OFDM MODEM

Quick start:

Create file uncoded.dat with 2048 bits of random data:

dd if=/dev/urandom of=uncoded.dat bs=1 count=256

Encode file uncoded.dat to encoded.wav WAV audio file with 48000 Hz sample rate, 16 bits and only 1 (real) channel:

./encode encoded.wav 48000 16 1 1500 ANONYMOUS QAM16 1/2 short uncoded.dat

Start recording to recorded.wav audio file and stop after 5 seconds:

sox -d -c 1 -e float recorded.wav

Start playing encoded.wav audio file:

play encoded.wav

Decode recorded.wav audio file to decoded.dat file:

./decode recorded.wav decoded.dat

Compare original uncoded.dat with decoded.dat:

diff -s uncoded.dat decoded.dat

Stream Audio

This currently works on macOS and Linux only: Stream live audio into the decoder:

sox -q -d -c 1 -e float -t wav - | ./decode - decoded.dat

Supported Modes

All modes need a bandwidth of 2400 Hz and there are two frame sizes.

These are the durations for each differential modulation scheme:

Modulation	Short	Normal
DBPSK	1.5s	2.6s
DQPSK	1.0s	2.6s
D8PSK	1.9s	3.4s

And these are the durations for each coherent modulation scheme:

Modulation	Short	Normal
QAM16	1.0s	2.6s
QAM64	1.9s	3.4s
QAM256	1.5s	2.6s
QAM1024	2.2s	4.0s
QAM4096	1.9s	3.4s

These are the numbers for the short modes with a 1/2 code rate:

Modulation	Payload	Bitrate
DBPSK	128B	0.7kb/s
DQPSK	128B	1.1kb/s
D8PSK	512B	2.1kb/s
QAM16	256B	2.1kb/s
QAM64	1024B	4.3kb/s
QAM256	1024B	5.4kb/s
QAM1024	2048B	7.5kb/s
QAM4096	2048B	8.6kb/s

These are the numbers for the normal modes with a 1/2 code rate:

Modulation	Payload	Bitrate
DBPSK	256B	0.8kb/s
DQPSK	512B	1.6kb/s
D8PSK	1024B	2.4kb/s
QAM16	1024B	3.2kb/s
QAM64	2048B	4.8kb/s
QAM256	2048B	6.3kb/s
QAM1024	4096B	8.3kb/s
QAM4096	4096B	9.6kb/s

These are the numbers for the short modes with a 2/3 code rate:

Modulation	Payload	Bitrate
DBPSK	171B	0.9kb/s
DQPSK	171B	1.4kb/s
D8PSK	684B	2.9kb/s
QAM16	342B	2.9kb/s
QAM64	1368B	5.7kb/s
QAM256	1368B	7.3kb/s
QAM1024	2736B	10.0kb/s
QAM4096	2736B	11.4kb/s

These are the numbers for the normal modes with a 2/3 code rate:

Modulation	Payload	Bitrate
DBPSK	342B	1.1kb/s
DQPSK	684B	2.1kb/s
D8PSK	1368B	3.2kb/s
QAM16	1368B	4.2kb/s
QAM64	2736B	6.4kb/s
QAM256	2736B	8.4kb/s
QAM1024	5472B	11.0kb/s
QAM4096	5472B	12.8kb/s

These are the numbers for the short modes with a 3/4 code rate:

Modulation	Payload	Bitrate
DBPSK	192B	1.0kb/s
DQPSK	192B	1.6kb/s
D8PSK	768B	3.2kb/s
QAM16	384B	3.2kb/s
QAM64	1536B	6.4kb/s
QAM256	1536B	8.2kb/s
QAM1024	3072B	11.2kb/s
QAM4096	3072B	12.8kb/s

These are the numbers for the normal modes with a 3/4 code rate:

Modulation	Payload	Bitrate
DBPSK	384B	1.2kb/s
DQPSK	768B	2.4kb/s
D8PSK	1536B	3.6kb/s
QAM16	1536B	4.7kb/s
QAM64	3072B	7.2kb/s
QAM256	3072B	9.5kb/s
QAM1024	6144B	12.4kb/s
QAM4096	6144B	14.4kb/s

These are the numbers for the short modes with a 5/6 code rate:

Modulation	Payload	Bitrate
DBPSK	213B	1.1kb/s
DQPSK	213B	1.8kb/s
D8PSK	852B	3.6kb/s
QAM16	426B	3.6kb/s
QAM64	1704B	7.1kb/s
QAM256	1704B	9.1kb/s
QAM1024	3408B	12.5kb/s
QAM4096	3408B	14.2kb/s

These are the numbers for the normal modes with a 5/6 code rate:

Modulation	Payload	Bitrate
DBPSK	426B	1.3kb/s
DQPSK	852B	2.6kb/s
D8PSK	1704B	4.0kb/s
QAM16	1704B	5.2kb/s
QAM64	3408B	8.0kb/s
QAM256	3408B	10.5kb/s
QAM1024	6816B	13.8kb/s
QAM4096	6816B	16.0kb/s

Simulating

Prerequisite: disorders

Encode uncoded.dat to analytic audio signal, add multipath, CFO, SFO, AWGN, decode and compare:

./encode - 48000 16 2 1500 ANONYMOUS QAM16 1/2 short uncoded.dat | ../disorders/multipath - - ../disorders/multipath.txt 10 | ../disorders/cfo - - 234.567 | ../disorders/sfo - - 147 | ../disorders/awgn - - -20 | ./decode - - | diff -q -s uncoded.dat -

Reading

• Robust frequency and timing synchronization for OFDM
  by Timothy M. Schmidl and Donald C. Cox - 1997
• On Timing Offset Estimation for OFDM Systems
  by H. Minn, M. Zeng, and V. K. Bhargava - 2000