Re: [Freetel-codec2] why 4, and fsk, psk redux
Thanks Glen for taking the time to explain that in such detail, it's useful to have it posted to a mailing list as a google-able future reference. I've attached a simple summary in PNG form, extracted from this presentation: http://www.rowetel.com/?p=4279 Cheers, David On 08/10/17 17:12, glen english wrote: Maybe I need to summarize a bit, and remove the ambiguities of the argument, as I think what I wrote had a few too many assumptions of argument. and I made a few mistakes , I was a little tired when I wrote , mixing coherent/incoherent spacings etc..(I don't run simulations, I just do the math) . Please allow me to try again : the nFSK debate very much revolves around whether it is bandwidth constrained , or not. If it is not bandwidth constrained, the higher orders nFSK (8,16,32FSK etc) will win because they swap sensitivity for bandwidth at a log2 rate. For a fixed total occupied bandwidth, linear incoherent demodulation, 4FSK has a 3dB sensitivity advantage over 2FSK. Simply put, We have 2x the number of receivers (tone receivers) each with half the bandwidth. Each tone receiver is a OOK (on off keyed) signal. The null to null BW of each of the FSK tones is the symbol rate (the fourier transform of a rectangular pulse train) . They must be spaced at a minimum by 1/T, the symbol rate so they there is zero cross correlation between the demodulator filters in the case of incoherent detection. Assuming we have plenty of bandwidth , it is worthwhile to keep increasing the number of tones. Just like WSJT variants , MFSK16 etc The situation is very different for a non linear discriminator detection (FM demod) IE DMR,P25. In this case , assuming a constant IF and baseband bandwidth : -distance in voltage (deviation) DIRECTLY affects SNR. Thus a 2 level modulation like 2FSK requires at least 6dB less baseband signal to noise than 4FSK . (note that the relationship between input carrier SNR is different to the demodulated detected baseband SNR due to the limiter action). - This translates into a system requiring more signal to noise thus lower sensitivity and more susceptibility to frequency selective multipath (that causes severe baseband distortions) . It's that multipath that hurts. - The IF noise bandwidth is greater for the FM discriminator system . With 4FSK, for the linear incoherent system., the noise bandwidth (of the tone filter) goes DOWN from 2FSK to 4FSK- (half), whereas in the non linear FM discriminator usage, the noise bandwidth of the limiter is unchanged from 2FSK to 4FSK . The limiter/FM demod wont produce useful baseband until at least 7dB CNR in the ~ 9kHz IF bandwidth Whereas a 4FSK linear system (2FdT=1) , 4800 symbols per second, with 4800 Hz BW per tone, while it would have wider bandwidth, the noise bandwidth is ~3dB less , and approx 6dB higher CNR requirement. The extra CNR requirement depends heavily on the modulation index because of the non linear demodulator. That is why DMR/P25 perform so poorly compared to the linear 4FSK system . ahh but the narrow bandwidth and simplicity. Now BPSK versus 4FSK: (incoherent) The bandwidth of 4FSK is double. For 1000 bps, that's 4 tones spaced 1kHz. Versus BPSK having a single carrier of 1kHz wide. However, modulation bandwidth filtering is required to keep the 2nd BPSK energy lobe in check which degrades performance. The individual OOK 4FSK tone receivers each have a bandwidth of 500Hz, which is half the BPSK bandwidth... With 4FSK, because there is an equal probability that if an incorrect decision (tone) is made, it could be equality likely to be any of the other 3 tones, more bits are affected - as we have parallel receivers with nFSK, and thus n x the probability of error in each of the tone receivers. The error rate is higher when considering all the tone receivers, as each of them is contributing an error into the symbol mapped digit. this is often overlooked. How much, I'll need to find/ do the math. glen On 8/10/2017 3:27 PM, glen english wrote: seems I replied to David and not the group yesterday re sent! Hi David Firstly I will clarify, my reference of poorer mobile channel performance for 4FSK compared with 2FSK pertains to incoherent, non linear discriminator detection . (4FSK is better than 2FSK for linear orthogonal -agreed) Now, lets get onto DMR first you say "For DRM/C4FSK they _are_ bandwidth constrained due to the high bit rate of AMBE/standards" Not really, they are bandwidth constrained because they have to fit in a 12.5 kHz channel ! In that usage, the channel bandwidth drives the codec and the modem The low SNR performance is poor due to the limiter / FM demodulator combination and FM clicks, and that the FM noise triangle is rather suboptimal . 