--- /dev/null
+% test_dsss.m
+% David Rowe Oct 2014
+%
+
+% Simulation to test FDM QPSK combined with DSSS. A low rate Codec
+% (e.g. 450 bit/s) is transmitted on Nc=4 FDM carriers. This same
+% information is repeated Nchip=4 times on bocks of carriers that are
+% delayed by up to Rs symbols. It's like spread spectrum with a
+% spreading code of 1111. Turns out this goes a long way to
+% converting a fading channel into an AWGN one. Good scatter diagram
+% and BER curve results. Disadvantage is more bandwidth is required.
+
+% When output error files used to simulate codec provided a few dB
+% drop to 1dB SNR for intelligable speech for 450 codec combined with
+% DSSS compared with legacy 1600 bit/s mode that has FEC. Improvement
+% not as great as hoped as 1600 codec can cope with higher BER.
+
+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_mag_only = sim_in.hf_mag_only;
+ Nchip = sim_in.Nchip;
+
+ bps = 2;
+ Nc = Nsymb = framesize/bps;
+ prev_sym_tx = qpsk_mod([0 0])*ones(1,Nc*Nchip);
+ prev_sym_rx = qpsk_mod([0 0])*ones(1,Nc*Nchip);
+
+ 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 = [];
+ errors_log = [];
+ Nerrs_log = [];
+
+ % init HF channel
+
+ hf_n = 1;
+
+ % simulation starts here-----------------------------------
+
+ for nn = 1: Ntrials
+
+ tx_bits = round( rand( 1, framesize) );
+
+ % modulate --------------------------------------------
+
+ tx_symb=zeros(1,Nc*Nchip);
+
+ for i=1:Nc
+ tx_symb(i) = qpsk_mod(tx_bits(2*(i-1)+1:2*i));
+ end
+
+ % Optionally copy to other carriers (spreading)
+
+ for i=Nc+1:Nc:Nc*Nchip
+ tx_symb(i:i+Nc-1) = tx_symb(1:Nc);
+ end
+
+ % Optionally DQPSK encode
+
+ if strcmp(modulation,'dqpsk')
+ for i=1:Nc*Nchip
+ tx_symb(i) *= prev_sym_tx(i);
+ prev_sym_tx(i) = tx_symb(i);
+ end
+ end
+
+ s_ch = tx_symb/sqrt(Nchip);
+
+ % HF channel simulation ------------------------------------
+
+ if hf_sim
+
+ % separation between carriers. Note this 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
+
+ hf_model(hf_n, :) = zeros(1,Nc);
+
+ for i=1:Nchip
+ time_shift = floor(i*Rs/4);
+ for k=1:Nc
+ ahf_model = hf_gain*(spread(hf_n+time_shift) + exp(-j*k*wsep*nhfdelay)*spread_2ms(hf_n+time_shift));
+ if hf_mag_only
+ s_ch((i-1)*Nc+k) *= abs(ahf_model);
+ else
+ s_ch((i-1)*Nc+k) *= ahf_model;
+ end
+ hf_model(hf_n, k) += ahf_model/Nchip;
+ end
+ end
+ hf_n++;
+ 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*Nchip) + j*randn(1,Nsymb*Nchip));
+ noise_log = [noise_log noise];
+
+ s_ch = s_ch + noise;
+
+ % de-modulate
+
+ for i=1:Nc*Nchip
+ rx_symb(i) = s_ch(i);
+ if strcmp(modulation,'dqpsk')
+ tmp = rx_symb(i);
+ rx_symb(i) *= conj(prev_sym_rx(i)/abs(prev_sym_rx(i)));
+ prev_sym_rx(i) = tmp;
+ end
+ end
+
+ % de-spread
+
+ for i=Nc+1:Nc:Nchip*Nc
+ rx_symb(1:Nc) = rx_symb(1:Nc) + rx_symb(i:i+Nc-1);
+ end
+
+ % demodulate
+
+ rx_bits = zeros(1, framesize);
+ for i=1:Nc
+ rx_bits((2*(i-1)+1):(2*i)) = qpsk_demod(rx_symb(i));
+ end
+ rx_symb_log = [rx_symb_log rx_symb(1:Nc)];
+
+ % Measure BER
+
+ error_positions = xor(rx_bits, tx_bits);
+ Nerrs = sum(error_positions);
+ Terrs += Nerrs;
+ Tbits += length(tx_bits);
+ errors_log = [errors_log error_positions];
+ Nerrs_log = [Nerrs_log Nerrs];
+ end
+
+ TERvec(ne) = Terrs;
+ BERvec(ne) = Terrs/Tbits;
+
+ if verbose
