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Anyone know of any work on sending Morse via PRN DSSS carrier symbols?
That is use a specified PRN to modulate the carrier to spread the spectrum and send a dit over more BW, e.g 1 kHz. This reduces interference with narrow band signalling systems and could even provide TDMA for the CW segments in addition to traditional FDMA.
Have Fun!
Reg
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Well, that should have been CDMA, not TDMA :-(
I've attached a short proof of the mathematics. It assumes synchronization, but I left out that detail to keep it to
a single page.
The objective is to increase the time * power * bandwidth product using DSSS to increase the BW term.
Have Fun!
Reg
|
Any linear encoding/decoding method boils down to which subspace does the signal live in, and which does the noise live in.? The extent of the overlap of the two determines the error probability.? If the signal and noise are described by Gaussian statistics, then the noise is completely described by its second-order statistics, and the ratio of the variance of the signal estimate to that of the noise in that estimate is the signal-to-noise ratio.? If the statistics are not Gaussian, but still have second order statistics, one can still get a SNR, though it does not directly map to an error probability.
When real channels are encountered, and one gets burst errors, impulse noise, and the like, error correcting codes can help reduce the probability of decoding error at the expense of greatly increased processing and often increased latency.?
If you're trying to produce a Morse-like channel, what are the qualities of a Morse channel, and what are the qualities to be preserved in the Morse-like channel??? Long latency removes the "immediacy" of communication, in that one must wait for a long decoding interval before one can respond.? Also, what part of Morse is preserved?? Should the information communicated be directly the dits, dahs, intraelement, and interelement pauses?? Should letters or words be communicated?? Should the timing of the sender be exactly preserved, or simplified to 1, 3, or 7 dit lengths??
For example, lets say you have these symbols: a "no symbol" symbol, a dit, a dah, a 1 dit length pause, a 3 dit length pause, and a 7 dit length pause.? Lets round it up to 8 symbols so that it is a power of two.? If you want the symbols to be orthogonal and time-invariant (no synchronization required) you can use 8FSK.? If time-invariant orthogonality is not necessary, you could use, for example, a Walsh-Hadamard code of 8 BPSK/BFSK symbols (see matrix below).? You can reserve one of the symbols as a sync code, for example the uniform symbol, and send that one three times, with the symbol in the middle with inverted phase (++++++++ -------- ++++++++).? The bit edges could be used for synchronization.? Alternatively, use BFSK if the channel has a very unstable phase.
 Decoding would be as simple as correlating the received code against all 8 code words and keeping the code word with the highest correlation.? This would be an inefficient but fairly robust and easy to implement linear code.? A similar code was used on the Mariner mission.? It would also keep latency relatively low.
Dan
On Thu, Jun 20, 2024 at 2:49?PM Reginald Beardsley via <pulaskite= [email protected]> wrote: Well, that should have been CDMA, not TDMA :-(
I've attached a short proof of the mathematics.? It assumes synchronization, but I left out that detail to keep it to
a single page.
The objective is to increase the time * power * bandwidth product using DSSS to increase the BW term.
Have Fun!
Reg
|
SCAMP is a mode that reminds of what it sounds like you're trying to accomplish here. Besides that there's Ebnaut, and WOLF - though those have different requirements for a transmitter.
Any linear encoding/decoding method boils down to which subspace does the signal live in, and which does the noise live in.? The extent of the overlap of the two determines the error probability.? If the signal and noise are described by Gaussian statistics, then the noise is completely described by its second-order statistics, and the ratio of the variance of the signal estimate to that of the noise in that estimate is the signal-to-noise ratio.? If the statistics are not Gaussian, but still have second order statistics, one can still get a SNR, though it does not directly map to an error probability.
When real channels are encountered, and one gets burst errors, impulse noise, and the like, error correcting codes can help reduce the probability of decoding error at the expense of greatly increased processing and often increased latency.?
