--- /dev/null
+% test_ucinter.m
+% David Rowe August 2014
+%
+
+% FDM QPSK modem simulation to test uncododed interleaving ideas on HF
+% channels without building a full blown modem.
+
+% [X] baseline QPSK simulation AWGN
+% [ ] Spreading function
+% [ ] visualise different carriers with and without spreading
+% [ ] prove perf same as AWGN when one carrier is knocked out
+% + AWGN and "faded channel" with same average SNR
+% + use contrived example
+% + then try less contrived but still well behaived maths channel
+
+% Ideas:
+% + decode quickly but then slow down while playing, using full interleave
+% + exp type window so we can decode using current symbols alone in gd SNR, or extend window over greater time
+% + like root nyq filtering, combining multiple symbols, weighted
+% + spreading could make it worse, e.g. short term average might be very low
+% + SSB spreads out over a long way. We could so this too! Like spread spectrum. Don't have to be related to
+% carrier width. Minimise amount of stuff that gets nailed. But didn't we try this with "1600 wide"? OK, so
+ key issue was BER. That, is what we need to impove, using "high areas".
+
+1;
+
+% main test function
+
+function sim_out = ber_test(sim_in, modulation)
+ Fs = 8000;
+
+ verbose = sim_in.verbose;
+ framesize = sim_in.framesize;
+ Ntrials = sim_in.Ntrials;
+ Esvec = sim_in.Esvec;
+ phase_offset = sim_in.phase_offset;
+ w_offset = sim_in.w_offset;
+ plot_scatter = sim_in.plot_scatter;
+ Rs = sim_in.Rs;
+ hf_sim = sim_in.hf_sim;
+ nhfdelay = sim_in.hf_delay_ms*Rs/1000;
+ hf_phase_only = sim_in.hf_phase_only;
+ hf_mag_only = sim_in.hf_mag_only;
+ Nc = sim_in.Nc;
+
+ bps = 2;
+ Nsymb = framesize/bps;
+ prev_sym_tx = qpsk_mod([0 0]);
+ prev_sym_rx = qpsk_mod([0 0]);
+
+ tx_bits_buf = zeros(1,2*framesize);
+ rx_bits_buf = zeros(1,2*framesize);
+ rx_symb_buf = zeros(1,2*Nsymb);
+
+ % Init HF channel model from stored sample files of spreading signal ----------------------------------
+
+ % convert "spreading" samples from 1kHz carrier at Fs to complex
+ % baseband, generated by passing a 1kHz sine wave through PathSim
+ % with the ccir-poor model, enabling one path at a time.
+
+ Fc = 1000; M = Fs/Rs;
+ fspread = fopen("../raw/sine1k_2Hz_spread.raw","rb");
+ spread1k = fread(fspread, "int16")/10000;
+ fclose(fspread);
+ fspread = fopen("../raw/sine1k_2ms_delay_2Hz_spread.raw","rb");
+ spread1k_2ms = fread(fspread, "int16")/10000;
+ fclose(fspread);
+
+ % down convert to complex baseband
+ spreadbb = spread1k.*exp(-j*(2*pi*Fc/Fs)*(1:length(spread1k))');
+ spreadbb_2ms = spread1k_2ms.*exp(-j*(2*pi*Fc/Fs)*(1:length(spread1k_2ms))');
+
+ % remove -2000 Hz image
+ b = fir1(50, 5/Fs);
+ spread = filter(b,1,spreadbb);
+ spread_2ms = filter(b,1,spreadbb_2ms);
+
+ % discard first 1000 samples as these were near 0, probably as
+ % PathSim states were ramping up
+
+ spread = spread(1000:length(spread));
+ spread_2ms = spread_2ms(1000:length(spread_2ms));
+
+ % decimate down to Rs
+
+ spread = spread(1:M:length(spread));
+ spread_2ms = spread_2ms(1:M:length(spread_2ms));
+
+ % Determine "gain" of HF channel model, so we can normalise
+ % carrier power during HF channel sim to calibrate SNR. I imagine
+ % different implementations of ccir-poor would do this in
+ % different ways, leading to different BER results. Oh Well!
