% gmsk.m
% David Rowe Dec 2014
%
-% GMSK modem simulation
+% GMSK modem implementation and simulations to test
+
%
% [X] plot eye diagram
% [X] BER curves with reas match to theoretical
% [X] coarse timing estimator (sync up to known test frames)
% [X] test with different coarse timing offsets
% [ ] file read/write interface
-% [ ] modify for 1200 bit/s (or any) operation, ie GMSK filter coeff generation
-% or re-sampling
+% [ ] refactor into tx/rx functions
+% [ ] modify for 1200 (or any) bit/s operation
+% + ie GMSK filter coeff generation
+% + or just re-sampling? e.g. ratio of Fs to Rs?
% [ ] way to measure input SNR to demod
+% + Maybe based on test tone/carrier from the other side?
+% + think about process ... total signal plus noise power? Increase power until S+N doubles?
+% [ ] generate curves for baseline modem and with sync algorithms
+% + used coarse sync code to remove need for knowing delays
% Filter coeffs From:
% https://github.com/on1arf/gmsk/blob/master/gmskmodem_codec2/API/a_dspstuff.h,
graphics_toolkit ("gnuplot");
fm;
-function gmsk_states = gmsk_init(gmsk_states)
+%
+% Functions that implement the GMSK modem ------------------------------------------------------
+%
+
+function gmsk_states = gmsk_init(gmsk_states, Rs)
% general
gmsk_states.Fs = 48000;
- gmsk_states.Rs = 4800;
+ gmsk_states.Rs = Rs;
M = gmsk_states.M = gmsk_states.Fs/gmsk_states.Rs;
global gmsk_mod_coeff;
global gmsk_demod_coeff;
+ gmsk_states.mod_coeff = (Rs/4800)*resample(gmsk_mod_coeff, 4800, Rs);
+ figure(12)
+ plot(gmsk_mod_coeff)
+ hold on;
+ plot(gmsk_states.mod_coeff,'g')
+ hold off;
% set up FM modulator
fm_states.Fs = gmsk_states.Fs;
fm_states.fc = 0;
- fm_max = fm_states.fm_max = 2400;
- fd = fm_states.fd = 1200;
+ fm_max = fm_states.fm_max = Rs/2;
+ fd = fm_states.fd = Rs/4;
fm_states.Ts = gmsk_states.M;
fm_states.pre_emp = fm_states.de_emp = 0;
fm_states.output_filter = 1;
gmsk_states.fm_states = analog_fm_init(fm_states);
- % configure delays for demod type
-
- [x i_mod] = max(gmsk_mod_coeff);
- [x i_demod] = max(gmsk_demod_coeff);
-
- if gmsk_states.coherent_demod
- gmsk_states.filter_delay = i_mod + i_mod;
- gmsk_states.Toff = -4;
- else
- gmsk_states.filter_delay = i_mod + i_demod + 100;
- gmsk_states.Toff = 3;
- end
-
- gmsk_states.dsam = dsam = gmsk_states.filter_delay;
-
endfunction
M = gmsk_states.M;
nsym = length(tx_bits);
nsam = nsym*M;
- global gmsk_mod_coeff;
% NRZ sequence of symbols
tx_symbols(1+(i-1)*M:i*M) = -1 + 2*tx_bits(i);
end
- tx_filt = filter(gmsk_mod_coeff, 1, tx_symbols);
+ tx_filt = filter(gmsk_states.mod_coeff, 1, tx_symbols);
+ figure(13)
+ clf
+ plot(tx_filt(1:M*10))
tx = analog_fm_mod(gmsk_states.fm_states, tx_filt);
endfunction
nsam = length(rx);
nsym = floor(nsam/M);
global gmsk_demod_coeff;
- global gmsk_mod_coeff;
wd = 2*pi*gmsk_states.fm_states.fd/gmsk_states.Fs;
- Toff = gmsk_states.Toff;
- dsam = gmsk_states.filter_delay;
if gmsk_states.coherent_demod
% matched filter
- rx_filt = filter(gmsk_mod_coeff, 1, rx);
+ rx_filt = filter(gmsk_states.mod_coeff, 1, rx);
% Property of MSK that re and im arms are sequences of 2T
% long symbols, can be demodulated like QPSK with matched filter
endfunction
+% Initial frequency offset estimation. Look for line a centre
+% frequency, which is the strongest component when ...101010... is
+% used to modulate the GMSK signal. Note just searching for a single
+% line will get false lock on random sine waves but that's OK for a
+% PoC. It could be improved by checking for other lines, or
+% demodulating the preamble and checking for bit errors.