If you're trying to produce a Morse-like channel, what are the qualities of a Morse channel, and what are the qualities to be preserved in the Morse-like channel??? Long latency removes the "immediacy" of communication, in that one must wait for a long decoding interval before one can respond.? Also, what part of Morse is preserved?? Should the information communicated be directly the dits, dahs, intraelement, and interelement pauses?? Should letters or words be communicated?? Should the timing of the sender be exactly preserved, or simplified to 1, 3, or 7 dit lengths??
For example, lets say you have these symbols: a "no symbol" symbol, a dit, a dah, a 1 dit length pause, a 3 dit length pause, and a 7 dit length pause.? Lets round it up to 8 symbols so that it is a power of two.? If you want the symbols to be orthogonal and time-invariant (no synchronization required) you can use 8FSK.? If time-invariant orthogonality is not necessary, you could use, for example, a Walsh-Hadamard code of 8 BPSK/BFSK symbols (see matrix below).? You can reserve one of the symbols as a sync code, for example the uniform symbol, and send that one three times, with the symbol in the middle with inverted phase (++++++++ -------- ++++++++).? The bit edges could be used for synchronization.? Alternatively, use BFSK if the channel has a very unstable phase.
 Decoding would be as simple as correlating the received code against all 8 code words and keeping the code word with the highest correlation.? This would be an inefficient but fairly robust and easy to implement linear code.? A similar code was used on the Mariner mission.? It would also keep latency relatively low.
Dan
On Thu, Jun 20, 2024 at 2:49?PM Reginald Beardsley via <pulaskite= [email protected]> wrote: Well, that should have been CDMA, not TDMA :-(
I've attached a short proof of the mathematics.? It assumes synchronization, but I left out that detail to keep it to
a single page.
The objective is to increase the time * power * bandwidth product using DSSS to increase the BW term.
Have Fun!
Reg
|
There is " dit" and "not dit". International Morse is defined in terms of those two primitives: fixed lengths of time on and off.
If you modulate a carrier with a 1 kHz PRN sequence that will spread the signal out in a manner which can be recovered by cross correlation using a single vector sum. If one has a set of orthogonal PRNs they can each serve as discrete, non-interfering channels while occupying the same frequency space.
Basic idea is to key a DSSS dit or series of dits as required with the appropriate "not dit" spaces inserted. The RX station has to do a synchronized sum over the frame to determine if it's a dit or not dit. That's computationally very cheap. For synchronization one can use a cross correlation with the decoded Morse character to adjust for frame variation every Nth character. IIRC the longest character requires about 2 kSa/word with zero padding. That's a pretty cheap FFT.
I've also considered decode by correlation at character level but question if it's worth the cost in moving electrons. Certainly worth testing. A path with fluttering delay might break dit frame, but not character frame correlation. It introduces character duration latency, but that is not a problem in conditions which would require it. The alternative would be no channel.
If B(t) has a 1 kHz BW, then a dit can be spread across 1 kHz by DSSS. I have always thought of this in terms of hard clipping. That's simply an accident of how I initially conceived of this 40+ years ago. Sign bit (aka hard clipping) was being used in the late 60's to record 1024 channels of Vibroseis data when most systems could only handle 48 channels. The sweeps were long enough they acquired 16 bit data.or better.
In fact, considering the matter last evening I realized that hard clipping is a nuisance and that driving the PA from a DAC would greatly simplify maintaining precise and accurate BW control.
With traditional narrow BW Morse one has only time and power as the variables in the Shannon-Nyquist Time-Power-Bandwidth product. The best technology available today allows about 20 CW channels in 1 kHz. In principle, it should be possible to increase that number dramatically by using a DSSS carrier with a single CQ code and a set of orthogonal codes such that on making contact the stations switch to a different code. This is effectively applying CDMA technology to HF communications using Morse code to maximize spectrum utilization.
Morse for the 21st century.
Have Fun!
Reg
On Friday, June 21, 2024 at 03:53:51 PM CDT, Daniel Marks <profdc9@...> wrote:
Any linear encoding/decoding method boils down to which subspace does the signal live in, and which does the noise live in.? The extent of the overlap of the two determines the error probability.? If the signal and noise are described by Gaussian statistics, then the noise is completely described by its second-order statistics, and the ratio of the variance of the signal estimate to that of the noise in that estimate is the signal-to-noise ratio.? If the statistics are not Gaussian, but still have second order statistics, one can still get a SNR, though it does not directly map to an error probability.