+
+ hf_gain = 1.0/sqrt(var(spread)+var(spread_2ms));
+
+ % Start Simulation ----------------------------------------------------------------
+
+ for ne = 1:length(Esvec)
+ EsNodB = Esvec(ne);
+ EsNo = 10^(EsNodB/10);
+
+ variance = 1/EsNo;
+ if verbose > 1
+ printf("EsNo (dB): %f EsNo: %f variance: %f\n", EsNodB, EsNo, variance);
+ end
+
+ Terrs = 0; Tbits = 0;
+
+ tx_symb_log = [];
+ rx_symb_log = [];
+ noise_log = [];
+
+ % init HF channel
+
+ hf_n = 1;
+ hf_angle_log = [];
+ hf_fading = ones(1,Nsymb); % default input for ldpc dec
+ hf_model = ones(Ntrials*Nsymb/Nc, Nc); % defaults for plotting surface
+
+ for nn = 1: Ntrials
+
+ tx_bits = round( rand( 1, framesize) );
+
+ % modulate --------------------------------------------
+
+ s = zeros(1, Nsymb);
+ for i=1:Nsymb
+ tx_symb = qpsk_mod(tx_bits(2*(i-1)+1:2*i));
+ if strcmp(modulation,'dqpsk')
+ tx_symb *= prev_sym_tx;
+ prev_sym_tx = tx_symb;
+ end
+ s(i) = tx_symb;
+ end
+ s_ch = s;
+
+ % HF channel simulation ------------------------------------
+
+ if hf_sim
+
+ % separation between carriers. Note this is
+ % effectively under samples at Rs, I dont think this
+ % matters. Equivalent to doing freq shift at Fs, then
+ % decimating to Rs.
+
+ wsep = 2*pi*(1+0.5); % e.g. 75Hz spacing at Rs=50Hz, alpha=0.5 filters
+
+ if Nsymb/Nc != floor(Nsymb/Nc)
+ printf("Error: Nsymb/Nc must be an integrer\n")
+ return;
+ end
+
+ % arrange symbols in Nsymb/Nc by Nc matrix
+
+ for i=1:Nc:Nsymb
+
+ % Determine HF channel at each carrier for this symbol
+
+ for k=1:Nc
+ hf_model(hf_n, k) = hf_gain*(spread(hf_n) + exp(-j*k*wsep*nhfdelay)*spread_2ms(hf_n));
+ hf_fading(i+k-1) = abs(hf_model(hf_n, k));
+ if hf_mag_only
+ s_ch(i+k-1) *= abs(hf_model(hf_n, k));
+ else
+ s_ch(i+k-1) *= hf_model(hf_n, k);
+ end
+ end
+ hf_n++;
+ end
+ end
+
+ tx_symb_log = [tx_symb_log s_ch];
+
+ % AWGN noise and phase/freq offset channel simulation
+ % 0.5 factor ensures var(noise) == variance , i.e. splits power between Re & Im
+
+ noise = sqrt(variance*0.5)*(randn(1,Nsymb) + j*randn(1,Nsymb));
+ noise_log = [noise_log noise];
+
+ % organise into carriers to apply frequency and phase offset
+
+ for i=1:Nc:Nsymb
+ for k=1:Nc
+ s_ch(i+k-1) = s_ch(i+k-1)*exp(j*phase_offset) + noise(i+k-1);
+ end
+ phase_offset += w_offset;
+ end
+
+ % de-modulate
+
+ rx_bits = zeros(1, framesize);
+ for i=1:Nsymb
+ rx_symb = s_ch(i);
+ if strcmp(modulation,'dqpsk')
+ tmp = rx_symb;
+ rx_symb *= conj(prev_sym_rx/abs(prev_sym_rx));
+ prev_sym_rx = tmp;
+ end
+ rx_bits((2*(i-1)+1):(2*i)) = qpsk_demod(rx_symb);
+ rx_symb_log = [rx_symb_log rx_symb];
+ end
+
+ % Measure BER
+
+ error_positions = xor(rx_bits, tx_bits);
+ Nerrs = sum(error_positions);
+ Terrs += Nerrs;
+ Tbits += length(tx_bits);
+ end
+
+ TERvec(ne) = Terrs;
+ BERvec(ne) = Terrs/Tbits;
