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.
-glen
On 6/10/2017 2:38 PM, David Rowe wrote:
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 Rowe <da...@rowetel.com> wrote:
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
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On 6/10/2017 5:01 PM, Adrian Musceac wrote:
On 10/6/17, glen english <g...@cortexrf.com.au> 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
????
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
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