and that also has a CGA spigot. A direct SLIP connection between two machines is sufficient to demonstrate the end-to-end capabilities, which are the important part. But the more machines, the merrier. It'll be fun to try the LCD projection display, I've been trying to find one of those for some time. I suspect, but do not actually know, that the Atlanta gang will be demoing tcp/ip on top of their 56kbps modems. They did that last year with a pair of full-blown ATs. Phil *** More *** #: 73750 S17/TAPR NNC/DSP 12-Apr-88 10:01:41 Sb: #73689-Dayton Hotel Fm: Barry McLarnon VE3JF 71470,3651 To: Tom Clark W3IWI 71260,3640 Ouch! Alright, already, I'll come... but I may have to get you to explain to my wife why this is so important (keeping the Free World safe from bit errors, etc... ?). :-) Barry #: 73765 S17/TAPR NNC/DSP 12-Apr-88 15:06:30 Sb: #73731-HF Modems Fm: Barry McLarnon VE3JF 71470,3651 To: Tom Clark W3IWI 71260,3640 OK, I'll bring several copies of the DSP Chronicles with me to Dayton for distribution to the folks on the team. Barry *** More *** #: 73766 S17/TAPR NNC/DSP 12-Apr-88 15:07:29 Sb: #73740-HF Modems Fm: Barry McLarnon VE3JF 71470,3651 To: Franklin Antonio, N6NKF 76337,1365 Fascinating, isn't it? Whether it's useful is quite another matter. Thanks for finding that follow-up letter, which I hadn't come across. I was particularly taken with 32-tone Newman signal, which resembles a swept tone. This suggests a different approach to minimizing crest factor, namely, start with a constant-envelope (or nearly so, at least) signal that has an approximately flat magnitude spectrum over the bandwidth of interest. In this case, it is a chirp (linear FM) signal. Then do a complex DFT on the signal, with the sample rate corresponding to the desired tone spacing. Then we can use tones to synthesize a signal resembling the constant-envelope signal we started with by setting the tone amplitudes to be all the same, and using the phases that we derived from the DFT. Getting back to your question re whether we can use the results of this paper to minimize the crest factor for a subset of the tones, I think the answer clearly is NO. Anything we do to modulate information onto the ensemble of tones, whether it be selecting n-of-m, OOK, FSK, PSK, or what have you, will violate the constraints and cause the crest factor to increase. In a sense, we have used up all the available degrees of freedom in order to minimize the crest factor, and have none left over to transmit information with! When the tones are not equally spaced, as in the n-of-m or multitone OOK schemes we've been talking about, I think we would have to resort to a computer search for the optimum phases of the component tones for EACH POSSIBLE SYMBOL. Once found, they can be stored in a lookup table which is referenced by the DSP modulator. This seems workable for a 300 bps/50 baud modem with 64 possible symbols, but gets unwieldy when you think about higher bit rates (which, of course, is exactly where we need it most). A colleague of mine has done some work on using the steepest descent algorithm to minimize crest factors when the tones are not equally spaced (S. Shlien, "Minimization of the peak amplitude of a waveform", Signal Processing, Vol.14, No.1, Jan. 1988). #: 73841 S17/TAPR NNC/DSP 14-Apr-88 19:30:11 Sb: #Crest Factor Invariance? Fm: Franklin Antonio, N6NKF 76337,1365 To: Barry McLarnon 71470,3651 (X) You make a waveform and push it in the audio input of an SSB rig, then it gets frequency shifted to HF, and goes to a power amplifer. We are concerned with the crest factor of the waveform as it hits the PA. This will be the same as the crest factor of the waveform we put in the audio input if crest factor is invariant under frequency shift. Is it? I haven't found a theoretical argument one way or the other, but here are some calculations... peak rms S(1) + S(2) + S(3) 2.50 1.225 S(2) + S(3) + S(4) 2.75 1.225 S(5) + S(6) + S(7) 2.95 1.225 where, S(f) = Sin(2pi*f*t), t in the interval [0,1]. So, S(1)+S(2)+S(3) would appear to change its crest factor when frequency shifted. Check out my calculations here; i could be fouled up. If crest factor is not invariant under frequency shift, then i'm not sure we know how to generate audio waveforms that will produce a low crest factor at the xmit PA. *** There is a reply: 73852 *** More *** #: 73852 S17/TAPR NNC/DSP 14-Apr-88 22:35:45 Sb: #73841-#Crest Factor Invariance? Fm: Tom Clark W3IWI 71260,3640 To: Franklin Antonio, N6NKF 76337,1365 (X) Franklin -- is the SSB xmtr has no filter distortion and all stages are perfectly linear, then the relative amplitudes and phases of all baseband components map directly to RF. Just think of each tone as a phasor, spinning merrily. All the perfect SSB xmtr does is to spin all tones faster by the same amount. If the SSB receiver is perfectly on frequency but has no way to re- construct the phase of the xmtr's oscillator, then it de-spins them but adds a constant phase shift to all components (the unknown phase difference between the LOs). It is only when the perfect filter (including the ionosphere as a dispersive filter whose properties can, at best, be only known in a statistical sense) and the perfect amplifier hypothesis breaks down that we get into trouble. *** There is a reply: 73867 *** More *** #: 73867 S17/TAPR NNC/DSP 15-Apr-88 06:20:26 Sb: #73852-Crest Factor Invariance? Fm: Franklin Antonio, N6NKF 76337,1365 To: Tom Clark W3IWI 71260,3640 I agree with your statement. Pls reread my original msg. The SSB xmtr frequency shifts the input signal. If crest factor is not invariant under frequency shift, then the crest factor of the signal at the PA (where we are voltage limited) will not be the same as the crest factor of the input audio signal. That's all i was saying. We also need to examine the magnitude of phase shifts within the SSB