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-rw-r--r--octave/hf_modem_curves.m272
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diff --git a/octave/hf_modem_curves.m b/octave/hf_modem_curves.m
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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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