When real channels are encountered, and one gets burst errors, impulse noise, and the like, error correcting codes can help reduce the probability of decoding error at the expense of greatly increased processing and often increased latency.?
If you're trying to produce a Morse-like channel, what are the qualities of a Morse channel, and what are the qualities to be preserved in the Morse-like channel??? Long latency removes the "immediacy" of communication, in that one must wait for a long decoding interval before one can respond.? Also, what part of Morse is preserved?? Should the information communicated be directly the dits, dahs, intraelement, and interelement pauses?? Should letters or words be communicated?? Should the timing of the sender be exactly preserved, or simplified to 1, 3, or 7 dit lengths??
For example, lets say you have these symbols: a "no symbol" symbol, a dit, a dah, a 1 dit length pause, a 3 dit length pause, and a 7 dit length pause.? Lets round it up to 8 symbols so that it is a power of two.? If you want the symbols to be orthogonal and time-invariant (no synchronization required) you can use 8FSK.? If time-invariant orthogonality is not necessary, you could use, for example, a Walsh-Hadamard code of 8 BPSK/BFSK symbols (see matrix below).? You can reserve one of the symbols as a sync code, for example the uniform symbol, and send that one three times, with the symbol in the middle with inverted phase (++++++++ -------- ++++++++).? The bit edges could be used for synchronization.? Alternatively, use BFSK if the channel has a very unstable phase.
![image.png]() Decoding would be as simple as correlating the received code against all 8 code words and keeping the code word with the highest correlation.? This would be an inefficient but fairly robust and easy to implement linear code.? A similar code was used on the Mariner mission.? It would also keep latency relatively low.
Dan
On Thu, Jun 20, 2024 at 2:49?PM Reginald Beardsley via <pulaskite= [email protected]> wrote: Well, that should have been CDMA, not TDMA :-(
I've attached a short proof of the mathematics.? It assumes synchronization, but I left out that detail to keep it to
a single page.
The objective is to increase the time * power * bandwidth product using DSSS to increase the BW term.
Have Fun!
Reg
|
Natural processes produce Gaussian noise. For the dit modulation one can choose any distribution one wishes.
Consider that you have a 100 sample PRN that represents a dit at 12 wpm.There are 2^100 possible binary sequences multiplied by however many bits of DAC drives the transmitter. That's a moderately large space.
The requirement is creating a 100 x M matrix which has the restricted isometry property. Such a matrix can be readily generated using a good PRN such as the the Merrsenne Twister. By constructing a 100 row table with many thousands of columns, selecting a random set of columns and summing the rows to generate 100 random values one can generate such a series. One can then test for the RIP by seeking a sparse L1 solution. If the solution exists, it follows that the RIP is met by the matrix and it can be used to generate an arbitrary number of sequences by summing a small number of columns.
Generate 1000 such 100 sample series. Designate one as CQ and the other 999 as open channels.
Present technology limits CW to about 20 channels per kHz of spectrum. I don't know whether using a DSSS modulated carrier can give 1000 channels in 1 kHz. My copy of Shannon is MIA.
The non-linear nature of the audio output transfer function suggests that experimental work to estimate the channel capacity is needed.
Have Fun!
Reg
Have Fun!
Reg
|
Erik,
Thanks for the video link.
SCAMP is not decodable by ear or sent with a key. It's an RTTY protocol. Very cool, and really well suited to overnight message transfer at very low power levels. However, it's also narrow BW.
My objective is to create a CW carrier which has a fixed BW and is selectable as a discreet CW channel even though it's one of many operating in the same spectrum segment.
Have Fun!
Reg
On Friday, June 21, 2024 at 09:01:26 PM CDT, Erik Nelson <erik.nels0n99@...> wrote:
SCAMP is a mode that reminds of what it sounds like you're trying to accomplish here. Besides that there's Ebnaut, and WOLF - though those have different requirements for a transmitter.
