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% hf_modem_curves
% David Rowe Feb 2017
%
% Ideal implementations of a bunch of different HF modems, used to
% generate plots for a blog post.
#{
[X] ideal AWGN/HF curves
[X] exp AWGN QPSK curves
[X] exp AWGN DQPSK curves
[X] exp HF channel model
[ ] diversity
[ ] COHPSK frames
+ would require multiple carriers
+ filtering or OFDM
#}
1;
% Gray coded QPSK modulation function
function symbol = qpsk_mod(two_bits)
two_bits_decimal = sum(two_bits .* [2 1]);
switch(two_bits_decimal)
case (0) symbol = 1;
case (1) symbol = j;
case (2) symbol = -j;
case (3) symbol = -1;
endswitch
endfunction
% Gray coded QPSK demodulation function
function two_bits = qpsk_demod(symbol)
bit0 = real(symbol*exp(j*pi/4)) < 0;
bit1 = imag(symbol*exp(j*pi/4)) < 0;
two_bits = [bit1 bit0];
endfunction
% Rate Rs modem simulation model -------------------------------------------------------
function sim_out = ber_test(sim_in)
bps = 2; % two bits/symbol for QPSK
Rs = 50; % symbol rate (needed for HF model)
verbose = sim_in.verbose;
EbNovec = sim_in.EbNovec;
hf_en = sim_in.hf_en;
% user can supply number of bits per point to get good results
% at high Eb/No
if length(sim_in.nbits) > 1
nbitsvec = sim_in.nbits;
nbitsvec += 100 - mod(nbitsvec,100); % round up to nearest 100
else
nbitsvec(1:length(EbNovec)) = sim_in.nbits;
end
% init HF model
if hf_en
% some typical values
dopplerSpreadHz = 1.0; path_delay = 1E-3*Rs;
nsymb = max(nbitsvec)/2;
spread1 = doppler_spread(dopplerSpreadHz, Rs, nsymb);
spread2 = doppler_spread(dopplerSpreadHz, Rs, nsymb);
hf_gain = 1.0/sqrt(var(spread1)+var(spread2));
% printf("nsymb: %d lspread1: %d\n", nsymb, length(spread1));
end
for ne = 1:length(EbNovec)
% work out noise power -------------
EbNodB = EbNovec(ne);
EsNodB = EbNodB + 10*log10(bps);
EsNo = 10^(EsNodB/10);
variance = 1/EsNo;
nbits = nbitsvec(ne);
nsymb = nbits/bps;
% modulator ------------------------
tx_bits = rand(1,nbits) > 0.5;
tx_symb = [];
prev_tx_symb = 1;
for s=1:nsymb
atx_symb = qpsk_mod(tx_bits(2*s-1:2*s));
if sim_in.dqpsk
atx_symb *= prev_tx_symb;
prev_tx_symb = atx_symb;
end
tx_symb = [tx_symb atx_symb];
end
% channel ---------------------------
rx_symb = tx_symb;
if hf_en
% simplified rate Rs simulation model that doesn't include
% ISI, just freq filtering. We assume perfect phase estimation
% so it's just amplitude distortion.
hf_model1 = hf_model2 = zeros(1, nsymb);
for s=1:nsymb
hf_model1(s) = hf_gain*(spread1(s) + exp(-j*path_delay)*spread2(s));
hf_model = abs(hf_model1(s));
if sim_in.diversity
% include amplitude information from another frequency in channel model
w1 = 7*2*pi;
hf_model2(s) = hf_gain*(spread1(s) + exp(-j*w1*path_delay)*spread2(s));
hf_model = 0.5*abs(hf_model1(s)) + 0.5*abs(hf_model2(s));
end
rx_symb(s) = rx_symb(s).*hf_model;
end
end
% variance is noise power, which is divided equally between real and
% imag components of noise
noise = sqrt(variance*0.5)*(randn(1,nsymb) + j*randn(1,nsymb));
rx_symb += noise;
% demodulator ------------------------------------------
% demodulate rx symbols to bits
rx_bits = [];
prev_rx_symb = 1;
for s=1:nsymb
arx_symb = rx_symb(s);
if sim_in.dqpsk
tmp = arx_symb;
arx_symb *= prev_rx_symb';
prev_rx_symb = tmp;
end
two_bits = qpsk_demod(arx_symb);
rx_bits = [rx_bits two_bits];
end
% count errors -----------------------------------------
error_pattern = xor(tx_bits, rx_bits);
nerrors = sum(error_pattern);
bervec(ne) = nerrors/nbits;