4FSK is required because with 9600 bps there would never make the bandwidth with 2FSK. I'll go through this from the basics so everyone can understand. Now for the simple, FM discriminator slicer
Re: [Freetel-codec2] why 4, and fsk, psk redux
Maybe I need to summarize a bit, and remove the ambiguities of the argument, as I think what I wrote had a few too many assumptions of argument. and I made a few mistakes , I was a little tired when I wrote , mixing coherent/incoherent spacings etc..(I don't run simulations, I just do the math) . Please allow me to try again : the nFSK debate very much revolves around whether it is bandwidth constrained , or not. If it is not bandwidth constrained, the higher orders nFSK (8,16,32FSK etc) will win because they swap sensitivity for bandwidth at a log2 rate. For a fixed total occupied bandwidth, linear incoherent demodulation, 4FSK has a 3dB sensitivity advantage over 2FSK. Simply put, We have 2x the number of receivers (tone receivers) each with half the bandwidth. Each tone receiver is a OOK (on off keyed) signal. The null to null BW of each of the FSK tones is the symbol rate (the fourier transform of a rectangular pulse train) . They must be spaced at a minimum by 1/T, the symbol rate so they there is zero cross correlation between the demodulator filters in the case of incoherent detection. Assuming we have plenty of bandwidth , it is worthwhile to keep increasing the number of tones. Just like WSJT variants , MFSK16 etc The situation is very different for a non linear discriminator detection (FM demod) IE DMR,P25. In this case , assuming a constant IF and baseband bandwidth : -distance in voltage (deviation) DIRECTLY affects SNR. Thus a 2 level modulation like 2FSK requires at least 6dB less baseband signal to noise than 4FSK . (note that the relationship between input carrier SNR is different to the demodulated detected baseband SNR due to the limiter action). - This translates into a system requiring more signal to noise thus lower sensitivity and more susceptibility to frequency selective multipath (that causes severe baseband distortions) . It's that multipath that hurts. - The IF noise bandwidth is greater for the FM discriminator system . With 4FSK, for the linear incoherent system., the noise bandwidth (of the tone filter) goes DOWN from 2FSK to 4FSK- (half), whereas in the non linear FM discriminator usage, the noise bandwidth of the limiter is unchanged from 2FSK to 4FSK . The limiter/FM demod wont produce useful baseband until at least 7dB CNR in the ~ 9kHz IF bandwidth Whereas a 4FSK linear system (2FdT=1) , 4800 symbols per second, with 4800 Hz BW per tone, while it would have wider bandwidth, the noise bandwidth is ~3dB less , and approx 6dB higher CNR requirement. The extra CNR requirement depends heavily on the modulation index because of the non linear demodulator. That is why DMR/P25 perform so poorly compared to the linear 4FSK system . ahh but the narrow bandwidth and simplicity. Now BPSK versus 4FSK: (incoherent) The bandwidth of 4FSK is double. For 1000 bps, that's 4 tones spaced 1kHz. Versus BPSK having a single carrier of 1kHz wide. However, modulation bandwidth filtering is required to keep the 2nd BPSK energy lobe in check which degrades performance. The individual OOK 4FSK tone receivers each have a bandwidth of 500Hz, which is half the BPSK bandwidth... With 4FSK, because there is an equal probability that if an incorrect decision (tone) is made, it could be equality likely to be any of the other 3 tones, more bits are affected - as we have parallel receivers with nFSK, and thus n x the probability of error in each of the tone receivers. The error rate is higher when considering all the tone receivers, as each of them is contributing an error into the symbol mapped digit. this is often overlooked. How much, I'll