+ av_tx_pwr = (tx_symb_log * tx_symb_log')/length(tx_symb_log);
+
+ printf("EsNo (dB): %f Terrs: %d BER %4.2f QPSK BER theory %4.2f av_tx_pwr: %3.2f", EsNodB, Terrs,
+ Terrs/Tbits, 0.5*erfc(sqrt(EsNo/2)), av_tx_pwr);
+ 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;
+ sim_out.errors_log = errors_log;
+
+ if plot_scatter
+ figure(2);
+ clf;
+ scat = rx_symb_log .* exp(j*pi/4);
+ plot(real(scat), imag(scat),'+');
+ title('Scatter plot');
+
+ if hf_sim
+ figure(3);
+ clf;
+
+ y = 1:(hf_n-1);
+ x = 1:Nc;
+ EsNodBSurface = 20*log10(abs(hf_model(y,:))) - 10*log10(variance);
+ EsNodBSurface(find(EsNodBSurface < -5)) = -5;
+ mesh(x,y,EsNodBSurface);
+ grid
+ axis([1 Nc 1 Rs*5 -5 15])
+ title('HF Channel Es/No');
+
+ if verbose
+ av_hf_pwr = sum(abs(hf_model(y)).^2)/(hf_n-1);
+ printf("average HF power: %3.2f over %d symbols\n", av_hf_pwr, hf_n-1);
+ end
+ end
+
+ figure(4)
+ clf
+ stem(Nerrs_log)
+ 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 = 8;
+ sim_in.Rs = 50;
+ sim_in.Nc = 4;
+
+ 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_mag_only = 0;
+
+ sim_in.Nchip = 1;
+endfunction
+
+function test_curves
+
+ sim_in = standard_init();
+
+ sim_in.verbose = 1;
+ sim_in.plot_scatter = 1;
+
+ sim_in.Esvec = 50;
+ sim_in.hf_sim = 0;
+ sim_in.Ntrials = 1000;
+
+ sim_qpsk_hf = ber_test(sim_in, 'qpsk');
+
+ sim_in.hf_sim = 0;
+ sim_in.plot_scatter = 0;
+ sim_in.Esvec = 5:15;
+ Ebvec = sim_in.Esvec - 10*log10(2);
+ BER_theory = 0.5*erfc(sqrt(10.^(Ebvec/10)));
+ sim_dqpsk = ber_test(sim_in, 'dqpsk');
+ sim_in.hf_sim = 1;
+ sim_in.hf_mag_only = 1;
+ sim_qpsk_hf = ber_test(sim_in, 'qpsk');
+ sim_in.hf_mag_only = 0;
+ sim_dqpsk_hf = ber_test(sim_in, 'dqpsk');
+ sim_in.Nchip = 4;
+ sim_dqpsk_hf_dsss = ber_test(sim_in, 'dqpsk');
+
+ figure(1);
+ clf;
+ semilogy(Ebvec, BER_theory,'r;QPSK theory;')
+ hold on;
+ semilogy(sim_dqpsk.Ebvec, sim_dqpsk.BERvec,'c;DQPSK AWGN;')
+ semilogy(sim_qpsk_hf.Ebvec, sim_qpsk_hf.BERvec,'b;QPSK HF;')
+ semilogy(sim_dqpsk_hf.Ebvec, sim_dqpsk_hf.BERvec,'k;DQPSK HF;')
+ semilogy(sim_dqpsk_hf_dsss.Ebvec, sim_dqpsk_hf_dsss.BERvec,'g;DQPSK DSSS HF;')
+ hold off;
+
+ xlabel('Eb/N0')
+ ylabel('BER')
+ grid("minor")
+ axis([min(Ebvec) max(Ebvec) 1E-3 1])
+endfunction
+
+function test_single
+
+ sim_in = standard_init();
+
+ sim_in.verbose = 1;
+ sim_in.plot_scatter = 1;
+
+ sim_in.Esvec = 10;
+ sim_in.hf_sim = 1;
+ sim_in.Nchip = 4;
+ sim_in.Ntrials = 500;
+
+ sim_qpsk_hf = ber_test(sim_in, 'dqpsk');
+endfunction
+
+function test_1600_v_450
+
+ sim_in = standard_init();
+
+ sim_in.verbose = 1;
+ sim_in.plot_scatter = 1;
+ sim_in.Ntrials = 500;
+ sim_in.hf_sim = 1;
+
+ sim_in.framesize = 32;
+ sim_in.Nc = 16;
+ sim_in.Esvec = 7;
+ sim_in.Nchip = 1;
+
+ sim_dqpsk_hf_1600 = ber_test(sim_in, 'dqpsk');
+
+ sim_in.framesize = 8;
+ sim_in.Nc = 4;
+ sim_in.Esvec = sim_in.Esvec + 10*log10(1600/450);
+ sim_in.Nchip = 4;
+
+ sim_dqpsk_hf_450 = ber_test(sim_in, 'dqpsk');
+
+ fep=fopen("errors_1600.bin","wb"); fwrite(fep, sim_dqpsk_hf_1600.errors_log, "short"); fclose(fep);
+ fep=fopen("errors_450.bin","wb"); fwrite(fep, sim_dqpsk_hf_450.errors_log, "short"); fclose(fep);
+
+endfunction
+
+
+% Start simulations ---------------------------------------
+
+more off;
+
+test_1600_v_450();
+test_curves();
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