--- /dev/null
+% test_pilot_.m
+% David Rowe Oct 2014
+%
+
+% Simulation to test pilot assisted coherent FDM QPSK. QPSK performs
+% about 4dB better than DQPSK on HF fading channels, even half of that
+% would be very useful.
+
+% reqd to make sure we can repeat tests exactly
+
+rand('state',1);
+randn('state',1);
+
+% main test function
+
+function sim_out = ber_test(sim_in, modulation)
+ Fs = 8000;
+
+ verbose = sim_in.verbose;
+ Ntrials = sim_in.Ntrials;
+ Esvec = sim_in.Esvec;
+ 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;
+ framesize = sim_in.framesize;
+ Np = sim_in.Np;
+ Ns = sim_in.Ns;
+ coh = sim_in.coh;
+
+ bps = 2;
+ Nc = Nsymb = framesize/bps; % total number of symbols
+
+ prev_sym_tx = qpsk_mod([0 0])*ones(1,Nc);
+ prev_sym_rx = qpsk_mod([0 0])*ones(1,Nc);
+
+ % 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 = [];
+ errors_log = [];
+ Nerrs_log = [];
+
+ % simulation starts here-----------------------------------
+
+ % generate all tx symbols and simulate on HF channel so we can
+ % use future and past samples for phase estimation. We
+ % simulate Ntrials+Np so we have enough samples for looking
+ % forward and backwards for phase estimation
+
+ tx_bits = zeros(Ntrials+Np*Ns, framesize);
+ tx_symb = zeros(1, Nc);
+ s_ch = zeros(Ntrials+Np*Ns, Nc);
+
+ for nn = 1: Ntrials+Np*Ns
+ tx_bits(nn,:) = round(rand(1,framesize));
+
+ % modulate --------------------------------------------
+
+ for c=1:Nc
+ tx_symb(c) = qpsk_mod(tx_bits(nn,(2*(c-1)+1):(2*c)));
+ if strcmp(modulation,'dqpsk')
+ tx_symb(c) *= prev_sym_tx(c);
+ prev_sym_tx(c) = tx_symb(c);
+ end
+ end
+ s_ch(nn,:) = tx_symb;
+ tx_symb_log = [tx_symb_log tx_symb];
+
+ 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
+
+ for c=1:Nc
+ hf_model(nn,c) = hf_gain*(spread(nn) + exp(-j*c*wsep*nhfdelay)*spread_2ms(nn));
+ %hf_model(nn,c) = 1;
+ if hf_mag_only
+ s_ch(nn,c) *= abs(hf_model(nn,c));
+ else
+ s_ch(nn,c) *= hf_model(nn,c);
+ end
+ end
+ end
+ end
+
+ % add channel noise
+
+ noise = sqrt(variance*0.5)*(randn(Ntrials+Np*Ns,Nc) + j*randn(Ntrials+Np*Ns,Nc));
+ s_ch += noise;
+ if hf_sim
+ hf_model_noise = hf_model + noise;
+ end
+
+ % phase estimation and demodulation
+
+ phi_ = zeros(Ntrials+Np*Ns, Nc);
+
+ for nn = floor(Np*Ns/2)+1:floor(Np*Ns/2)+Ntrials
+
+ % pilot assisted phase estimation
+
+ if coh
+ for c=1:Nc
+ k = 1;
+ for i = -floor(Np*Ns/2):Ns:floor(Np*Ns/2)
+ % ignore centre sample as that is the current symbol
+ if i != 0
+ phase_samples(k) = hf_model_noise(nn+i,c);
+ %printf("i: %d symb phase: %f\n", i, angle(phase_samples(k)));
+ k++;
+ end
+ end
+ phi_(nn,c) = angle(sum(phase_samples));
+ %printf("phi: %f phi_: %f\n", angle(hf_model(nn,c)), phi_(nn,c));
+ s_ch(nn,c) *= exp(-j*phi_(nn,c));
+ end
+ end
+
+ % de-modulate
+
+ rx_bits = zeros(1, framesize);
+ for c=1:Nc
+ rx_symb(c) = s_ch(nn,c);
+ if strcmp(modulation,'dqpsk')
+ tmp = rx_symb(c);
+ rx_symb(c) *= conj(prev_sym_rx(c)/abs(prev_sym_rx(c)));
+ prev_sym_rx(c) = tmp;
