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README_fsk

A FSK modem with a non-coherent demodulator. Performance is within a fraction of a dB of ideal. The demodulator automagically estimates the tone frequencies and tracks frequency drift.

Here is a typical Bit Error Rate (BER) versus Eb/No curve:

Note how close the theory line is to measured performance.

This modem can demodulate FSK signals that sound like this sample; and is used to receive images from the edge of space:

Credits

The Octave version of the modem was developed by David Rowe. Brady O'Brien ported the modem to C, and wrote the C/Octave tests. The modem is being maintained by David Rowe. Mark Jessop has helped improve the modem operation by testing against various balloon telemtry waveforms. Bill Cowley has developed the Log Likelihood Ratio (LLR) algorithms for 4FSK.

Quickstart

Build codec2:

$ cd codec2 && mkdir build_linux && cmake .. && make

Generate 1000 test bits, modulate them using 2FSK using a 8000 Hz sample rate, 100 bits/s, play on your sound card:
```
$ cd ~/codec2/build_linux/src
$ ./fsk_get_test_bits - 1000 | ./fsk_mod 2 8000 100 1200 1200 - - | aplay -f S16_LE
```
The low tone frequency is 1200Hz, and the upper tone 1200 + 1200 = 2400Hz.

Add the demodulator and measure the bit error rate over 10,000 bits of 100 bit/s 2FSK:

$ ./fsk_get_test_bits - 10000 | ./fsk_mod 2 8000 100 1200 100 - - | ./fsk_demod 2 8000 100 - - | ./fsk_put_test_bits -
<snip>
[0099] BER 0.000, bits tested   9900, bit errors    0
PASS

We get a Bit Error Rate (BER) of 0, as there is no channel noise to induce bit errors.

Same thing but this time with 4FSK, and less verbose output:

$ ./fsk_get_test_bits - 10000 | ./fsk_mod 4 8000 100 1200 100 - - | ./fsk_demod 4 8000 100 - - | ./fsk_put_test_bits -q -
<snip>
[0099] BER 0.000, bits tested   9900, bit errors    0
PASS

Lets add some channel noise:
```
$ ./fsk_get_test_bits - 10000 | ./fsk_mod 2 8000 100 1200 100 - - | ./cohpsk_ch - - -26 --Fs 8000 | ./fsk_demod 2 8000 100 - - | ./fsk_put_test_bits -b 0.015 -
<snip>
SNR3k(dB): -5.76 C/No: 29.0 PAPR:  3.0 
[0099] BER 0.010, bits tested   9900, bit errors  103
PASS
```
The cohpsk_ch utility takes the FSK modulator signal, and adds calibrated noise to it (the -26 value specifies the noise). Try changing the noise level, and note how the Bit Error Rate (BER) changes. The BER is 0.01, which is right on theory for this sort of FSK demodulator at this SNR (2FSK non-coherent demodulator Eb/No=9dB).

The SNR is calculated using the signal power divided by the noise power in 3000 Hz. The C/No value is the same thing, but uses a noise bandwidth of 1 Hz. There is less noise power when you look at just 1Hz, so C/No is higher. Peak to Average Power ratio (PAPR) is 3dB as a FSK signal is just a single sine wave, and a sine wave peak is 3dB higher than it's average.

You can visualise the C modem operation with a companion python script, for example:

$ ./fsk_get_test_bits - 10000 | ./fsk_mod -p 10 4 8000 400 400 400 - - | ./fsk_demod -p 10 -t1 4 8000 400 - /dev/null 2>stats.txt
$ python ../../octave/plot_fsk_demod_stats.py stats.txt

Send some digital voice using FSK at 800 bits/s, and try the two 2400 bits/s FSK modes:

$ ./freedv_tx 800XA ../../raw/ve9qrp.raw - | ./freedv_rx 800XA - - -vv | aplay -f S16_LE
$ ./freedv_tx 2400A ../../raw/ve9qrp.raw - | ./freedv_rx 2400A - - -vv | aplay -f S16_LE
$ ./freedv_tx 2400B ../../raw/ve9qrp.raw - | ./freedv_rx 2400B - - -vv | aplay -f S16_LE

LDPC encoded 4FSK, with framing:

