From rec.radio.amateur.homebrew 937 Path: ucbvax!agate!howland.reston.ans.net!vixen.cso.uiuc.edu!sdd.hp.com!col.hp.com!srgenprp!news.dtc.hp.com!hpscit.sc.hp.com!rkarlqu From: rkarlqu@scd.hp.com (Richard Karlquist) Newsgroups: rec.radio.amateur.homebrew Subject: Optimum FSK shift Message-ID: <2gab1t$5v2@hpscit.sc.hp.com> Date: 3 Jan 94 23:51:25 GMT Organization: Hewlett-Packard Lines: 61 NNTP-Posting-Host: hpscrj.scd.hp.com I mentioned in passing that an FSK shift of .8 times the baud rate is optimum in the sense of minimizing BER vs. Eb/No. This seems to have raised a few eyebrows around here (even famous netizen Gary Coffman was surprised to hear this). I would like to go into some detail about this for you skeptics out there. For incoherently detected FSK (as is done in ham radio), the minimum shift that will give orthogonality is a shift equal to the baud rate. For coherently detected FSK, the minimum shift that will give orthogonality is half the baud rate. This shift is commonly called "Minimum Shift Keying (MSK)" and is normally used with coherent detection. Shifts that are any integral multiple of half the baud rate are also orthogonal. In between shifts are not orthogonal. Orthogonality (loosely speaking) means that the mark and space tones don't interfere with each other (I don't want to get too mathematical here). It turns out that a shift of about .75 to .8 times the baud rate, although it is not orthogonal, gives the lowest bit error rate (BER) for a given energy per bit to noise spectral density ratio (Eb/No). Eb/No is proportional to S/N (signal to noise ratio), by the way. Even though it is a disadvantage to be non- orthogonal, the extra shift increases the detected signal more than enough to compensate for it. The optimum shift is .83 dB. better than the orthogonal shifts. Wider shifts are suboptimal because the receiver filter has to be wider and takes in more noise. For "60 WPM" 5 bit RTTY, where the baud rate is 45.45, the shifts discussed above would be: Minimum shift keying: 22.73 Hz. Optimum shift keying: 34 Hz. Minimum shift for orthogonality with non-coherent detection: 45.45 Hz. In a communications theory sense, there is no reason to use more than 45.45 Hz. shift at 60 WPM. The only reason for using a ridiculously wide shift of 170 Hz. (or even 850 Hz.) is the frequency stability issue (admittedly a real issue). One way of partially fixing this problem is to detect the mark and space tones separately as ASK signals with separate narrow filters for each one. ------------------------------------- Reference: Digital Communications Systems by Peyton Z. Peebles Prentice-Hall 1987 Page 267, last paragraph. Also, first sentence on p. 268. Note that delta-omega in Peeble's book is *half* of the shift, as it is normally defined. -------------------------------------- Rick Karlquist N6RK rkarlqu@scd.hp.com From rec.radio.amateur.homebrew 945 Path: ucbvax!hplabs!sdd.hp.com!col.hp.com!srgenprp!alanb From: alanb@sr.hp.com (Alan Bloom) Newsgroups: rec.radio.amateur.homebrew Subject: Re: Optimum FSK shift Message-ID: Date: 6 Jan 94 20:37:38 GMT References: <2gggf4$jhn@darkstar.UCSC.EDU> Sender: news@srgenprp.sr.hp.com (News Administrator) Organization: HP Sonoma County (SRSD/MWTD/MID) Lines: 32 X-Newsreader: TIN [version 1.1 PL9.4] James H. Haynes (haynes@cats.ucsc.edu) wrote: : In article <2gfk79$bcb@hpscit.sc.hp.com> rkarlqu@scd.hp.com (Richard Karlquist) writes: : >Like I said originally, if 170 is so good, 850 ought to be even better. : >So why did everyone change from 850 to 170? : We started out with 850 because that was the military standard Right. I think there were two reasons for switching to 170 Hz shift. One was to reduce interference / allow space for more channels per band. The other was to allow narrower IF filtering. With 850 Hz, you had to use your SSB filter, around 2.5 kHz wide. With 170 Hz shift, you could switch in your CW filter, generally 400 or 500 Hz wide. This gave a big advantage