rig, (which are essentially all in the crystal filters). Sadly, many rigs have two crystal filters, and use both of them on both xmit and rcv. But before we get into details like phase shifts, we oughta make sure we're understanding the effect of the frequency shift, which is more fundamental. I think you misunderstood my original mail. Sounds like you interpreted my concern as being the 2nd order effect from mistuning of the rcvr, or something like that. No. When i say frequency shift, i'm talking about the fundamental SSB mixing operation going on in the transmitter, ie in at 1kHz, out at 7MHz. #: 73849 S17/TAPR NNC/DSP 14-Apr-88 22:34:49 Sb: #73766-HF Modems Fm: Tom Clark W3IWI 71260,3640 To: Barry McLarnon VE3JF 71470,3651 (X) Re the Newman (Alfred E.?) chirp scheme. It sounds like this is a group delay encoding trick since group delay = - (d phase)/(d freq) [oh to have math symbols available!]. Given the dispersive character of the ionosphere I fear this kind of scheme is frought with peril. I suspect we'd spend all our computing horsepower (and more) trying to adaptively equalize delay twiddles from the medium. #: 73899 S17/TAPR NNC/DSP 15-Apr-88 15:59:47 Sb: #73849-HF Modems Fm: Barry McLarnon VE3JF 71470,3651 To: Tom Clark W3IWI 71260,3640 What, me worry? I wasn't proposing this as a signalling technique... just thought it was interesting that that particular mathematical trick to minimize crest factor of a group of sinusoids turned out to synthesize a chirp-like waveform. Of course, if we really wanted to use a chirp, it would be easier to use a dispersive delay line to generate and demodulate it. Chirp modulation actually has been used successfully in HF modems as a spread-spectrum technique for beating multipath, e.g., do an "up-chirp" to send a 1, and a "down-chirp" to send a 0. But you need bandwidth >> data rate to get a decent amount of processing gain out of it, so it is only good for low data rates (< 300 bps) if you are feeding it through an SSB rig. *** More *** #: 73900 S17/TAPR NNC/DSP 15-Apr-88 16:00:24 Sb: #73841-Crest Factor Invariance? Fm: Barry McLarnon VE3JF 71470,3651 To: Franklin Antonio, N6NKF 76337,1365 Good point! The crest factor is definitely NOT invariant under a frequency shift. If we have a baseband signal s(t) and apply it to an SSB modulator to shift it to RF, the envelope of the new signal becomes: 2 2 0.5 { [s(t)] + [h(t)] } where h(t) is the Hilbert transform of s(t). The only signal whose envelope is invariant under this transformation is a single sine wave. Whether the crest factor of a given signal is greatly altered by the transformation depends entirely on how well-behaved its Hilbert transform is. For instance, the Hilbert transform of a square wave has infinite peaks, so you can get a really nasty peaky RF waveform if you feed one into an SSB transmitter. Fortunately, the Hilbert transform of most signals of interest does not blow up like this, and I think the effect of SSB modulation on the crest factor of signals like voice or multitone FSK is quite small. I just read Tom's reply to you, and I think he is skating on thin ice. Conventional mixing produces a DSB signal which preserves the envelope of the baseband signal, but SSB modulation does not. #: 73915 S17/TAPR NNC/DSP 15-Apr-88 23:48:00 Sb: #73900-#Crest Factor Invariance? Fm: Tom Clark W3IWI 71260,3640 To: Barry McLarnon VE3JF 71470,3651 (X) It looks to me that the 'thin ice' is only that the DC component of the baseband signal is indeterminate in the SSBSC case. . Franklin's point on filters is well taken. In past years I spent a lot of effort characterizing the filters (many are ceramic) in various radios for our satellite links. I found that the stock filters used in FT726's were very bad both for 1200 baud FSK and 400 baud Manchester (equivalent to 800 baud biphase) PSK. PSK was even more twichy with the 1200 baud modems. FT726s with the cheap Jap ceramic filters would work at 1200 baud only on LSB, but not on upper, due to the combination of filter and radio (audio) passband problems. The PSK data had to be centered at 1500-1600 Hz. Took a look at Kenwood and was very impressed with TS711/811 for VHF and TS940 on HF (that's why I bought them). The 711/811 have a bit more amplitude slope with frequency than I'd like but the group delay performance seems pretty good. Never tried ICOMs after the IC720 which was also quite good. In general my impression is that the filters in most modern radios are pretty good. Make sure that the modulation spectrum only fills about the central 80% of the passband, since the multi-pole filters give horrendous delay distortion as you get near the filter skirts. . Franklin -- never saw a reply on mouses -- does your interface assume stock Microsoft mouse? *** There is a reply: 73928 *** More *** #: 73928 S17/TAPR NNC/DSP 16-Apr-88 03:48:29 Sb: #73915-Crest Factor Invariance? Fm: Franklin Antonio, N6NKF 76337,1365 To: Tom Clark W3IWI 71260,3640 (X) Thank you for the summary of your SSB rig filter results. I had been meaning to ask you for same, but you beat me to it. Re mouse interface in my spectrum analyzer pgm.. I assume the presence of a mouse driver for whatever mouse you have. I make mouse driver calls that are compatible with both the microsoft mouse driver and the mouse systems corp mouse driver. (and have tested with both) I assume that most clone mice come with compatible drivers, and therefore should work. Re filters again... how many poles in typical SSB rig IF filter? maybe 6? *** More *** #: 73926 S17/TAPR NNC/DSP 16-Apr-88 03:40:13 Sb: #73900-Crest Factor Invariance? Fm: Franklin Antonio, N6NKF 76337,1365 To: Barry McLarnon VE3JF 71470,3651 (X) Oh. Of course! Ok, now i'm calibrated again. Now i remember why i've always looked at this sort of thing using the complex signal model. I will go back to that way of thinking immediately. #: 74049 