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% mfsk.m
% David Rowe Nov 2015
% Simulation to test m=2 and m=4 FSK demod
1;
function sim_out = fsk_ber_test(sim_in)
Fs = 96000;
M = sim_in.M;
Rs = sim_in.Rs;
Ts = Fs/Rs;
verbose = sim_in.verbose;
nbits = sim_in.nbits;
nsym = sim_in.nbits*2/M;
nsam = nsym*Ts;
EsNodB = sim_in.EbNodB + 10*log10(M/2);
% printf("M: %d nbits: %d nsym: %d\n", M, nbits, nsym);
if M == 2
f(1) = -Rs/2;
f(2) = Rs/2;
end
if M == 4
f(1) = -3*Rs/2;
f(2) = -Rs/2;
f(3) = Rs/2;
f(4) = 3*Rs/2;
end
% simulate over a range of Eb/No values
for ne = 1:length(EsNodB)
Nerrs = Terrs = Tbits = 0;
aEsNodB = EsNodB(ne);
EsNo = 10^(aEsNodB/10);
variance = Fs/(Rs*EsNo);
% Modulator -------------------------------
tx_bits = round(rand(1, nbits));
tx = zeros(1,nsam);
tx_phase = 0;
for i=1:nsym
if M == 2
tone = tx_bits(i) + 1;
else
tone = (tx_bits(2*(i-1)+1:2*i) * [2 1]') + 1;
end
tx_phase_vec = tx_phase + (1:Ts)*2*pi*f(tone)/Fs;
tx((i-1)*Ts+1:i*Ts) = exp(j*tx_phase_vec);
tx_phase = tx_phase_vec(Ts) - floor(tx_phase_vec(Ts)/(2*pi))*2*pi;
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
% Demodulator -----------------------------
% non-coherent FSK demod
rx_bb = rx;
dc = zeros(M,nsam);
for m=1:M
dc(m,:) = rx_bb .* exp(-j*(0:nsam-1)*2*pi*f(m)/Fs);
end
rx_bits = zeros(1, nsym);
for i=1:nsym
st = (i-1)*Ts+1;
en = st+Ts-1;
for m=1:M
int(m,i) = abs(sum(dc(m,st:en)));
end
if m == 2
rx_bits(i) = int(1,i) < int(2,i);
else
[max_amp tone] = max([int(1,i) int(2,i) int(3,i) int(4,i)]);
if tone == 1
rx_bits(2*(i-1)+1:2*i) = [0 0];
end
if tone == 2
rx_bits(2*(i-1)+1:2*i) = [0 1];
end
if tone == 3
rx_bits(2*(i-1)+1:2*i) = [1 0];
end
if tone == 4
rx_bits(2*(i-1)+1:2*i) = [1 1];
end
end
end
error_positions = xor(rx_bits, tx_bits);
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: %4.3f \n", aEsNodB - 10*log10(M/2), Terrs, Terrs/Tbits);
end
end
sim_out.TERvec = TERvec;
sim_out.BERvec = BERvec;
endfunction
function run_fsk_curves
sim_in.M = 2;
sim_in.Rs = 1200;
sim_in.nbits = 12000;
sim_in.EbNodB = 0:2:20;
sim_in.verbose = 1;
EbNo = 10 .^ (sim_in.EbNodB/10);
fsk_theory.BERvec = 0.5*exp(-EbNo/2); % non-coherent BFSK demod
fsk2_sim = fsk_ber_test(sim_in);
sim_in.M = 4;
fsk4_sim = fsk_ber_test(sim_in);
% BER v Eb/No curves
figure(1);
clf;
semilogy(sim_in.EbNodB, fsk_theory.BERvec,'r;2FSK theory;')
hold on;
semilogy(sim_in.EbNodB, fsk2_sim.BERvec,'g;2FSK sim;')
semilogy(sim_in.EbNodB, fsk4_sim.BERvec,'b;4FSK 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)")
end
function run_fsk_single
sim_in.M = 4;
sim_in.Rs = 1200;
sim_in.nbits = 5000;
sim_in.EbNodB = 8;
sim_in.verbose = 1;
fsk_sim = fsk_ber_test(sim_in);
endfunction
rand('state',1);
randn('state',1);
graphics_toolkit ("gnuplot");
run_fsk_curves
%run_fsk_single
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