$ cd ~/codec2/build_linux/src
$ ./ldpc_enc /dev/zero - --code H_256_512_4 --testframes 200 |
  ./framer - - 512 5186 | ./fsk_mod 4 8000 100 1000 100 - - |
  ./cohpsk_ch - - -24 --Fs 8000  |
  ./fsk_demod -s 4 8000 100 - - |
  ./deframer - - 512 5186  |
  ./ldpc_dec - /dev/null --code H_256_512_4 --testframes
<snip>
SNR3k(dB): -7.74 C/No: 27.0 PAPR:  3.0 
Raw   Tbits: 100352 Terr:   6701 BER: 0.067
Coded Tbits:  50176 Terr:    139 BER: 0.003
      Tpkts:    196 Tper:      4 PER: 0.020

In this example the unique word is the 16 bit sequence 5186. See also several ctests using these application. Other codes are also available:

$ ./ldpc_enc --listcodes

H2064_516_sparse     rate 0.80 (2580,2064) 
HRA_112_112          rate 0.50 (224,112) 
HRAb_396_504         rate 0.79 (504,396) 
H_256_768            rate 0.33 (768,256) 
H_256_512_4          rate 0.50 (512,256) 
HRAa_1536_512        rate 0.75 (2048,1536) 
H_128_256_5          rate 0.50 (256,128)

If you change the code you also need to change the frameSizeBits argument in framer/deframer (512 in the example above).

The FSK/LDPC/framer steps above have been combined in a FreeDV API mode. See "FSK LDPC Raw Data Mode" in README_data.md.

FSK modem C files in codec2/src:

File	Description
fsk.c/fsk.h	core FSK modem library
fsk_mod.c	command line modulator
fsk_demod.c	command line demodulator
fsk_get_test_bits.c	source of test bits
fsk_put_test_bits.c	test bit sync, counts bit errors and packet errors
fsk_mod_ext_vco.c	modulator that uses an external FSK oscillator
framer.c	adds a unique word to a frame of bits to implement frame sync for LDPC codewords
deframer.c	locates and strips a unique word to implement frame sync for LDPC codewords
tollr.c	converts bits to LLRs for testing LDPC framing

GNU Octave files in codec2/octave:

File	Description
fsk_lib.m	Core FSK modem library
fsk_lib_demo.m	A demonstration of fsk_lib, runs a single point BER test
fsk_demod_file.m	Demodulates FSK signals from a file, useful for debugging FSK waveforms
fsk_lock_down.m	simulations to support the "lock down" low SNR waveform
tfsk.m	automated test that compares the C and Octave versions of the modem
fsk_cml.m	Symbol rate experiments with FSK modem LLR estimation and LDPC
fsk_cml_sam.m	Sample rate experiments with FSK modem LLR estimation and LDPC
fsk_llr_plot.m	Plots curves from fsk_cml.m & fsk_cml_sam.m
fsk_lib_ldpc_demo.m	CML library LLR routines and LDPC codes with fsk_lib.m

You can run many of them from the Octave command line:

$ octave --no-gui
octave:1> fsk_lib_demo

A suite of automated ctests that exercise the C and Octave code:

$ cd ~/codec2/build_linux
$ ctest -R test_fsk
1/9 Test #39: test_fsk_lib ......................   Passed    3.37 sec
3/9 Test #41: test_fsk_modem_octave_port ........   Passed    4.17 sec
4/9 Test #42: test_fsk_modem_mod_demod ..........   Passed    0.06 sec
5/9 Test #43: test_fsk_2fsk_ber .................   Passed    0.24 sec
6/9 Test #44: test_fsk_4fsk_ber .................   Passed    0.12 sec
7/9 Test #45: test_fsk_4fsk_ber_negative_freq ...   Passed    0.07 sec
8/9 Test #46: test_fsk_4fsk_lockdown ............   Passed    2.84 sec
9/9 Test #47: test_fsk_vhf_framer ...............   Passed    0.06 sec

These are written in codec2/CmakeLists.txt, inspect them to find out how we test the modem.

fsk_demod_file.m is useful for peering inside the modem, for example when debugging.

$ cd ~/codec2/build_linux/src
$ ./fsk_get_test_bits - 1000 | ./fsk_mod 2 8000 100 1000 1000 - ../../octave/fsk.s16
$ octave --no-gui
octave:1> fsk_demod_file("fsk.s16",format="s16",8000,100,2)

8.9 KiB Czysty Wina Historia

README_fsk

Credits

Quickstart

Further Reading

8.9 KiB

Czysty Wina Historia