S17/TAPR NNC/DSP 18-Apr-88 16:40:17 Sb: #73915-#Crest Factor Invariance? Fm: Barry McLarnon VE3JF 71470,3651 To: Tom Clark W3IWI 71260,3640 (X) Tom, I think we're talking apples and oranges here. The SSB signal can certainly be demodulated to yield an exact replica of the original baseband signal (with the possible exception, as you say, of a DC component). All I'm saying is that the MODULATED SSB signal that you transmit will in general have a different waveform and crest factor than the baseband signal. If the SSB waveform is ill-behaved, that makes it harder to transmit it faithfully such that the baseband signal can be recovered at the demodulator. *** There is a reply: 74056 *** More *** #: 74056 S17/TAPR NNC/DSP 18-Apr-88 18:33:37 Sb: #74049-#Crest Factor Invariance? Fm: Bob McGwier N4HY 74615,1366 To: Barry McLarnon VE3JF 71470,3651 (X) I don't understand this. Let us suppose that the baseband modulation is (say) 300 Hz wide and I multiply it by a complex sinusoid (modulate in a fashion that will allow me to derive SSB, these are completely equivalent). The amplitude of the sum of the tones (even multiplied) is less than or equal to the sum of the amplitudes by Pythagorean theorem. The amplitude of the individual tones is TOTALLY UNAFFECTED by the multiplication by the complex sinusoid and the sum of the baseband waveforms is less than max over the sum of the amplitudes of the individuals making it up. Thus the crest factor would be unaffected since it is this max. What have I missed? If the 300Hz were put in the center of the SSB radio filters and it were reasonably flat etc etc is the reason for that at the beginning. Bob *** There is a reply: 74065 *** More *** #: 74065 S17/TAPR NNC/DSP 18-Apr-88 22:55:03 Sb: #74056-Crest Factor Invariance? Fm: Franklin Antonio, N6NKF 76337,1365 To: Bob McGwier N4HY 74615,1366 I have worked out an explanation of the mathematics, and am preparing to type up and upload same. Crest factor is defn'tly affected by SSB modulation. Darned hard to type this in plain ascii file without math symbols, etc. #: 74051 S17/TAPR NNC/DSP 18-Apr-88 18:05:49 Sb: #73447-HF Modems, Part 2 Fm: Bob McGwier N4HY 74615,1366 To: Phil Karn, KA9Q 73210,1526 No problem doing soft decision decoding on these, I do it all the time but I have the DAMNDEST time remembering what is or isn't transmittable if you catch the drift. I will check into it and I am sure that Barry and Franklin will know about ways to soft decision decode these fellows, then I will know what the limits are. Bob *** More *** #: 74053 S17/TAPR NNC/DSP 18-Apr-88 18:06:35 Sb: #73458-HF Modems Fm: Bob McGwier N4HY 74615,1366 To: Barry McLarnon VE3JF 71470,3651 (X) 1800 Hz sounds right. These VBP tuning rigs are nice. Bob #: 74069 S17/TAPR NNC/DSP 18-Apr-88 23:08:55 Sb: RV-FFT's Fm: Franklin Antonio, N6NKF 76337,1365 To: Bob McGwier 74615,1366 Found yet another article on Real-Valued FFTs that appears to be very similar to the Sorensen et al paper. "Improved Fourier and Hartley Transform Algorithms application to Cyclic Convolution of Real Data" by Duhamel & Vetterli, IEEE-ASSP Jun '87. Interesting data: The article claims they wrote TMS32010 code that does 128-point real FFT in 572uS. If i just multiply that up to what one would expect for a 1024-pt xform taking into account only required # arithmetic operations, i get 7mS! Of course, 128 pts is small enough to fit in internal memory, so one should multiply in another factor of idunno what. Vetterli is at Columbia U. (martin@ctr.columbia.edu) I sent him mail asking for the sources. He forwarded my request to Duhamel (who works for a company called CNET in France somewhere). He replied in the negative. Apparently CNET considers it proprietary. Well poo. These guys shouldn't be allowed to publish articles claiming discovery of new ("the best") algorithms without publishing source code. That's the only proof that the algorithm is completely thought out! I've read i dunno how many papers on the new Number-Theoretic-Transform techniques for example... everybody claims to have the next big hit algorithm, but none of them have thought it thru to the point where they have even programmed it... and they expect me to? Back to Vetterli & Duhamel.. Does it sound like their FFT runs faster than the RVFFT you're writing? If so, maybe it's worth a 2nd shot to see if they might donate same. I delegate this task to you. You're much more agressive than I. #: 74080 S17/TAPR NNC/DSP 19-Apr-88 08:24:50 Sb: Crest Factor ***!!!*** Fm: Franklin Antonio, N6NKF 76337,1365 To: ALL I have just written a small writeup on my ideas re Peak-to-Average Ratio vs Crest Factor, how these change under SSB modulation, etc etc. Was gonna be a coupla pieces of mail, but it got out of hand. It's now 13K long, so i'm uploading it to DL17. This comes complete with mathematical doodles to augment the astoundingly clear and concise text. I have inserted one small mathematical error to keep you on your toes, so read carefully. [76337,1365] CREST.TXT 19-Apr-88 13171 Keywords: N6NKF CREST-FACTOR FSK HF PHASOR Writeup discussing Crest-Factor and Peak-to-Average Envelope Ratio of signals composed of a sum of equal amplitude sinusoids. These signals arise in (n,m)-ary FSK modulation. SSB modulation changes the crest- factor of a signal, and this effect is discussed in detail. Crest Factor Evaluation of Multitone Waveforms under SSB Modulation Franklin Antonio, N6NKF, 4/19/88 5am edition Summary: Crest Factor of a multitone waveform under SSB modulation is discussed. Equations for crest factor of the transmitted waveform are developed. Crest Factor causes a loss in transmit power, which is calculated as Waveform Xmit Power Loss -------- --------------- 1-tone 0 db 2-tones 3 db (any phases, any frequencies) 3-tones depends on frequencies and phases optimum unknown. Probably >2 db Discussion: Barry McLarnon has