+
+ if verbose
+ printf("EsNo (dB): %f Terrs: %d BER %f BER theory %f", EsNodB, Terrs,
+ Terrs/Tbits, 0.5*erfc(sqrt(EsNo/2)));
+ printf("\n");
+ end
+ if verbose > 1
+ printf("Terrs: %d BER %f BER theory %f C %f N %f Es %f No %f Es/No %f\n\n", Terrs,
+ Terrs/Tbits, 0.5*erfc(sqrt(EsNo/2)), var(tx_symb_log), var(noise_log),
+ var(tx_symb_log), var(noise_log), var(tx_symb_log)/var(noise_log));
+ end
+ end
+
+ Ebvec = Esvec - 10*log10(bps);
+ sim_out.BERvec = BERvec;
+ sim_out.Ebvec = Ebvec;
+ sim_out.TERvec = TERvec;
+
+ if plot_scatter
+ figure(2);
+ clf;
+ scat = rx_symb_log .* exp(j*pi/4);
+ plot(real(scat), imag(scat),'+');
+ title('Scatter plot');
+
+ figure(3);
+ clf;
+
+ y = 1:Rs*2;
+ x = 1:Nc;
+ EsNodBSurface = 20*log10(abs(hf_model(y,:))) - 10*log10(variance);
+ mesh(x,y,EsNodBSurface);
+ grid
+ axis([1 Nc 1 Rs*2 -5 15])
+ title('HF Channel Es/No');
+
+ figure(4);
+ clf;
+ %mesh(x,y,unwrap(angle(hf_model(y,:))));
+ subplot(211)
+ plot(y,abs(hf_model(y,1)))
+ title('HF Channel Carrier 1 Mag');
+ subplot(212)
+ plot(y,angle(hf_model(y,1)))
+ title('HF Channel Carrier 1 Phase');
+
+ figure(6)
+ tmp = [];
+ for i = 1:hf_n-1
+ tmp = [tmp abs(hf_model(i,:))];
+ end
+ hist(tmp);
+ end
+
+endfunction
+
+% 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)
+ if isscalar(symbol) == 0
+ printf("only works with scalars\n");
+ return;
+ end
+ bit0 = real(symbol*exp(j*pi/4)) < 0;
+ bit1 = imag(symbol*exp(j*pi/4)) < 0;
+ two_bits = [bit1 bit0];
+endfunction
+
+function sim_in = standard_init
+ sim_in.verbose = 1;
+ sim_in.plot_scatter = 0;
+
+ sim_in.Esvec = 5;
+ sim_in.Ntrials = 30;
+ sim_in.framesize = 576;
+ sim_in.Rs = 100;
+ sim_in.Nc = 8;
+
+ sim_in.phase_offset = 0;
+ sim_in.w_offset = 0;
+ sim_in.phase_noise_amp = 0;
+
+ sim_in.hf_delay_ms = 2;
+ sim_in.hf_sim = 0;
+ sim_in.hf_phase_only = 0;
+ sim_in.hf_mag_only = 1;
+endfunction
+
+function test_ideal
+
+ sim_in = standard_init();
+
+ sim_in.verbose = 1;
+ sim_in.plot_scatter = 1;
+
+ sim_in.Esvec = 5;
+ sim_in.hf_sim = 1;
+ sim_in.Ntrials = 30;
+
+ sim_qpsk_hf = ber_test(sim_in, 'qpsk');
+
+ sim_in.hf_sim = 0;
+ sim_in.plot_scatter = 0;
+ sim_in.Esvec = 2:5;
+ Ebvec = sim_in.Esvec - 10*log10(2);
+ BER_theory = 0.5*erfc(sqrt(10.^(Ebvec/10)));
+ sim_qpsk = ber_test(sim_in, 'qpsk');
+ sim_dqpsk = ber_test(sim_in, 'dqpsk');
+
+ figure(1);
+ clf;
+ semilogy(Ebvec, BER_theory,'r;QPSK theory;')
+ hold on;
+ semilogy(sim_qpsk.Ebvec, sim_qpsk.BERvec,'g;QPSK AWGN;')
+ semilogy(sim_dqpsk.Ebvec, sim_dqpsk.BERvec,'c;DQPSK AWGN;')
+ hold off;
+
+ xlabel('Eb/N0')
+ ylabel('BER')
+ grid("minor")
+ axis([min(Ebvec) max(Ebvec) 1E-3 1])
+endfunction
+
+
+% Start simulations ---------------------------------------
+
+more off;
+
+test_ideal();
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