Any linear encoding/decoding method boils down to which subspace does the signal live in, and which does the noise live in.? The extent of the overlap of the two determines the error probability.? If the signal and noise are described by Gaussian statistics, then the noise is completely described by its second-order statistics, and the ratio of the variance of the signal estimate to that of the noise in that estimate is the signal-to-noise ratio.? If the statistics are not Gaussian, but still have second order statistics, one can still get a SNR, though it does not directly map to an error probability.
When real channels are encountered, and one gets burst errors, impulse noise, and the like, error correcting codes can help reduce the probability of decoding error at the expense of greatly increased processing and often increased latency.?
If you're trying to produce a Morse-like channel, what are the qualities of a Morse channel, and what are the qualities to be preserved in the Morse-like channel??? Long latency removes the "immediacy" of communication, in that one must wait for a long decoding interval before one can respond.? Also, what part of Morse is preserved?? Should the information communicated be directly the dits, dahs, intraelement, and interelement pauses?? Should letters or words be communicated?? Should the timing of the sender be exactly preserved, or simplified to 1, 3, or 7 dit lengths??
For example, lets say you have these symbols: a "no symbol" symbol, a dit, a dah, a 1 dit length pause, a 3 dit length pause, and a 7 dit length pause.? Lets round it up to 8 symbols so that it is a power of two.? If you want the symbols to be orthogonal and time-invariant (no synchronization required) you can use 8FSK.? If time-invariant orthogonality is not necessary, you could use, for example, a Walsh-Hadamard code of 8 BPSK/BFSK symbols (see matrix below).? You can reserve one of the symbols as a sync code, for example the uniform symbol, and send that one three times, with the symbol in the middle with inverted phase (++++++++ -------- ++++++++).? The bit edges could be used for synchronization.? Alternatively, use BFSK if the channel has a very unstable phase.
![image.png]() Decoding would be as simple as correlating the received code against all 8 code words and keeping the code word with the highest correlation.? This would be an inefficient but fairly robust and easy to implement linear code.? A similar code was used on the Mariner mission.? It would also keep latency relatively low.
Dan
On Thu, Jun 20, 2024 at 2:49?PM Reginald Beardsley via <pulaskite= [email protected]> wrote: Well, that should have been CDMA, not TDMA :-(
I've attached a short proof of the mathematics.? It assumes synchronization, but I left out that detail to keep it to
a single page.
The objective is to increase the time * power * bandwidth product using DSSS to increase the BW term.
Have Fun!
Reg
|
I finally found my copy of Shannon. I've attached scans of 4 pages I think especially relevant to what I am proposing. The entire paper can be found online if you search on "bell system technical journal". UPenn.edu has an Internet Archive link to volume 27 in which the paper appeared.
Note the first sentence of the preface about trading bandwidth for signal to noise ratio.
Shannon helpfully gives the effective capacity of Morse telegraphy as 0.539*2*dits per second. For 12 wpm, 5 dits per second, that gives a channel capacity of ~5 bits per second.
A 1 kHz BW signal has a capacity of 1000 bits per second. That places an upper limit on the number of CW channels which a 1 kHz DSSS channel can support at 200 12 wpm channels .
Present CW practices achieve about 20 channels in the same BW as can be readily observed on a waterfall display during a contest.
Thus use of a DSSS carrier for CW should provide 5-10 times the spectral efficiency of the current 50 Hz separation between stations.
I hope to have a numerical demonstration within a week or two (dependent on other activities) with which to evaluate the degradation behavior as one approaches the BW imposed capacity.
Have Fun!
Reg
|
Hi Reg,
I believe there's still an OOK based submode of SCAMP included, not just the 2FSK. These links should go into more detail:
On Sat, Jun 22, 2024, 3:33 PM Reginald Beardsley via <pulaskite= [email protected]> wrote: Erik,
Thanks for the video link.
SCAMP is not decodable by ear or sent with a key. It's an RTTY protocol. Very cool, and really well suited to overnight message transfer at very low power levels. However, it's also narrow BW.
My objective is to create a CW carrier which has a fixed BW and is selectable as a discreet CW channel even though it's one of many operating in the same spectrum segment.
Have Fun!