need to find/ do the math. glen On 8/10/2017 3:27 PM, glen english wrote: > seems I replied to David and not the group yesterday > > re sent! > > > Hi David > > Firstly I will clarify, my reference of poorer mobile channel > performance for 4FSK compared with 2FSK pertains to incoherent, non > linear discriminator detection . (4FSK is better than 2FSK for linear > orthogonal -agreed) > > Now, lets get onto DMR first > > you say "For DRM/C4FSK they _are_ bandwidth constrained due to the high > bit rate of AMBE/standards" > > Not really, they are bandwidth constrained because they have to fit in a > 12.5 kHz channel ! > > In that usage, the channel bandwidth drives the codec and the modem > > The low SNR performance is poor due to the limiter / FM demodulator > combination and FM clicks, and that the FM noise triangle is rather > suboptimal . > > 4FSK is required because with 9600 bps there would never make the > bandwidth with 2FSK. > > I'll go through this from the basics so everyone can understand. > > Now for the simple, FM discriminator slicer detection case , which is in > general, the means of demodulation in many of the DMR/P25 radios > > For a given/fixed post detection bandwidth and peak deviation, > Incoherent FSK , discriminator detect, there are 4 levels to detect over > ± 1V peak detector output -
Re: [Freetel-codec2] why 4, and fsk, psk
seems I replied to David and not the group yesterday re sent! Hi David Firstly I will clarify, my reference of poorer mobile channel performance for 4FSK compared with 2FSK pertains to incoherent, non linear discriminator detection . (4FSK is better than 2FSK for linear orthogonal -agreed) Now, lets get onto DMR first you say "For DRM/C4FSK they _are_ bandwidth constrained due to the high bit rate of AMBE/standards" Not really, they are bandwidth constrained because they have to fit in a 12.5 kHz channel ! In that usage, the channel bandwidth drives the codec and the modem The low SNR performance is poor due to the limiter / FM demodulator combination and FM clicks, and that the FM noise triangle is rather suboptimal . 4FSK is required because with 9600 bps there would never make the bandwidth with 2FSK. I'll go through this from the basics so everyone can understand. Now for the simple, FM discriminator slicer detection case , which is in general, the means of demodulation in many of the DMR/P25 radios For a given/fixed post detection bandwidth and peak deviation, Incoherent FSK , discriminator detect, there are 4 levels to detect over ± 1V peak detector output - that is -1V, -0.333V, 0.333V, +1V. generally the deviation steps are non straight line (not as shown here for the simple illustration) . 2FSK, we have two levels represented, -1V and +1V, or 2V between the steps. IE 2V difference between levels rather than 0.666V 4FSK provides twice the bit rate so we have 3dB to put in there in favour of 4FSK, so the difference is more like 9.55-3 = 6.55dB When there is frequency selective multipath, the baseband distortion produced by the non linear demodulator chain is awful... it's not just a delayed ghost signal as many simplistic analysis discuss. The extra SNR requirement of 4FSK in this case, 6dB, is a impediment to low SNR, frequency selective channel cases with high baseband distortions (for the FM discriminator detection) and THIS is why most of the DMR/P25 4FSK systems perform so poorly. FM discriminator detection. They need lots of SNR ... Some of the newer radios and base stations use linear detection. (for everyone - David I am not trying to teach u how to suck eggs ) Now, back to orthogonal FSK , linearly incoherently demodulated , and for orthogonal FSK, the tone spacing must satisfy : 2 Fd T = 1,2,3... , this is in order to satisfy the condition of zero correlation between the tones over a bit period T, and thus minimum error probability. For a fixed SYMBOL rate, the bandwidth is proportional to the number of tones Now, as the number of tones is increased, the signalling speed increases Log2(n) For 4FSK, this is a special case Log2M = 2. When we double the number of tones from 2 to 4, we halve the symbol rate per tone and so we halve the bandwidth per tone (filter). The bandwidth per tone is half , but we have more tones , and are ahead of 2FSK , assuming a maximum likelihood decision making. 