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-rw-r--r--octave/fsk_v_afsk.m232
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-% fsk.m
-% David Rowe Nov 2014
-
-% Ideal non-coherent FSK and AFSK-over-analog-FM simulation. Can draw
-% Eb/No curves or run single point simulations
-
-rand('state',1);
-randn('state',1);
-graphics_toolkit ("gnuplot");
-
-fm;
-
-function sim_out = fsk_ber_test(sim_in)
- Fs = 96000;
- fmark = sim_in.fmark;
- fspace = sim_in.fspace;
- Rs = sim_in.Rs;
- Ts = Fs/Rs;
- emphasis = 50E-6;
- verbose = sim_in.verbose;
-
- nsym = sim_in.nsym;
- nsam = nsym*Ts;
- EbNodB = sim_in.EbNodB;
-
- fm = sim_in.fm;
-
- if fm
- fm_states.pre_emp = 0;
- fm_states.de_emp = 0;
- fm_states.Ts = Ts;
- fm_states.Fs = Fs;
- fm_states.fc = Fs/4;
- fm_states.fm_max = 3E3;
- fm_states.fd = 5E3;
- fm_states.output_filter = 1;
- fm_states = analog_fm_init(fm_states);
- end
-
- % simulate over a range of Eb/No values
-
- for ne = 1:length(EbNodB)
- Nerrs = Terrs = Tbits = 0;
-
- % randn() generates noise spread across the entire Fs bandwidth.
- % The power (aka variance) of this noise is N = NoFs, or No =
- % N/Fs. The power of each bit is C=1, so the energy of each bit
- % is Eb=1/Rs. We want to find N as a function of Eb/No, so:
-
- % Eb/No = (1/Rs)/(N/Fs) = Fs/(RsN)
- % N = Fs/(Rs(Eb/No))
-
- aEbNodB = EbNodB(ne);
- EbNo = 10^(aEbNodB/10);
- variance = Fs/(Rs*EbNo);
-
- % Modulator -------------------------------
-
- tx_bits = round(rand(1, nsym));
- tx = zeros(1,nsam);
- tx_phase = 0;
-
- for i=1:nsym
- for k=1:Ts
- if tx_bits(i) == 1
- tx_phase += 2*pi*fmark/Fs;
- else
- tx_phase += 2*pi*fspace/Fs;
- end
- tx_phase = tx_phase - floor(tx_phase/(2*pi))*2*pi;
- tx((i-1)*Ts+k) = exp(j*tx_phase);
- end
- end
-
- % Optional AFSK over FM modulator
-
- if sim_in.fm
- % FM mod takes real input; +/- 1 for correct deviation
- tx = analog_fm_mod(fm_states, real(tx));
- end
-
- % Channel ---------------------------------
-
- % We use complex (single sided) channel simulation, as it's convenient
- % for the FM simulation.
-
- noise = sqrt(variance/2)*(randn(1,nsam) + j*randn(1,nsam));
- rx = tx + noise;
- if verbose > 1
- printf("EbNo: %f Eb: %f var No: %f EbNo (meas): %f\n",
- EbNo, var(tx)*Ts/Fs, var(noise)/Fs, (var(tx)*Ts/Fs)/(var(noise)/Fs));
- end
- save fsk tx_bits rx
-
- % Optional AFSK over FM demodulator
-
- if sim_in.fm
- % scaling factor for convenience to match pure FSK
- rx_bb = 2*analog_fm_demod(fm_states, rx);
- else
- rx_bb = rx;
- end
-
- % Demodulator -----------------------------
-
- % non-coherent FSK demod
-
- mark_dc = rx_bb .* exp(-j*(0:nsam-1)*2*pi*fmark/Fs);
- space_dc = rx_bb .* exp(-j*(0:nsam-1)*2*pi*fspace/Fs);
-
- rx_bits = zeros(1, nsym);
- for i=1:nsym
- st = (i-1)*Ts+1;
- en = st+Ts-1;