Reg
SCAMP is a mode that reminds of what it sounds like you're trying to accomplish here. Besides that there's Ebnaut, and WOLF - though those have different requirements for a transmitter.
Any linear encoding/decoding method boils down to which subspace does the signal live in, and which does the noise live in.? The extent of the overlap of the two determines the error probability.? If the signal and noise are described by Gaussian statistics, then the noise is completely described by its second-order statistics, and the ratio of the variance of the signal estimate to that of the noise in that estimate is the signal-to-noise ratio.? If the statistics are not Gaussian, but still have second order statistics, one can still get a SNR, though it does not directly map to an error probability.
When real channels are encountered, and one gets burst errors, impulse noise, and the like, error correcting codes can help reduce the probability of decoding error at the expense of greatly increased processing and often increased latency.?
If you're trying to produce a Morse-like channel, what are the qualities of a Morse channel, and what are the qualities to be preserved in the Morse-like channel??? Long latency removes the "immediacy" of communication, in that one must wait for a long decoding interval before one can respond.? Also, what part of Morse is preserved?? Should the information communicated be directly the dits, dahs, intraelement, and interelement pauses?? Should letters or words be communicated?? Should the timing of the sender be exactly preserved, or simplified to 1, 3, or 7 dit lengths??
For example, lets say you have these symbols: a "no symbol" symbol, a dit, a dah, a 1 dit length pause, a 3 dit length pause, and a 7 dit length pause.? Lets round it up to 8 symbols so that it is a power of two.? If you want the symbols to be orthogonal and time-invariant (no synchronization required) you can use 8FSK.? If time-invariant orthogonality is not necessary, you could use, for example, a Walsh-Hadamard code of 8 BPSK/BFSK symbols (see matrix below).? You can reserve one of the symbols as a sync code, for example the uniform symbol, and send that one three times, with the symbol in the middle with inverted phase (++++++++ -------- ++++++++).? The bit edges could be used for synchronization.? Alternatively, use BFSK if the channel has a very unstable phase.
![image.png]() Decoding would be as simple as correlating the received code against all 8 code words and keeping the code word with the highest correlation.? This would be an inefficient but fairly robust and easy to implement linear code.? A similar code was used on the Mariner mission.? It would also keep latency relatively low.
Dan
On Thu, Jun 20, 2024 at 2:49?PM Reginald Beardsley via <pulaskite= [email protected]> wrote: Well, that should have been CDMA, not TDMA :-(
I've attached a short proof of the mathematics.? It assumes synchronization, but I left out that detail to keep it to
a single page.
The objective is to increase the time * power * bandwidth product using DSSS to increase the BW term.
Have Fun!
Reg
|
Daniel,
Is this correct? I saw no mention of it anything on the RFBitbanger that I read.
Have Fun!
Reg
On Monday, June 24, 2024 at 07:14:23 PM CDT, Erik Nelson <erik.nels0n99@...> wrote:
Hi Reg,
I believe there's still an OOK based submode of SCAMP included, not just the 2FSK. These links should go into more detail:
On Sat, Jun 22, 2024, 3:33 PM Reginald Beardsley via <pulaskite= [email protected]> wrote: Erik,
Thanks for the video link.
SCAMP is not decodable by ear or sent with a key. It's an RTTY protocol. Very cool, and really well suited to overnight message transfer at very low power levels. However, it's also narrow BW.
My objective is to create a CW carrier which has a fixed BW and is selectable as a discreet CW channel even though it's one of many operating in the same spectrum segment.
Have Fun!
Reg
SCAMP is a mode that reminds of what it sounds like you're trying to accomplish here. Besides that there's Ebnaut, and WOLF - though those have different requirements for a transmitter.
Any linear encoding/decoding method boils down to which subspace does the signal live in, and which does the noise live in.? The extent of the overlap of the two determines the error probability.? If the signal and noise are described by Gaussian statistics, then the noise is completely described by its second-order statistics, and the ratio of the variance of the signal estimate to that of the noise in that estimate is the signal-to-noise ratio.? If the statistics are not Gaussian, but still have second order statistics, one can still get a SNR, though it does not directly map to an error probability.