+
function [freq_offset_est ratio] = gmsk_est_freq_offset(gmsk_states, rx, verbose)
Fs = gmsk_states.Fs;
Rs = gmsk_states.Rs;
f = fft(rx .* hanning(length(rx))', ndft);
f = fftshift(f);
- % Look for line a centre frequency, which is the strongest component
- % when 101010 .... is used to modulate the GMK signal. Note just
- % searching for a single line will get false lock on random sine
- % waves but that's OK for a PoC. It could be improved by checking
- % for other lines, or demodulating the preamble and checking for bit
- % errors.
-
- start_bin = 1+ Fs/2-Rs/2;
- stop_bin = start_bin + Rs;
+ start_bin = 1+ Fs/2-Rs/4;
+ stop_bin = start_bin + Rs/2;
[max_val max_bin] = max(abs(f(start_bin:stop_bin)));
- max_bin -= Rs/2 + 1;
+
+ max_bin -= Rs/4 + 1;
if verbose > 1
printf("ndft: %d start_bin: %d stop_bin: %d max_bin: %d\n", ndft, start_bin, stop_bin, max_bin);
end
subplot(211)
plot(rx,'+')
subplot(212)
- plot(-Rs/2:Rs/2, 20*log10(abs(f(start_bin:stop_bin))));
- axis([-Rs/2 Rs/2 0 80]);
+ plot(-Rs/4:Rs/4, 20*log10(abs(f(start_bin:stop_bin))));
+ axis([-Rs/4 Rs/4 0 80]);
end
endfunction
+%
+% Functions for Testing the GMSK modem --------------------------------------------------------
+%
function sim_out = gmsk_test(sim_in)
nsym = sim_in.nsym;
tx_bits(1:2:nsym) = 0;
[tx tx_filt tx_symbols] = gmsk_mod(gmsk_states, tx_bits);
nsam = length(tx);
- %tx_bits(1:10)
+
noise = sqrt(variance/2)*(randn(1,nsam) + j*randn(1,nsam));
rx = tx*exp(j*pi/2) + noise;
function run_gmsk_curves
sim_in.coherent_demod = 1;
- sim_in.nsym = 4800;
+ sim_in.nsym = 2400;
sim_in.EbNodB = 2:10;
sim_in.verbose = 1;
% [ ] extra stuff at begining/end for filter delays
function run_test_freq_offset
+ Rs = 4800;
verbose = 1;
aEbNodB = 6;
phase_offset = 0;
- freq_offset = 1025.3;
- timing_offset = 1207;
- sample_clock_offset_ppm = 500;
- nsym = 4800*4;
+ freq_offset = 0;
+ timing_offset = 0;
+ sample_clock_offset_ppm = 0;
+ nsym = 4800*2;
npreamble = 480;
gmsk_states.coherent_demod = 1;
gmsk_states.phase_track = 1;
- gmsk_states = gmsk_init(gmsk_states);
+ gmsk_states = gmsk_init(gmsk_states, Rs);
Fs = gmsk_states.Fs;
Rs = gmsk_states.Rs;
M = gmsk_states.M;
tx = resample(tx, 1E6, 1E6-sample_clock_offset_ppm);
tx = [zeros(1,timing_offset) tx];
nsam = length(tx);
-
+ figure(11);
+ subplot(211)
+ plot(real(tx(1:M*10)))
+ subplot(212)
+ plot(imag(tx(1:M*10)))
+
EbNo = 10^(aEbNodB/10);
variance = Fs/(Rs*EbNo);
noise = sqrt(variance/2)*(randn(1,nsam) + j*randn(1,nsam));
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