4FSK is the biggest bang for the buck. It's not so rosy for higher n , like 8, 16FSK log2M means in order to double the signalling speed, we need to quadruple the number of tones. for 1000bps, orthogonal incoherent FSK, M=1 (2.Fd.T = 1) for 2FSK, symbol rate = 1000 bps, BW= 1.5kHz . for 4FSK, symbol rate = 500 bps, BW = 1.75kHz - sweet spot. half the detection bandwidth, only 0.7dB more bandwidth So I put 4FSK as 2.3dB better than 2FSK. depends a bit on your definition of bandwidth. for 8FSK, symbol rate = 333 bps, BW = 1.83, for 16 FSK, symbol rate = 250bps , BW =2.375kHz for 32 FSK, symbol rate = 200 bps, BW = 3.5kHz so what is going on here ? look at log2 of the symbol rate which mirrors detection bandwidth of each tone. Sensitivity for a tone increases (due to narrowing bandwidth) but the number of them increases. We are swapping bandwidth for SNR, but with diminishing returns. This is what happens on the left hand side of the shannon curve ! Of course you can go on and swap bandwidth for SNR forever, but only with Log2(n) result... For orthogonal 4FSK, if the phase trajectory is inspected, it is not unlike O-QPSK... For BPSK, this is another topic...The BPSK argument is strongly influenced by what sort of filter you use. The 2nd lobe of a PSK signal contains significant energy (-13) and cannot be ignored (without reducing performance) . The 2nd lobe of MSK is -26. Coherent BPSK has in its advantage a lower error probability than 2FSK (3dB) because the orthogonal signalling methods have two sided noise power spectrums , where as a binary antipodal modulation can be one or the other (the noise power spectrum extended only one side of each decision) (I think that is how to describe it ..- David ?) The nFSK signal, the wrong decision for a maximum likelihood threshold decision maker (looking at the higher level from each frequency correlator) can be EQUALLY any one of the n-1 tones. Grey coding doesn't help you here. OK 4FSK ain't all bad.
Re: [Freetel-codec2] why 4, and fsk, psk
On 10/6/17, glen englishwrote: > Considering we are not bandwidth constrained, why is everyone so > enamoured with 4 level waveforms like 4FSK , When two level/ two state > waveforms like BPSK and 2FSK are far more robust in a mobile environment > > Hi Glen, I'll give you two of my reasons: 1. trellis encoding -> higher order modulation 2. for OFDMA with multiple carriers (not FSK of course), where you still need to fit inside the channel spacing allocation. Spectrum is not cheap :) Cheers, Adrian -- Check out the vibrant tech community on one of the world's most engaging tech sites, Slashdot.org! http://sdm.link/slashdot ___ Freetel-codec2 mailing list Freetel-codec2@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/freetel-codec2
Re: [Freetel-codec2] why 4, and fsk, psk
If implemented correctly, 4FSK gets you 3dB over 2FSK on an AWGN channel. The FSKs can use class C PAs. For DRM/C4FSK they _are_ bandwidth constrained due to the high bit rate of AMBE/standards (which is black box with a bit rate so they have no choice over). I presume this is the reason for poorly spaced 4FSK tones and a performance hit of 6-ish dB. Or maybe low SNR performance doesn't matter in the use-cases for those standards. Why is 2FSK more robust than 4FSK (both non-coherent demods) on a UHF/VHF mobile channel? - David On 06/10/17 10:57, glen english wrote: Considering we are not bandwidth constrained, why is everyone so enamoured with 4 level waveforms like 4FSK , When two level/ two state waveforms like BPSK and 2FSK are far more robust in a mobile environment Differential BPSK is an easy demod , 2FSK is also an easy demod. BPSK having the slight edge due to being a antipodal waveform compared to being an orthogonal waveform. (though the full 3dB gain (BER = 1e-04) of an antipodal waveform only occurs with coherent demod) . (gain at very low SNR closer to 2dB) complexity of a DBPSK incoherent demod and incoherent 2FSK demod are similar DBPSK leaves open the option of a highly productive coherent demod, and 2FSK leaves open the option of highly simplified demodulators (slicing FM demod). -glen Vk1xx On 6/10/2017 11:02 AM, Adrian Musceac wrote: Hi David, Thanks very much for the tips! Would you suggest that the matched filter approach is better