suggested the use of (n,m)-ary FSK modulation for an amateur radio HF modem. During each modulation interval, the modulator would generate n out of m possible audio frequency sinusoids add them, and send them into the microphone input of an HF SSB transceiver. An important characteristic of such multi-tone waveforms is their "crest factor". This is the ratio of the waveform peak value to the waveform's RMS value. Simple sine waves have a crest factor of sqrt(2), or 3db. The power amplifier in the HF transceiver is voltage limited, and we must reduce the power level until the amplifer can handle the peaks. (or at least nearly so) For example, if a PA is rated at 100W PEP (Peak Envelope Power), and we feed it a waveform with a crest factor = CF, then we must reduce average power by 2/(CF^2). If CF = 10, we must reduce our 100W rig to 2W, a 17db loss! There has been some discussion of designing multi-tone waveforms specifically so that they will have a low crest factor. One example in the literature is "Multitone Signals with Low Crest Factor", by Stephen Boyd, IEEE Ckts & Syst, Oct 1986, pp1018-1022, and "Comments on Multitone...", Ouderaa, Schoukens, Renneboog, IEEE C&S, Sept 1987, pp1125-1127. They looked at waveforms of the form.. s(t) = cos(W*t+P1) + cos(2*W*t+P2) + cos(3*W*t+P3) + ... + cos(n*W+Pn) (1) They then describe methods for choosing the phase offsets P1...Pn to minimize (or nearly minimize) the crest factor of s(t). These guys have great sounding names, and they solve an interesting problem, but it isn't our problem. Important is the fact that we really care about the crest factor of the waveform AFTER SSB MODULATION. (because that's where the power amp lives) SSB modulation changes the crest factor of a waveform. To understand why, we have to do some math, which follows. Boyd, Ouderra, etc (BOSR) define crest-factor in a manner which doesn't directly help us, because they didn't deal with SSB modulation, yet we must. You cannot derive the crest-factor after SSB modulation by knowing only the crest-factor before modulation. If you minimize the crest factor of a signal by varying some parameter of the signal (such as the relative phases of two sinusoidal components) then you haven't necessarily minimized the crest factor after SSB modulation. Gobldegook, but it gets clearer later... What is SSB modulation anyway? It's really just a frequency shift, but that's easier to say than to write mathematically. Consider a signal s(t). Now what does that turn into when it's SSB modulated? ssb(s(t)) = cos(Wc*t+Pc)*s(t) - sin(Wc*t+Pc)*H(s(t)) (2) where, Wc and Pc are the frequency and phase of the local oscillator, and H() represents a Hilbert Transform. The Hilbert Transform of a signal is simply the signal with every frequency component phase shifted 90 degrees. Now let's try it with an example signal. How about a square wave? [Square wave example was Barry's idea] A square wave has the marvelous property that it's crest factor = 1 !!! Can't do better than that. Would it be a reasonable waveform to stick into an SSB modulator? Remember a description of a square wave from some class on Fourier theory... s(t) = sin(t) + (1/3)sin(3t) + (1/5)sin(5t) + ... (3) Because it's represented here as a sum of sin()'s, we immediately know how to compute it's Hilbert transform too. Shift a sin() 90 degrees, and you just get a -cos().. H(s(t)) = - cos(t) - (1/3)cos(3t) - (1/5)cos(5t) - ... (4) Now note that while this example s(t) is very well behaved (ie CF=1), it's Hilbert Transform is very badly behaved. It's crest factor is infinite! In particular, at t=0, we have - 1 - (1/3) - (1/5) - ... which is a series that doesn't converge, ie is infinite. (minus infinite actually) Right here we have a hint that something that wasn't immediately obvious is going on. Substituting (3) and (4) into (2)... ssb(s(t)) = cos(Wc*t+Pc) * [ sin(t)+(1/3)sin(3t)+(1/5)sin(5t)... ] - sin(Wc*t+Pc) * [ cos(t)+(1/3)cos(3t)+(1/5)cos(5t)... ] (5) We can decide what waveform we generate and send to the SSB modulator, and might, in some systems, be able to control the LO frequency Wc, but typically we will be entirely unable to control the LO phase Pc. If we could choose Wc and Pc precisely, then we could make the large peaks of the cos(t)+... term occur when sin(Wc*t+Pc) was exactly zero. We get to choose the signal we generate, but the devil can choose Pc, so to "rotate" our waveform thru any phase angle he chooses. In the example, this means that ssb(s(t)) can take on very large (infinite actually) values. All the devil has to do is choose Pc to make Wc*t+Pc be nonzero at time t=0, and the resulting ssb(t) blows up. Actually, because the frequency of the carrier, Wc, is large (maybe 14 MHz) relative to the frequency components of the input signal (audio frequencies), the carrier is whipping around so fast (ie Wc*t+Pc is changing so rapidly) that the carrier samples all the good and bad parts of both s(t) and H(s(t)). BOSR only deals with the case where Wc=0, Pc=0, hence they ignore H(s(t)). We took a waveform with Crest Factor = 1, and put it thru an SSB modulator. What came out had Crest Factor = Infinity. This is not good. Now it turns out that luckily most waveforms are more well behaved than square waves under SSB modulation. Most waveforms don't blow up like this, but the lesson is that we must look for the maximum value of the crest factor of ssb(t) under all possible local oscillator phases. Lets define a new measure, call it.. Peak/Avg Envelope Ratio (PAR): PAR(s(t)) = MAX [ CrestFactor( ssb(s(t)) ) ] / sqrt(2) (6) maximum taken over time and all possible values of Pc. PAR() is the measure we should care about. The sqrt(2) divisor makes PAR=1 (ie 0db) for a single sine wave. When we look at other signals, PAR tells us how far we have to turn down the signal power at the power-amplifer RELATIVE to the power level we