- mark_int(i) = sum(mark_dc(st:en));
- space_int(i) = sum(space_dc(st:en));
- rx_bits(i) = abs(mark_int(i)) > abs(space_int(i));
- end
-
- if fm
- d = fm_states.nsym_delay;
- error_positions = xor(rx_bits(1+d:nsym), tx_bits(1:(nsym-d)));
- else
- error_positions = xor(rx_bits, tx_bits);
- end
- Nerrs = sum(error_positions);
- Terrs += Nerrs;
- Tbits += length(error_positions);
-
- TERvec(ne) = Terrs;
- BERvec(ne) = Terrs/Tbits;
-
- if verbose > 1
- figure(2)
- clf
- Rx = 10*log10(abs(fft(rx)));
- plot(Rx(1:Fs/2));
- axis([1 Fs/2 0 50]);
-
- figure(3)
- clf;
- subplot(211)
- plot(real(rx_bb(1:Ts*20)))
- subplot(212)
- Rx_bb = 10*log10(abs(fft(rx_bb)));
- plot(Rx_bb(1:3000));
- axis([1 3000 0 50]);
-
- figure(4);
- subplot(211)
- stem(abs(mark_int(1:100)));
- subplot(212)
- stem(abs(space_int(1:100)));
- end
-
- if verbose
- printf("EbNo (db): %3.2f Terrs: %d BER: %3.2f \n", aEbNodB, Terrs, Terrs/Tbits);
- end
- end
-
- sim_out.TERvec = TERvec;
- sim_out.BERvec = BERvec;
-endfunction
-
-
-function run_fsk_curves
- sim_in.fmark = 1200;
- sim_in.fspace = 2200;
- sim_in.Rs = 1200;
- sim_in.nsym = 12000;
- sim_in.EbNodB = 0:2:20;
- sim_in.fm = 0;
- sim_in.verbose = 1;
-
- EbNo = 10 .^ (sim_in.EbNodB/10);
- fsk_theory.BERvec = 0.5*exp(-EbNo/2); % non-coherent BFSK demod
- fsk_sim = fsk_ber_test(sim_in);
-
- sim_in.fm = 1;
- fsk_fm_sim = fsk_ber_test(sim_in);
-
- % BER v Eb/No curves
-
- figure(1);
- clf;
- semilogy(sim_in.EbNodB, fsk_theory.BERvec,'r;FSK theory;')
- hold on;
- semilogy(sim_in.EbNodB, fsk_sim.BERvec,'g;FSK sim;')
- semilogy(sim_in.EbNodB, fsk_fm_sim.BERvec,'b;FSK over FM sim;')
- hold off;
- grid("minor");
- axis([min(sim_in.EbNodB) max(sim_in.EbNodB) 1E-4 1])
- legend("boxoff");
- xlabel("Eb/No (dB)");
- ylabel("Bit Error Rate (BER)")
-
- % BER v C/No (1 Hz noise BW and Eb=C/Rs=1/Rs)
- % Eb/No = (C/Rs)/(1/(N/B))
- % C/N = (Eb/No)*(Rs/B)
-
- RsOnB_dB = 10*log10(sim_in.Rs/1);
- figure(2);
- clf;
- semilogy(sim_in.EbNodB+RsOnB_dB, fsk_theory.BERvec,'r;FSK theory;')
- hold on;
- semilogy(sim_in.EbNodB+RsOnB_dB, fsk_sim.BERvec,'g;FSK sim;')
- semilogy(sim_in.EbNodB+RsOnB_dB, fsk_fm_sim.BERvec,'b;FSK over FM sim;')
- hold off;
- grid("minor");
- axis([min(sim_in.EbNodB+RsOnB_dB) max(sim_in.EbNodB+RsOnB_dB) 1E-4 1])
- legend("boxoff");
- xlabel("C/No for Rs=1200 bit/s and 1 Hz noise bandwidth (dB)");
- ylabel("Bit Error Rate (BER)")
-end
-
-function run_fsk_single
- sim_in.fmark = 1000;
- sim_in.fspace = 2000;
- sim_in.Rs = 1000;
- sim_in.nsym = 2000;
- sim_in.EbNodB = 7;
- sim_in.fm = 0;
- sim_in.verbose = 1;
-
- fsk_sim = fsk_ber_test(sim_in);
-endfunction
-
-# choose one of these functions below
-
-run_fsk_curves
-#run_fsk_single
-
generated by cgit v1.2.3 (git 2.46.0) at 2026-01-26 22:14:03 +0000