for 4FSK as well? I am using it for 2FSK and it works well, it's just that being lazy I wanted to avoid too much complexity in the code for the 4FSK variant. Regarding PSK: I have several things to try and real world tests will show which one is more practical. Right now for PSK I am using Codec2 at 1400 bits as what I find a good compromise between quality and bitrate. This gives me just enough space for synchronization bits and other protocol data (which may span on multiple frames). I am considering moving down to 700 bits per second and I wanted to ask you if you think you will be making major changes to it's quality in the near future. This would give me 3 additional dB to play with, but at this point I don't think we can afford to have more than 1% errors per frame, as each bit carries a lot of information. I tried rate 1/2 convolutional encoding with real world tests and it seems to give an additional 2 dB of space. The advantage is that frame sizes are short, so we don't have large gaps when errors occur. On top of that, Viterbi soft symbol decoding and trellis to 8PSK add to the computational cost, which I have a low budget for. Best regards, Adrian On 10/6/17, David Rowewrote: Hi Adrian, It's very important to avoid using an analog FM demodulator with FSK - it's the reason C4FM/DMR are such a poor performers: http://www.rowetel.com/?p=3799 http://www.rowetel.com/?p=4279 At 1% BER, Eb/Nos reqd are roughly: 2FSK 9dB 4FSK 6dB PSK 4dB The PSK results are for coherent demodulation, which is hard to do without overhead (e.g. pilot symbols or a unique word). I suspect non-coherent PSK is worse than FSK, so not worth doing unless you are really concerned about bandwidth. The FSK results are for non-coherent demodulators which are really simple to implement and get real-world results right on ideal. Convolutional codes are a bit old hat - we're getting gd results on HF with short-ish LDPC codes. But best to sort out your uncoded demodulator performance first. Cheers, David On 05/10/17 20:05, Adrian Musceac wrote: Hi David, Thanks for the answer! I have just simulated a 2FSK modem on AWGN channel, but this time without using FM demodulation. It performs just like you said, ~2 dB worse than QPSK (at 5% frames dropped). This means that the FM demodulator I used for 2400A must be introducing some symbol errors. What I can't figure out is the 10 dB difference to analog FM. My experimental results (test in urban environment, with distances between 500 meters and 1 km between sender and receiver) show ~6 dB between QPSK and analog FM (with 2.5 kHz deviation) and no more than 4 dB between 4FSK and FM. Could the non-coherent demodulation explain this? I know I can obtain up to 6 dB SNR improvement by going to Codec2 700 bits/sec and using Viterbi soft symbol decoding, but I'd like to get the optimal results before. Would convolutional encoding in 2400A be worth considering? Thanks, Adrian -- Check out the vibrant tech community on one of the world's most engaging tech sites, Slashdot.org! http://sdm.link/slashdot ___ Freetel-codec2 mailing list Freetel-codec2@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/freetel-codec2 -- Check out the vibrant tech
Re: [Freetel-codec2] why 4, and fsk, psk
There was some neat AM designs a couple of years ago, but I think they all petered out last year. Narrow-band FM still remains king on VHF and up. I play around a little bit with an used FT-857d, but that's a Cadillac radio, and I use it mostly on HF. I think that's the problem with the current SSB radios, is that they throw in the kitchen sink. I think there would be a market for a single-band SSB rig designed for the whole 2 metre band. No FM capability. 25 Watts, highly stable, with PSK, and QAM modes and narrow/wideband codecs. A huge heat sink with attachment to wrap around your automobiles freon accumulator/dryer (that really cold wet thing under the hood) :-) Oops, I'm off on a tangent again... 73/Steve On Thu, Oct 5, 2017 at 7:27 PM, glen englishwrote: > Considering we are not bandwidth constrained, -- Check out the vibrant tech community on one of the world's most engaging tech sites, Slashdot.org! http://sdm.link/slashdot ___ Freetel-codec2 mailing list Freetel-codec2@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/freetel-codec2