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

Stream audio out of the encoder:

./encode - 48000 32 1 1500 ANONYMOUS QAM16 1/2 short uncoded.dat | play -q -

Supported Modes

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

These are the durations for each modulation scheme:

Modulation	Short	Normal
BPSK	1.5s	2.6s
QPSK	1.0s	2.6s
8PSK	1.9s	3.4s
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
BPSK	128B	0.7kb/s
QPSK	128B	1.1kb/s
8PSK	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
BPSK	256B	0.8kb/s
QPSK	512B	1.6kb/s
8PSK	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
BPSK	171B	0.9kb/s
QPSK	171B	1.4kb/s
8PSK	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
BPSK	342B	1.1kb/s
QPSK	684B	2.1kb/s
8PSK	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
BPSK	192B	1.0kb/s
QPSK	192B	1.6kb/s
8PSK	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
BPSK	384B	1.2kb/s
QPSK	768B	2.4kb/s
8PSK	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
BPSK	213B	1.1kb/s
QPSK	213B	1.8kb/s
8PSK	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
BPSK	426B	1.3kb/s
QPSK	852B	2.6kb/s
8PSK	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 32 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