could handle for a single sine wave. A simpler definition of PAR() follows. The math will get easier, and the sqrt(2) will go away. Fortunately, we don't have to compute ssb(s(t)) for all possible Pc to figure out PAR(s(t)). We can do it algebraically. I prefer to do the algebra with complex exponentials instead of sin()'s and cos()'s. Sometimes it's simpler. We use, exp(j*(W1*t+P1)) (7) to represent a sinusoid. Here, j = sqrt(-1). This seems gnarly to those who aren't used to it. Remember in the above calculations, i had to evaluate the Hilbert Transform of signals. You may think about the complex exponential as mathematical trick that carries the Hilbert Transform around with every signal, so that i don't have to calculate it as i go. This is sometimes called the complex signal model. Such complex signals are also sometimes called phasors. I will try to use capital leters for phasors, and lowercase for scalar (ie ordinary) signals. Also, re[], and im[] mean the real and imaginary part of a phasor. For example, re[ Exp(j*W1*t+P1) ] = cos(W1*t+P1) (8) im[ Exp(j*W1*t+P1) ] = sin(W1*t+P1) In this notation, the formula for SSB modulation is simpler than before... ssb(S(t)) = re[ exp(j*(Wc*t+Pc)) * S(t) ] (9) SSB modulation simply means multiply the signal phasor by the carrier phasor, then take the real part. We can also now redefine Peak-to-Average Envelope Ratio now in phasor terms. It becomes... PAR(S(t)) = MAX [ Mag(S(t)) ] / RMS[ Mag(S(t)) ] (10) Now i only need take the MAX over time, whereas before the MAX was also over all possible LO phases. The phasors carry around with them all the info i need to evaluate all phases simultaniously. This definition is equivalent to the the previous one. Phasors on stun! ... Let's immediately jump to some useful waveforms, ie (n,m)-ary FSK, for which each waveform of interest is a sum of n equal amplitude sinusoids of specified phase, and compute PAR. Start with (2,m)-ary FSK. If i generate a signal by adding two equal amplitude tones, can i cleverly pick the relative phases of the two tones to minimize the Peak-to-Average Envelope ratio? Here's such a two-tone signal, represented as a phasor. The sqrt(2) normalizes S(t) so that it's RMS value is 1. S(t) = (1/sqrt(2)) * [ Exp(j*W1*t+P1) + Exp(j*W2*t+P2) ] (11) Now, using the following identities... Exp(j*x) = cos(x) + j*sin(x) sin(a) + sin(b) = 2 * sin((1/2)*(a+b)) * cos((1/2)*(a-b)) cos(a) + cos(b) = 2 * cos((1/2)*(a+b)) * cos((1/2)*(a-b)) we can put S(t) into a more form which makes it's properties more intuitive.. S(t) = sqrt(2) * cos[ ((W1-W2)*t+(P1-P2))/2] * Exp[j*((W1+W2)*t+(P1+P2))/2] (12) Ok, so at first it doesn't look very intuitive. Ignore the stuff inside the parenthesis for a moment. The Exp[] is a complex exponential which always has magnitude = 1. The cos[] has it's maximum value = 1. So, by immediate observation, we see that PAR(S(t)) = sqrt(2) (13) You can choose the relative phases of the two sinusoids, P1 & P2, but you won't affect the Peak-to-Average Envelope! It's always sqrt(2). Ie you have to turn down the power by 3db to xmit the sum of two sinusoids. How about that for a no-hope answer! Interestingly, it doesn't generalize... What happens for a sum of 3 sinusoids? (ie for (3,m)-ary FSK) S(t) = (1/sqrt(3)) * [ Exp(j*W1*t+P1) + Exp(j*W2*t+P2) + Exp(j*W3*t+P3) ] (14) The trig identity gods aren't with us this time, so the thing doesn't pop out magically into something obvious. (at least not under my hand) But we can get an interesting result. We want to put this thing into the form S(t) = a(t) * Exp( b(t) ) (15) where a(t) and b(t) are real, just as before. Then we'll look at the maximum of a(t), and ignore b(t). I'll spare you the intermediate trig doodles... a(t) = sqrt[ 1 + (2/3)*cos((W1-W2)*t+(P1-P2)) (16) + (2/3)*cos((W2-W3)*t+(P2-P3)) + (2/3)*cos((W3-W1)*t+(P3-P1)) ] Now, because we started with the goal of doing (3,m)-ary FSK, we know the frequencies of the tones we want to generate, so W1,W2,W3 are known and fixed. We now get to pick the relative phases RP1=P1-P2, and RP2=P2-P3. For the case W1,W2,W3 = 1,2,3, the phases RP1=0, RP2=pi produce PAR(S(t))=1.29, (ie 2.2 db) which is probably near optimum for this choice of frequencies. Other frequency triplets will have other optimum phases. So for every set of (W1,W2,W3) in the (n,m)-ary FSK, we can optimize RP1,RP2 to minimize PAR(S(t)). Because minimizing sqrt(x) is the same as minimizing x, we can drop the sqrt[] function and minimize what's inside. Interestingly, this looks a lot like what BOSR were doing, but it isn't the same. In the case of a 3-tone signal, they chose phases to minimize abs [ cos(W1*t+P1) + cos(W2*t+P2) + cos(W3*t+P3) ] (17) and instead, we choose phases to minimize 1 + (2/3)*cos((W1-W2)*t+(P1-P2)) + (2/3)*cos((W2-W3)*t+(P2-P3)) + (2/3)*cos((W3-W1)*t+(P3-P1)) (18) which, amazingly, is a nearly equivalent form. Unfortunately, the phase values that minimize one do not necessarily minimize the other. The equations above for the 3-tone case can be easily generalized for the n-tone case. I haven't been able to solve for the optimal values of PAR or the phases producing same directly, but a computer program could be easily written to evaluate (18) for every frequency triple (W1,W2,W3), trying phases RP1,RP2 each in [0,2pi], on a 64x64 grid, for each calculation varying t in [0,lcm periods 1/W1,1/W2,1/W3]. Franklin Antonio, N6NKF #: 74101 S17/TAPR NNC/DSP 19-Apr-88 16:34:17 Sb: #74056-Crest Factor Invariance? Fm: Barry McLarnon VE3JF 71470,3651 To: Bob McGwier N4HY 74615,1366 The only incorrect statement you've made is "the crest factor would be unaffected since it is this max". The crest factor can be much less than the sum of the max amplitudes of the individual sinusoids if you're clever about how you choose their frequencies, amplitudes, and phases. The problem is that the SSB frequency shift messes up