Differential PSK should be more reliable in the presence of frequency drift and
Doppler spread. There are two ways to do this: 1) compare the phase with the
previous phase of the same subcarrier or 2) compare the phase with the phase of
the next higher or lower subcarrier. In the first case, the first symbol
transmitted is always all zeroes. In the second case, there would have to be at
least one pilot subcarrier that is unmodulated. If you want pilot subcarriers,
it should be possible to put them 62.5 Hz above and below the outermost data
subcarriers as they take no extra space if they are not modulated.
A good way to do FEC is to use trellis-coded modulation (TCM). One bit is added
to the data stream for each subcarrier. This, 1 data bit is sent using QPSK and
2 data bits are sent using 8PSK. The advantage of sending the data and ECC bits
on one subcarrier is that the error-correcting code can be designed so that no
extra bandwith is needed and that the addition of the extra bit actually
decreases the required SNR rather than increasing it as you would first expect
by increasing the number of points in the constellation. Ungerboek came up with
a set of codes that can decrease the required SNR by 3-6 dB (with no fading)
when going from QPSK with no ECC to 8PSK with ECC. The improvement is larger
when fading occurs.
The amount of improvement provided by TCM depends on the complexity of the
state machine used to generate the ECC bit. However, a simple algorithm with 4
states provides a 3 dB improvement. A Viterbi decoder is used to calculate the
most probable set of state transitions that the incoming signal has taken from
symbol to symbol and then backtracks to determine the most likely combination
over an entire data frame. It can also make decisions based on the actual value
of the incoming signal rather than on 3 already decoded buts. This adds another
2 dB of improvement.
Its probably useful to place the audio subcarrier frequencies in the 500-1000
Hz range or higher so that harmonics of low frequency subcarriers don't
interfere with higher-frequency subcarriers.
73,
John
KD6OZH
----- Original Message -----
From: Rud Merriam
To: digitalradio@yahoogroups.com
Sent: Wednesday, October 24, 2007 10:03 UTC
Subject: [digitalradio] OFDM Proposal: Details
For your amusement and consternation here are my latest thoughts on doing an
OFDM protocol.
Symbol rate: 62.5 Hz (128 samples @ 8000 Hz)
Guard interval: 2, 4, 8 ms adaptive to conditions
Subchannels: 8 (62.5 125 187.5 250 312.5 375 437.5 500)
Bandwidth: 437.5 Hz
Raw BPS: 1778, 1600, 1333 adaptive (guard band change)
Base frequency: undetermined
MODULATION (somewhat firm)
Waveform: DQPSK with constellation at 45, 135, 225, 315 degrees
Generation: 8 separate generators providing continuous waves through the
guard bands
Phase change: start of symbol period
Shaping: post generation raised cosine over symbol and guard period
DEMODULATION (somewhat speculative)
FT: 128 bin every 32 samples for locating subchannels
Synchronization: square of subchannels identified by FT
to locate bottom subchannel by 125 Hz signal
Frequency drift: subchannel selection based on output of synchronization
Phase detection: phase averaged over symbol period,
differential with last symbol
A main goal is to keep the bandwidth within 500 Hz.
The symbol rate is as suggested by John KD6OZH. First testing will probably
be with his 8 ms guard band but I would like to make it adaptive to short that
period if multipath conditions allow.
DQPSK to get more throughput and because getting the absolute phase is a
challenge. Any suggestion to use absolute phase would be appreciated since that
gains a couple dB.
The Fourier transform is mainly to identify the potential subchannel
locations to allow adjusting for frequency drift. Once high energy bins are
determined the signal is filtered at various of those frequencies and the
square used to detect the doubled lowest frequency (125 Hz). That also locates
the symbol period for synchronization. Actually, the possible frequency
includes the guard band so it may be one of three values. By determining that
value the guard band period is also determined and the actual guard band
removed.
Rud Merriam K5RUD
ARES AEC Montgomery County, TX
http://TheHamNetwork.net
