From c149a99d2fff5910789ba096732742068d308d8f Mon Sep 17 00:00:00 2001 From: drowe67 Date: Thu, 9 Oct 2014 00:59:59 +0000 Subject: [PATCH] pilot symbol based coherent QPSK, reas results on fading channels, time to combine with DSSS and see if we have anything useful git-svn-id: https://svn.code.sf.net/p/freetel/code@1881 01035d8c-6547-0410-b346-abe4f91aad63 --- codec2-dev/octave/test_pilot.m | 388 +++++++++++++++++++++++++++++++++ 1 file changed, 388 insertions(+) create mode 100644 codec2-dev/octave/test_pilot.m diff --git a/codec2-dev/octave/test_pilot.m b/codec2-dev/octave/test_pilot.m new file mode 100644 index 00000000..0117541b --- /dev/null +++ b/codec2-dev/octave/test_pilot.m @@ -0,0 +1,388 @@ +% 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(); -- 2.25.1