the relationship you've so carefully constructed. Consider what it takes to make a signal with a low crest factor like a square wave: a series of odd-order harmonically-related sinusoids with just the right amplitude and phase. In other words, a bunch of phasors spinning merrily in sync so that they never can gang up and create a big peak. Now if we do a frequency shift, we have destroyed the harmonic relationship. The series becomes divergent, and the phasors are free to run amok and mess up the crest factor. Barry #: 74109 S17/TAPR NNC/DSP 19-Apr-88 18:54:10 Sb: #74065-#Crest Factor Invariance? Fm: Bob McGwier N4HY 74615,1366 To: Franklin Antonio, N6NKF 76337,1365 (X) Please do since I am really confused. You should have seen me trying to do differential equations and multiple integrals in ascii before a meeting in Boulder last year so that the Phase IV team could see my attitude control work for the geo satellite. Tom can attest to the fact that it was painful to say the least. Bob *** There is a reply: 74145 *** More *** #: 74145 S17/TAPR NNC/DSP 20-Apr-88 14:46:27 Sb: #74109-Crest Factor Invariance? Fm: Franklin Antonio, N6NKF 76337,1365 To: Bob McGwier N4HY 74615,1366 CREST.TXT has been uploaded. Have you grabbed a copy yet? I'd like to get some consensus on this before i upload the next bombshell. *** More *** #: 74113 S17/TAPR NNC/DSP 19-Apr-88 18:54:42 Sb: #74101-Crest Factor Invariance? Fm: Bob McGwier N4HY 74615,1366 To: Barry McLarnon VE3JF 71470,3651 (X) I agree that can be done so long as the frequencies are not rationally related. That is all that means. They must have an irrational ONLY relationship to fall below the max amplitude or else you are guaranteed that the max amplitude will be achieved. This is like beat notes achieving the sum of the amplitudes only if the angular frequencies are rationally related. If what I have said here is wrong, I am really confused. Bob *** More *** #: 74110 S17/TAPR NNC/DSP 19-Apr-88 18:54:18 Sb: #74069-RV-FFT's Fm: Bob McGwier N4HY 74615,1366 To: Franklin Antonio, N6NKF 76337,1365 (X) Yes I found that one in the same journal you pointed out to me and have a copy of it. I am working on that code now. Tom picked up your board a little while ago and will be bringing it to Dayton. See you there. Bob *** More *** #: 74111 S17/TAPR NNC/DSP 19-Apr-88 18:54:27 Sb: #74069-RV-FFT's Fm: Bob McGwier N4HY 74615,1366 To: Franklin Antonio, N6NKF 76337,1365 (X) Sure I will go after them. Etienne Pardoux, their boss, invited me to give a talk there and at INRIA next spring. Think I should include that in the price of admission? I will definitely try and code that. I was already going to do all of them as I believe, as you do, that "the proof is in the pudding" or the code as it were. Bob #: 74126 S17/TAPR NNC/DSP 19-Apr-88 23:26:46 Sb: TMS320C25 development Fm: Bob McGwier N4HY 74615,1366 To: ALL I have to report a little "luck of the Irish." I had to go to the UK as many of you know and I couldn't attend ICASSP (Int. Conf. on Acoustics, Speech, and Signal Pro.) in NYC. I had tickets to several events that T.I. had put on while there. I gave them to my partner in crime at work, Maureen Quirk (hey, with a Ph. D. in E.E. in DSP and Irish to boot how could we not be partners). Dutifully putting these tickets in the proper place at the meeting, she won a $5000 in TMS320C25 plug in card for the PC with all their development software and other stuff. She said, "I couldn't figure out how I would use it and started to give it back but figuring that you would ring my neck if I gave it back, I brought it home to see if you could use it." I plugged it in today and had a bit of fun to say the least. It has an indefinite home ;-). Bob #: 74155 S17/TAPR NNC/DSP 20-Apr-88 21:51:58 Sb: #74145-Crest Factor Invariance? Fm: Bob McGwier N4HY 74615,1366 To: Franklin Antonio, N6NKF 76337,1365 (X) I have downloaded it but have not made it through it. I am spending all free time calculating moments of inertia and center of gravity for PACSAT for the Ariane Espace which have to have them by next Friday and I leave for D.C. to spend a couple of days with Tom and for work there on Monday so they have to be done before the Dayton festivities start. Bob *** More *** #: 74173 S17/TAPR NNC/DSP 21-Apr-88 08:36:24 Sb: #74145-Crest Factor Invariance? Fm: Barry McLarnon VE3JF 71470,3651 To: Franklin Antonio, N6NKF 76337,1365 Looks good to me, Ace. Let's have the next installment! *** More *** #: 74172 S17/TAPR NNC/DSP 21-Apr-88 08:36:05 Sb: #74113-Crest Factor Invariance? Fm: Barry McLarnon VE3JF 71470,3651 To: Bob McGwier N4HY 74615,1366 Hmmm. Just a problem of semantics, I guess. I'm not sure whether we have any disagreement here at all. Anyway, onward! #: 74189 S17/TAPR NNC/DSP 21-Apr-88 22:26:43 Sb: #74172-Crest Factor Invariance? Fm: Bob McGwier N4HY 74615,1366 To: Barry McLarnon VE3JF 71470,3651 (X) Right. I sure am looking forward to Dayton, see you there! Bob #: 74213 S17/TAPR NNC/DSP 22-Apr-88 10:42:00 Sb: Mailing Fm: Lyle Johnson, WA7GXD 76246,565 To: DSPers I gave the four sheets of schematics to Cris this afternoon, along with nine pages of notes. She will get them duplicated and mailed out tomorrow, so we slipped the schedule again... Eric is getting his PC set up to do PC layout work. When I get back from Chicago, I will get the CAD package copy out to Tom so we can exchange board layouts, schematics, etc., via CIS up/down load, or diskettes, or whatever. If you think you are on the list for this information, and don't have your copy by the end of next week, let Cris know at the office (not me!) and she will verifyand get the stuff eroute to you. Cheers -- and enjoy Dayton for me, I won't be back on here until then -- Lyle #: 74259 S17/TAPR NNC/DSP 23-Apr-88 20:16:43 Sb: #74173-Crest Factor Invariance? Fm: Franklin Antonio, N6NKF 76337,1365 To: Barry McLarnon VE3JF 71470,3651 (X) I just finished the long awaited 2nd installment of the crest factor writeup. This one includes results of computer search for optimum phases for (3,10)-ary FSK. Even reaches a conclusion. File uploaded into DL17 as CRES2.TXT. [76337,1365] CRES2.TXT 23-Apr-88 6267 Accesses: 3 Keywords: N6NKF CREST-FACTOR FSK Results of experiments to optimize the phases of individual tones within an (n,m)-ary FSK waveform to minimize waveform peaks. This writeup is 2nd in a series. First writeup can be found in CREST.TXT. If you haven't read the first one yet, read this at your own risk. Results of (n,m)-ary FSK Phase Optimization Experiment 4/23/88 11am Franklin Antonio, N6NKF (this is a working paper -- do not republish) The idea was to find relative phases of three sinusoids, such that when they are added, the peak-to-average envelope ratio of the result is held as low as possible. This problem arises out of the desire to use a modulation where during each modulation symbol time, n out of a possible m tones are transmitted (ie (n,m)-ary FSK). Power amplifiers in SSB rigs are peak-power-limited, so the peak-to-average envelope ratio, (PAR), if greater than 1, will force us to reduce the average power level at the transmitter. If some parameter, say for example, the relative phases of the n tones, could be chosen to minimize PAR, and thus allow us a higher average power, then it should be. In the previous writeup, i argued that peak-to-average envelope is the right measure to use, and developed equations from which PAR can be calculated given the frequencies and phases of the tones. In the previous writeup (CREST.TXT) i showed that for the (2,m)-ary FSK case, PAR always = sqrt(2), no matter what phases are used. This means you can't choose optimum phases in the two-tone case, 'cause there aren't any. In the three tone case, i derived eqn-16, for the envelope of a unit power three-tone signal as a function of the frequencies and phases of the three tones. Because the signal is unit power, this is the PAR directly, ie we don't have to divide by the RMS power. I sure hope this equation is correct. a(t) = sqrt[ 1 + (2/3)*cos((W1-W2)*t+(P1-P2)) (16) + (2/3)*cos((W2-W3)*t+(P2-P3)) + (2/3)*cos((W3-W1)*t+(P3-P1)) ] For any values of W1,W2,W3,P1,P2,P3, PAR is simply this equation, maximized over all values of t in [0,2pi]. Assuming we want to transmit (3,10)-ary FSK, we want to try all combinations of three out of 10 tones. That is, we want to try every combination of W1,W2,W3 chosen from [1,2,3,4,5,6,7,8,9,10], and for each such case, find optimum phases and the resulting PAR. I wrote a Fortran program to do this. The program uses a brute force search procedure. The program assumed P1=0, and did it's two-dimensional search over P2 & P3 in [0,2pi]. (There are really only two free variables, because it's the relative phases that matter.) To verify that this program was running correctly, i made an Excel spreadsheet into which i could pop the resulting frequencies and phases, and get on-screen plots of the resulting waveforms. (I ran the optimizing program on the IBM-AT, and did the spreadsheet on the MAC+.) Hopefully, this verifies correctness of eqn-16, and the optimization program. (but feel free to verify this yourself) Here are some of the results. The first three columns are the frequencies, the next three are the optimum phases, and finally, the PAR. Remember, PAR = 1 = 0 db is as good as a single sinusoid, while PAR = sqrt(3) = 1.73 = 4.77 db is as bad as it is possible to do with three sinusoids, at the worst possible phases. You will note that the P1 column is always 0. [For those of you who think in terms of 'crest factor'... Crest factor is defined including another sqrt(2), so you can add 3 db to all the PAR's ] The first case that cranked out was encouraging... W1 W2 W3 P1 P2 P3 PAR 1 2 3 .0000 2.356 1.570 1.291 That's not bad. 20*log10(1.29) = 2.2 db. An encouraging result. Ok, one down, 119 cases left to try. Another interesting point, is that all the other cases with equally-spaced tones, ie the triplets [2,3,4], [3,4,5], [4,5,6],...[1,3,5],[2,4,6],...[1,4,7],[2,5,8],...[1,5,9],[2,6,10], all have optimum phases which produce a PAR = 1.29 . Here are some more of the results... 1 2 4 .0000 2.356 3.926 1.533 1 2 5 .0000 .0000 3.141 1.622 1 2 6 .0000 1.571 4.712 1.664 1 2 7 .0000 .7854 1.571 1.683 1 2 8 .0000 .0000 3.141 1.693 1 2 9 .0000 1.571 3.141 1.699 1 2 10 .0000 .0000 3.141 1.710 ... 1 3 4 .0000 1.571 .7854 1.534 1 3 5 .0000 .0000 3.141 1.289 1 3 6 .0000 .0000 1.571 1.657 1 3 7 .0000 1.571 1.571 1.531 1 3 8 .0000 1.571 .7854 1.692 ... 3 4 5 .0000 1.963 .7854 1.291 3 4 6 .0000 1.571 1.571 1.535 3 4 7 .0000 .3927 4.712 1.624 3 4 8 .0000 .0000 3.141 1.665 3 4 9 .0000 .0000 3.141 1.686 3 4 10 .0000 .3927 5.890 1.699 Some patterns emerge. First, all those phases look familiar, don't they? They're simple rational numbers * pi. 0.3927 = pi/8, for example. Makes me wish i had solved the thing algebraically. As a practical matter, of course, brute force computer generated numbers are as good as any. There are multiple solutions, ie multiple values of P2,P3 that achieve the same PAR. For example, whenever W1=1 & W2=2, the phases (0,0,pi) are also solutions. The computer simply picks one of the possibilities. It also appears that whenever W1=1 & W2=3, one of the following sets of phases (but not both): (0,0,pi) or (0,0,pi/2) always works. I haven't tried to prove this. I just discovered it while playing around. Notice that as the spacing between the tones becomes more disparate, the best achievable PAR gets worse and worse. For most choices of frequencies, in fact, the best possible PAR is very very close to the worst possible PAR. 1.710 --> 4.66 db best possible for tones @ 1,2,10 sqrt(3) --> 4.77 db worst possible any 3 tone freq & phase Conclusion: A few combinations of tones have optimized