When real channels are encountered, and one gets burst errors, impulse noise, and the like, error correcting codes can help reduce the probability of decoding error at the expense of greatly increased processing and often increased latency.?
If you're trying to produce a Morse-like channel, what are the qualities of a Morse channel, and what are the qualities to be preserved in the Morse-like channel??? Long latency removes the "immediacy" of communication, in that one must wait for a long decoding interval before one can respond.? Also, what part of Morse is preserved?? Should the information communicated be directly the dits, dahs, intraelement, and interelement pauses?? Should letters or words be communicated?? Should the timing of the sender be exactly preserved, or simplified to 1, 3, or 7 dit lengths??
For example, lets say you have these symbols: a "no symbol" symbol, a dit, a dah, a 1 dit length pause, a 3 dit length pause, and a 7 dit length pause.? Lets round it up to 8 symbols so that it is a power of two.? If you want the symbols to be orthogonal and time-invariant (no synchronization required) you can use 8FSK.? If time-invariant orthogonality is not necessary, you could use, for example, a Walsh-Hadamard code of 8 BPSK/BFSK symbols (see matrix below).? You can reserve one of the symbols as a sync code, for example the uniform symbol, and send that one three times, with the symbol in the middle with inverted phase (++++++++ -------- ++++++++).? The bit edges could be used for synchronization.? Alternatively, use BFSK if the channel has a very unstable phase.
![image.png]() Decoding would be as simple as correlating the received code against all 8 code words and keeping the code word with the highest correlation.? This would be an inefficient but fairly robust and easy to implement linear code.? A similar code was used on the Mariner mission.? It would also keep latency relatively low.
Dan
On Thu, Jun 20, 2024 at 2:49?PM Reginald Beardsley via <pulaskite= [email protected]> wrote: Well, that should have been CDMA, not TDMA :-(
I've attached a short proof of the mathematics.? It assumes synchronization, but I left out that detail to keep it to
a single page.
The objective is to increase the time * power * bandwidth product using DSSS to increase the BW term.
Have Fun!
Reg
|
FWIW
My goal in this thread is to clearly state the mathematics. I taught myself compressive sensing in complete isolation. It took me 3 years of continuous effort in large part because I had no one with whom to discuss the subject.
The mathematics of DSSS is moderately advanced and moving from author to author it is painfully easy to misinterpret what is being said because of minor nuances of notation and naming. As this is not as daunting as compressive sensing, I'm hoping that someone else has read and understands the math well enough to catch misunderstandings on my part.
Aside from Shannon, section 5.7 of:
Spread Spectrum Communications Handbook
Simon et al
Revised Edition
McGraw-Hill 1994
explicitly treats Direct Sequence Multiple Access systems such as I am proposing. Gold originally discussed this concept in a 1967 paper.
The processing gain for 1000 Hz BPSK modulation and a 100 ms dit is 10 dB c.f. middle of p. 6 in Simon et al. That and a 5x increase in the number of CW stations which can operate in 1 kHz band segment seem very attractive to me.
Have Fun!
Reg
|
On Fri, Jun 21, 2024 at 03:53 PM, Daniel Marks wrote: Any linear encoding/decoding method boils down to which subspace does the
signal live in, and which does the noise live in. The extent of the
overlap of the two determines the error probability. If the signal and
noise are described by Gaussian statistics, then the noise is completely
described by its second-order statistics, and the ratio of the variance of
the signal estimate to that of the noise in that estimate is the
signal-to-noise ratio. If the statistics are not Gaussian, but still have
second order statistics, one can still get a SNR, though it does not
directly map to an error probability.
Daniel, I am troubled by your assertion that one cannot determine an error probability unless both processes are Gaussian because the independence of random variables requires that p(x,y) = p(x)p(y). The Gaussian case is so trivial and invoked so often I refer to it as "sprinkling Gauss water on the problem". I have observed it being invoked in many cases where there was no justification and some where it was provably wrong. But the independence of random processes imposes no constraint on the distributions that I am aware of. Would you be so kind as to explain your reasoning? Have Fun! Reg
|
Erik Nelson