These techniques all end up using more bandwidth than a simple scheme,
and the larger bandwidth itself increase the N in SNR.
There is actually a theory for the case of idealised white noise and no
other degradation (both of which are likely to be assumed in the cases
previously discussed), that sets a theoretical limit to the error free
digital communication rate of channel, based on bandwidth and SNR. This
is the Shannon - Hartley theorem, and states that the capacity in bits
per second is:
bandwidth * log2 (1 + Signal / Noise)
Note that this formula still has a positive result even if the signal is
only minutely greater than zero.
The holy grail of communications coding is to get as close as possible
to this without having excessive latency.
Maybe a better figure of merit for these, "below the noise" digital
systems would be to quote the channel capacity as a percentage of the
Shannon limit. I think the system used for 5G mobile phones get very close.
One does have to be careful with bits per second, as I understand that
FT8 relies on some parts of transmissions carrying less bits than needed
to encode the characters in the standard code used, e.g. the number of
bits actually represented by a call sign is log2 (number of possible
callsigns) and the number encoded in FT8 is log2 (number of active FT8
callsigns).
--
David Woolley
Owner K2 06123
On 19/05/2019 19:15, Joe Subich, W4TV wrote:
There is one place that digital modes (like those by Joe Taylor and
associates) can improve the decoded SNR beyond simply reducing the
detection bandwidth. If the modulation/encoding supports N states
but the encoding only uses M of those states, the decoding software
can make use of the "sparse constellation" to recognize states that
are impacted by noise and select the "closest" valid state.
This "coding gain" can improve the overall SNR beyond that provided
simply by the "matched" (or optimal) noise bandwidth. However, with
all amateur modes (CW to FT8 & FT4) the majority of the SNR improvement
over SSB (or AM) is simply due to the use of optimal bandwidth to
reduce extraneous noise in the detector bandwidth. Even with SSB,
properly tailoring the IF bandwidth will make several dB difference
in the detected SNR. For example, a 2 KHz bandwidth (500 - 2500 Hz)
can provide significant improvement over a 2.8 KHz bandwidth (200 -
3000 Hz) under noisy conditions.
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