+ end
+ rx_bits((2*(c-1)+1):(2*c)) = qpsk_demod(rx_symb(c));
+ rx_symb_log = [rx_symb_log rx_symb(c)];
+ end
+
+ % Measure BER
+
+ error_positions = xor(rx_bits, tx_bits(nn,:));
+ Nerrs = sum(error_positions);
+ Terrs += Nerrs;
+ Tbits += framesize;
+ 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): %3.1f Terrs: %d BER %4.3f QPSK BER theory %4.3f av_tx_pwr: %3.2f", EsNodB, Terrs,
+ Terrs/Tbits, 0.5*erfc(sqrt(EsNo/2)), av_tx_pwr);
+ printf("\n");
+ 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:Ntrials+floor(Np/2);
+ 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
+ [m n] = size(hf_model);
+ av_hf_pwr = sum(sum(abs(hf_model(:,:)).^2))/(m*n);
+ printf("average HF power: %3.2f over %d symbols\n", av_hf_pwr, m*n);
+ end
+
+ figure(5);
+ clf
+ subplot(211)
+ [m n] = size(hf_model);
+ plot(angle(hf_model(1:m,1)),'g;HF channel phase;')
+ hold on;
+ plot(phi_(1:m,1),'r+;Estimated HF channel phase;')
+ ylabel('Phase (rads)');
+ subplot(212)
+ plot(abs(hf_model(1:m,1)))
+ ylabel('Amplitude');
+ xlabel('Time (symbols)');
+ 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.Rs = 50;
+ sim_in.framesize = 8;
+ sim_in.ml = 0;
+
+ sim_in.hf_delay_ms = 2;
+ sim_in.hf_sim = 0;
+ sim_in.hf_mag_only = 0;
+endfunction
+
+
+function test_curves
+
+ sim_in = standard_init();
+
+ sim_in.Ntrials = 2000;
+
+ 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_in.coh = 0;
+ sim_in.Np = 2;
+ sim_in.Ns = 8;
+ sim_in.Rs = 100;
+
+ sim_dqpsk = ber_test(sim_in, 'dqpsk');
+ sim_in.hf_sim = 1;
+ sim_dqpsk_hf = ber_test(sim_in, 'dqpsk');
+
+ sim_in.hf_mag_only = 1;
+ sim_qpsk_hf_ideal = ber_test(sim_in, 'qpsk');
+ sim_in.hf_mag_only = 0;
+ sim_in.coh = 1;
+ sim_in.Np = 2;
+ sim_in.Ns = 4;
+ sim_in.Rs = 100;
+ sim_qpsk_hf_coh1 = ber_test(sim_in, 'qpsk');
+ sim_in.Np = 4;
+ sim_in.Ns = 4;
+ sim_in.Rs = 200;
+ sim_qpsk_hf_coh2 = ber_test(sim_in, 'qpsk');
+ sim_in.Np = 4;
+ sim_in.Ns = 8;
+ sim_in.Rs = 200;
+ sim_qpsk_hf_coh3 = ber_test(sim_in, 'qpsk');
+
+ figure(1);
+ clf;
+ semilogy(Ebvec, BER_theory,'r;QPSK theory;')
+ hold on;
+ semilogy(sim_dqpsk.Ebvec, sim_dqpsk.BERvec,'k;DQPSK AWGN;')
+ semilogy(sim_dqpsk_hf.Ebvec, sim_dqpsk_hf.BERvec,'k;DQPSK HF;')
+ semilogy(sim_qpsk_hf_ideal.Ebvec, sim_qpsk_hf_ideal.BERvec,'c;QPSK HF ideal;')
+ semilogy(sim_qpsk_hf_coh1.Ebvec, sim_qpsk_hf_coh1.BERvec,'g;QPSK HF Rs=100 Np=2 Ns=4;')
+ semilogy(sim_qpsk_hf_coh2.Ebvec, sim_qpsk_hf_coh2.BERvec,'r;QPSK HF Rs=200 Np=4 Ns=4;')
+ semilogy(sim_qpsk_hf_coh3.Ebvec, sim_qpsk_hf_coh3.BERvec,'b;QPSK HF Rs=200 Np=4 Ns=8;')
+ 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.Ntrials = 1000;
+
+ sim_in.hf_mag_only = 0;
+ sim_in.hf_sim = 1;
+ sim_in.Esvec = 10;
+ sim_in.coh = 1;
+ sim_in.Rs = 100;
+ sim_in.Np = 2;
+ sim_in.Ns = 1;
+
+ sim_qpsk_hf = ber_test(sim_in, 'qpsk');
+endfunction
+
+
+% Start simulations ---------------------------------------
+
+more off;
+
+test_curves();
+%test_single();
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