if verbose
printf("EbNodB: % 3.1f nbits: %5d nerrors: %5d ber: %4.3f\n", EbNodB, nbits, nerrors, bervec(ne));
if verbose == 2
figure(2); clf;
plot(rx_symb*exp(j*pi/4),'+','markersize', 10);
mx = max(abs(rx_symb));
axis([-mx mx -mx mx]);
if sim_in.diversity && sim_in.hf_en
figure(3);
plot(1:nsymb, abs(hf_model1), 1:nsymb, abs(hf_model2), 'linewidth', 2);
end
end
end
end
sim_out.bervec = bervec;
endfunction
% -------------------------------------------------------------
function run_single
sim_in.verbose = 2;
sim_in.nbits = 1000;
sim_in.EbNovec = 4;
sim_in.dqpsk = 0;
sim_in.hf_en = 0;
sim_in.diversity = 0;
sim_qpsk = ber_test(sim_in);
endfunction
function run_curves
max_nbits = 1E5;
sim_in.verbose = 1;
sim_in.EbNovec = 0:10;
sim_in.dqpsk = 0;
sim_in.hf_en = 0;
sim_in.diversity = 0;
% AWGN -----------------------------
ber_awgn_theory = 0.5*erfc(sqrt(10.^(sim_in.EbNovec/10)));
sim_in.nbits = min(max_nbits, floor(500 ./ ber_awgn_theory));
sim_qpsk = ber_test(sim_in);
sim_in.dqpsk = 1;
sim_dqpsk = ber_test(sim_in);
% HF -----------------------------
hf_sim_in = sim_in; hf_sim_in.dqpsk = 0; hf_sim_in.hf_en = 1;
hf_sim_in.EbNovec = 0:16;
EbNoLin = 10.^(hf_sim_in.EbNovec/10);
ber_hf_theory = 0.5.*(1-sqrt(EbNoLin./(EbNoLin+1)));
hf_sim_in.nbits = min(max_nbits, floor(500 ./ ber_hf_theory));
sim_qpsk_hf = ber_test(hf_sim_in);
hf_sim_in.dqpsk = 1;
sim_dqpsk_hf = ber_test(hf_sim_in);
hf_sim_in.dqpsk = 0;
hf_sim_in.diversity = 1;
sim_qpsk_hf_div = ber_test(hf_sim_in);
% Plot results --------------------
close all;
figure (1, 'position', [100, 10, 600, 400]); clf;
semilogy(sim_in.EbNovec, ber_awgn_theory,'r+-;QPSK AWGN theory;', 'linewidth', 2)
xlabel('Eb/No (dB)')
ylabel('BER')
grid("minor")
axis([min(sim_in.EbNovec) max(sim_in.EbNovec) 1E-3 1])
hold on;
semilogy([0 4 4], [ber_awgn_theory(5) ber_awgn_theory(5) 1E-3],'k--', 'linewidth', 2);
hold off;
figure (2, 'position', [300, 10, 600, 400]); clf;
semilogy(sim_in.EbNovec, ber_awgn_theory,'r+-;QPSK AWGN theory;','markersize', 10, 'linewidth', 2)
hold on;
semilogy(sim_in.EbNovec, sim_qpsk.bervec,'g+-;QPSK AWGN simulated;','markersize', 10, 'linewidth', 2)
semilogy(sim_in.EbNovec, sim_dqpsk.bervec,'b+-;DQPSK AWGN simulated;','markersize', 10, 'linewidth', 2)
xlabel('Eb/No (dB)')
ylabel('BER')
grid("minor")
axis([min(sim_in.EbNovec) max(sim_in.EbNovec) 1E-3 1])
figure (3, 'position', [400, 10, 600, 400]); clf;
semilogy(sim_in.EbNovec, ber_awgn_theory,'r+-;QPSK AWGN theory;','markersize', 10, 'linewidth', 2)
hold on;
semilogy(sim_in.EbNovec, sim_qpsk.bervec,'g+-;QPSK AWGN simulated;','markersize', 10, 'linewidth', 2)
semilogy(sim_in.EbNovec, sim_dqpsk.bervec,'b+-;DQPSK AWGN simulated;','markersize', 10, 'linewidth', 2)
semilogy(hf_sim_in.EbNovec, ber_hf_theory,'r+-;QPSK HF theory;','markersize', 10, 'linewidth', 2)
semilogy(hf_sim_in.EbNovec, sim_dqpsk_hf.bervec,'b+-;DQPSK HF simulated;','markersize', 10, 'linewidth', 2)
semilogy(hf_sim_in.EbNovec, sim_qpsk_hf.bervec,'g+-;QPSK HF simulated;','markersize', 10, 'linewidth', 2)
semilogy(hf_sim_in.EbNovec, sim_qpsk_hf_div.bervec,'c+-;QPSK Diversity HF simulated;','markersize', 10, 'linewidth', 2)
hold off;
xlabel('Eb/No (dB)')
ylabel('BER')
grid("minor")
axis([min(hf_sim_in.EbNovec) max(hf_sim_in.EbNovec) 1E-3 1])
endfunction
% -------------------------------------------------------------
more off;
rand('seed',1); randn('seed', 1);
run_curves
#run_single
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