in interference rejection. I don't think most amateur TU's (TU = Terminal Unit = demodulator) got much benefit from diversity anyway. Typical block diagram: ___________ __________ __________ | High-Tone | | Positive | | | +---| BP Filter |--| Detector |--| | | |___________| |__________| | "Slicer" | Receiver --+ ___________ __________ | (Voltage |--> Digital Audio | | Low-Tone | | Negative | | compar- | output +---| BP Filter |--| Detector |--| ator) | to keyer |___________| |__________| |__________| Sometimes post-detection low pass filters would be included as well. AL N1AL From rec.radio.amateur.homebrew 951 Path: ucbvax!dog.ee.lbl.gov!agate!howland.reston.ans.net!europa.eng.gtefsd.com!emory!kd4nc!ke4zv!gary From: gary@ke4zv.atl.ga.us (Gary Coffman) Newsgroups: rec.radio.amateur.homebrew Subject: Re: Optimum FSK shift Message-ID: <1994Jan4.141513.21531@ke4zv.atl.ga.us> Date: 4 Jan 94 14:15:13 GMT References: <2gab1t$5v2@hpscit.sc.hp.com> Reply-To: gary@ke4zv.atl.ga.us (Gary Coffman) Organization: Destructive Testing Systems Lines: 56 In article <2gab1t$5v2@hpscit.sc.hp.com> rkarlqu@scd.hp.com (Richard Karlquist) writes: > >I mentioned in passing that an FSK shift of .8 times the baud rate >is optimum in the sense of minimizing BER vs. Eb/No. This seems >to have raised a few eyebrows around here (even famous netizen >Gary Coffman was surprised to hear this). I would like to go >into some detail about this for you skeptics out there. I'm not skeptical at all of MSK, Richard, it has a clear advantage in the presence of pure Gaussian noise. The Heatherington modem uses it. It's just that "narrow shift" for ordinary FSK of the type used on HF normally means 170 Hz. I was also somewhat startled to see you say that only hams used a shift as wide as 170 Hz for 45.45 baud RTTY. Commercial wire service signals use either 450 Hz or 850 Hz. Multiplex RTTY and SITOR also typically use wider shifts than 170 Hz. I'll talk about why below. >In a communications theory sense, there is no reason to use more >than 45.45 Hz. shift at 60 WPM. The only reason for using a >ridiculously wide shift of 170 Hz. (or even 850 Hz.) is the >frequency stability issue (admittedly a real issue). One way of >partially fixing this problem is to detect the mark and space >tones separately as ASK signals with separate narrow filters for >each one. Now the discussion of why a wider shift may be better at HF than the "optimum" shift. While frequency stabliity for autostart operations may be a consideration with simple detectors, the real reason is the nature of the channel errors at HF. The source of channel errors at HF is rarely Gaussian noise, so the BER advantage of MSK in Gaussian noise is usually moot. Most channel errors at HF are burst errors caused by impulse type noises, selective fading, or interference. By using a wide shift, separate mark and space filters, and a soft decision circuit, it's possible to maintain solid copy even though mark or space may be momentarily obliterated by a channel error. That's why PLL type detectors are generally inferior to filter type detectors for HF RTTY. They only have one filter, necessarily of channel width, which exposes them to more sources of channel error than two very narrow filters with suitable decision networks staggered for mark and space detection. An error anywhere in the bandwidth unlocks the PLL, but the filter detector continues to work as long as it copies either mark or space. By use of synchronous oversampling, extremely narrow mark and space filters can be synthesized. They aren't optimum from the standpoint of recovering maximum signal energy vis Gaussian noise, but that's a good trade at HF where other sources of error predominate and signal levels are usually fairly high. Gary -- Gary Coffman KE4ZV | You make it, | gatech!wa4mei!ke4zv!gary Destructive Testing Systems | we break it. | uunet!rsiatl!ke4zv!gary 534 Shannon Way | Guaranteed! | emory!kd4nc!ke4zv!gary Lawrenceville, GA 30244 | |