phases that can reduce the peak-to- average by as much as 2.6 db (ie reduce from 4.7 db for naive adding, to 2.2 db as in the case of the optimized 1-2-3 signal). Unfortunately, there are many other combinations of tones for which the optimum is within a few percent of the worst possible choice of phases. My conclusion, at this point, is that optimization of phases in a 3-tone signal is NOT worthwhile. #: 74405 S17/TAPR NNC/DSP 26-Apr-88 13:14:29 Sb: #74259-Crest Factor Invariance? Fm: Barry McLarnon VE3JF 71470,3651 To: Franklin Antonio, N6NKF 76337,1365 Thanks for your analysis. I agree with your conclusion as far as n = 3 is concerned. To wax philosophical a bit, I think this all makes sense from an information theory point of view. We have a set of tones with a certain number of degrees of freedom, in terms of amplitude, frequency, and phase. If we use these degrees of freedom to the max in order to transmit information at something approaching the channel capacity, we have nothing left over to control the crest factor with. On the other hand, if we minimize the crest factor, we have little or no degrees of freedom left with which to send information. The only open question, I think, is whether some useful engineering tradeoffs might exist between the two extremes for n >> 3. #: 74446 S17/TAPR NNC/DSP 26-Apr-88 23:41:40 Sb: #74405-Crest Factor Invariance? Fm: Franklin Antonio, N6NKF 76337,1365 To: Barry McLarnon VE3JF 71470,3651 (X) Your philosophical argument is a bit hand-wavey. ... but agrees with a fundamental principle i hold dear... "conservation of difficulty". My intuition at this point makes me believe that nothing will help you (including n >> 3) if you want tones that are not evenly spaced. In general, a sum of tones will always achieve the worst case peak except for the very very special case where they are evenly spaced, or nearly so. Of course, that's just my intuitive reaction to the results so far. I can't prove it. Doing computer optimization for n>>3 will be real hard unless we get some more results from the math to help us. Notice that all the computer optimized phases came out to be pi * ratio of small integers. If we could PROVE that that would always happen, then the computer search could be MUCH faster. If you have any ideas along these lines, pls share 'em. My thoughts at this point are to look to waveforms other than sums of sinusoids. My pgm to optimize for n=3 was a quick & dirty. Used floating-point math, etc. Probably would have to be redone from scratch to do anything useful beyold maybe n=4. #: 74458 S17/TAPR NNC/DSP 27-Apr-88 08:26:49 Sb: HF Modem Stuff Fm: Barry McLarnon VE3JF 71470,3651 To: DSP'ers One of my colleagues recently returned from the IEE Conference on HF Radio Systems and Techniques. I just had a look through his copy of the proceedings, and thought I'd relate a few tidbits. High-speed adaptive serial modems continue to be a hot area for research, stimulated by the interest in same in military circles. As you'd expect, these modems make heavy use of DSP techniques. Just to give you the flavor of what's involved in making one of these beasties run, consider the 2400 bps design described by GEC/Marconi in the UK. It uses a single QPSK signal with a raw symbol rate of 1500 baud, of which 300 baud is used for adaptation of the equalizer by inserting a 40-symbol training sequence into the data, 7.5 times/sec. Processing power needed to implement the demodulator? A cool 40 MIPS or so! It uses a multiprocessor architecture and bit-slice technology. They use 12-bit (yeah!) A/D conversion and 12 kHz sample rate in the modem front end. Coming back to reality... Harris Corp described their "automated link establishment" HF data system, which uses 8-ary FSK and a symbol rate of 125 baud to achieve a throughput of 375 bps. Four ms (2 ms at each end) of the 8 ms symbol period are discarded in the demodulator to protect against multipath ISI. The modem is implemented in a single (unspecified) DSP chip. They also mention the use of Golay (24,12) error-correction coding, but no details are given. Golay seems to be the "in" code these days, as I saw it mentioned as part of at least three different HF systems. On a more ominous note, there were no fewer than 10 papers on HF radar. The authors were from 4 different countries (UK, France, Australia, China), so it looks like lots of people want to get into the game with the two superpowers currently engaging in this form of spectral pollution. #: 74461 S17/TAPR NNC/DSP 27-Apr-88 10:13:42 Sb: #74446-Crest Factor Invariance? Fm: Barry McLarnon VE3JF 71470,3651 To: Franklin Antonio, N6NKF 76337,1365 Hand-waving arguments are my specialty! I have no proofs either, but your intuition seems sound enough. There seems little doubt that the best cases are those with even spacing. While this may or may not prove to be useful, it is something to keep in mind when choosing a set of waveforms for signalling. Taking your example of (10,3)-ary FSK, for instance, we could choose 64 of the 120 possibilities as our signal set, and signal at 6 bits/baud. On the other hand, 20 (or so) of the combinations have evenly-spaced tones, so we could choose 16 of these and signal at 4 bits/baud. So we can trade off bit rate (or bandwidth) to get improved crest factor. This sort of tradeoff *might* be useful when we're talking about 300 bps modems, but seems very doubtful at 1200 bps. Here's another thought, just to muddy the waters a bit more: How long does it take for an ensemble of sinusoids with a particular set of starting phases to reach their worst case peak? Perhaps we should be trying to minimize the crest factor of the waveform only over a finite duration, namely, one symbol period. We don't care what happens after that, since we will be starting a new waveform at that point. Does this additional constraint help at all? BCNU@Dayton!