> I think that we said the data rate was 30-50 bps in the meeting. The
> bandwidth will be determined by the rate of the error-correcting code.
> Phil needs to determine that. More coding makes for a wider signal which
> reduces the effect of spin modulation. However, it also means more
> processing in the SDX.
The signal bandwidth has no effect on spin modulation as the fades are
pretty much flat over frequency. So there's no frequency diversity and
no benefit to spectral spreading here. You need either space or time
diversity to get you through a spin fade, and that means either 1)
another pair of physically separate TX and RX antennas, and/or 2)
interleaving in combination with FEC coding.
As for optimal code rates, it depends on the modulation and especially
the type of demodulator and the channel. On a fully coherent channel
with fixed power you get steadily more capacity as bandwidth goes to
infinity. Most of the gain comes with relatively little excess bandwidth
and then you reach diminishing returns. Between 1 bit/sec/Hz and zero
bps/Hz (i.e., infinite bandwidth) the increase is only 1.6 dB.
Fully coherent means the receiver has perfect knowledge of carrier
phase. This doesn't come out of thin air. You can derive carrier phase
from the data itself, or you can dedicate some fraction of the
transmitter power to a reference pilot (carrier).
Deriving carrier phase from data is a non-linear squaring process. It
works well at high SNR, but breaks down at low SNRs. That means you
can't use it with strong, low-rate FEC codes, especially if the carrier
phase is changing rapidly and unpredictably as it is on a fading
channel. You have to put some power into a reference pilot that can be
tracked linearly, and that takes power away from the data.
The extreme form of deriving carrier phase from the data is non coherent
demodulation, e.g., the differentially coherent BPSK I used on AO-40. It
uses each symbol as the phase reference for the next. This responds very
quickly to the carrier phase changes that occur during a spin null, but
the squaring loss is very high.
The non coherent demodulator essentially has a threshold effect just
like a FM demodulator. Below some SNR, the output SNR falls much more
rapidly than the input SNR. Because a very low rate code puts very
little energy into each channel symbol, you fall below the demodulator
threshold and you lose more than you gain from the code.
So on a non coherent channel there's an optimum code rate. It depends on
the order of the modulation (binary, M-ary, etc) and the nature of the
fading, if any, but rate 1/3 to rate 1/2 is the usual rule of thumb. My
FEC scheme for AO-40, which I designed to be as strong as possible
against spin fading, was rate 0.4, i.e., rate 1/2 convolutional *
(160,128) Reed Solomon, i.e. 0.5 * (128/160) = 0.5 * 0.8 = 0.4.
In my AO-40 system I figure I lost about 3-4 dB because of my use of non
coherent BPSK, but that was the price I paid to deal with deep, rapid
spin fading. It's a trade off, so I really need to know whether fading
is going to be a serious problem here or not. If it will be some of the
time but not others, then perhaps we need two modes.
In practice, nobody seems to go lower than rate 1/6 on deep space
channels even when they don't fade and coherent demodulation is used.
The Cassini convolutional code is rate 1/6, and the lowest CCSDS
standard Turbo code is also rate 1/6. I wouldn't go any lower than this.
--Phil
