From: drowe67 Date: Mon, 10 Apr 2017 21:40:32 +0000 (+0000) Subject: added BIll's ml_pd and comparedwith some curves X-Git-Url: http://git.whiteaudio.com/gitweb/?a=commitdiff_plain;h=dc04c3772d21969f21bba1e6ca7bf1586132627c;p=freetel-svn-tracking.git added BIll's ml_pd and comparedwith some curves git-svn-id: https://svn.code.sf.net/p/freetel/code@3094 01035d8c-6547-0410-b346-abe4f91aad63 --- diff --git a/codec2-dev/octave/bpsk_hf.m b/codec2-dev/octave/bpsk_hf.m deleted file mode 100644 index fc635929..00000000 --- a/codec2-dev/octave/bpsk_hf.m +++ /dev/null @@ -1,484 +0,0 @@ -% bpsk_hf.m -% David Rowe Mar 2017 -% -% Rate Rs BPSK simulation to explore phase estimation -% over multiple carriers in HF channel - -#{ - TODO: - [X] sim pilot based phase est using known symbols - [X] test AWGN BER with averaging pilots from adj carriers - [X] refactor to insert pilot rows - [X] add border cols, not used for data - [X] centre est on current carrier, extend to > 3 - [X] test single points - + 1dB IL @ 6dB HF, 0.4 dB @ 2dB AWGN - [ ] try linear interpolation - [ ] try longer time windows - [ ] try combining mod stripping phase est inside frame - [ ] curves taking into account pilot losses - [ ] remove border carriers, interpolate edge carrier -#} - -1; - -function sim_out = run_sim(sim_in) - Rs = 100; - - EbNodB = sim_in.EbNodB; - verbose = sim_in.verbose; - hf_en = sim_in.hf_en; - hf_phase = sim_in.hf_phase; - phase_offset = sim_in.phase_offset; - - Ns = sim_in.Ns; % step size for pilots - Nc = sim_in.Nc; % Number of cols, aka number of carriers - - Nbitsperframe = (Ns-1)*Nc; - printf("Nbitsperframe: %d\n", Nbitsperframe); - Nrowsperframe = Nbitsperframe/Nc; - printf("Nrowsperframe: %d\n", Nrowsperframe); - - % Important to define run time in seconds so HF model will evolve the same way - % for different pilot insertion rates. So lets work backwards from approx - % seconds in run to get Nbits, the total number of payload data bits - - % frame has Ns-1 data symbols between pilots, e.g. for Ns=3: - % - % PPP - % DDD - % DDD - % PPP - - Nrows = sim_in.Nsec*Rs; - Nframes = floor((Nrows-1)/Ns); - Nbits = Nframes * Nbitsperframe; % number of payload data bits - - Nr = Nbits/Nc; % Number of data rows to get Nbits total - - if verbose - printf("Nc.....: %d\n", Nc); - printf("Ns.....: %d (step size for pilots, Ns-1 data symbols between pilots)\n", Ns); - printf("Nr.....: %d\n", Nr); - printf("Nbits..: %d\n", Nbits); - end - - % double check if Nbits fit neatly into carriers - - assert(Nbits/Nc == floor(Nbits/Nc), "Nbits/Nc must be an integer"); - - printf("Nframes: %d\n", Nframes); - - Nrp = Nr + Nframes + 1; % number of rows once pilots inserted - % extra row of pilots at end - printf("Nrp....: %d (number of rows including pilots)\n", Nrp); - - % set up HF model - - if hf_en - - % some typical values - - dopplerSpreadHz = 1.0; path_delay = 1E-3*Rs; - - randn('seed',1); - spread1 = doppler_spread(dopplerSpreadHz, Rs, sim_in.Nsec*Rs*1.1); - spread2 = doppler_spread(dopplerSpreadHz, Rs, sim_in.Nsec*Rs*1.1); - - % sometimes doppler_spread() doesn't return exactly the number of samples we need - - assert(length(spread1) >= Nrp, "not enough doppler spreading samples"); - assert(length(spread2) >= Nrp, "not enough doppler spreading samples"); - - hf_gain = 1.0/sqrt(var(spread1)+var(spread2)); - % printf("nsymb: %d lspread1: %d\n", nsymb, length(spread1)); - end - - % construct an artificial phase countour for testing, linear across freq and time - - if sim_in.phase_test - phase_test = ones(Nrp, Nc+2); - for r=1:Nrp - for c=1:Nc+2 - phase_test(r,c) = -pi/2 + c*pi/(Nc+2) + r*0.01*2*pi; - phase_test(r,c) = phase_test(r,c) - 2*pi*floor((phase_test(r,c)+pi)/(2*pi)); - end - end - end - - % simulate for each Eb/No point ------------------------------------ - - for nn=1:length(EbNodB) - rand('seed',1); - randn('seed',1); - - EbNo = 10 .^ (EbNodB(nn)/10); - variance = 1/(EbNo/2); - noise = sqrt(variance)*(0.5*randn(Nrp,Nc+2) + j*0.5*randn(Nrp,Nc+2)); - - % generate tx bits and insert pilot rows and border cols - - tx_bits = []; tx_bits_np = []; - for f=1:Nframes - tx_bits = [tx_bits; ones(1,Nc+2)]; - for r=1:Nrowsperframe - arowofbits = rand(1,Nc) > 0.5; - tx_bits = [tx_bits; [1 arowofbits 1]]; - tx_bits_np = [tx_bits_np; arowofbits]; - end - end - tx_bits = [tx_bits; [1 ones(1,Nc) 1]]; % final row of pilots - [nr nc] = size(tx_bits); - assert(nr == Nrp); - %tx_bits - - tx = 2*tx_bits - 1; - - rx = tx * exp(j*phase_offset); - - if sim_in.phase_test - rx = rx .* exp(j*phase_test); - end - - if hf_en - - % simplified rate Rs simulation model that doesn't include - % ISI, just freq filtering. - - % Note Rs carrier spacing, sample rate is Rs - - hf_model = zeros(Nr,Nc+2); phase_est = zeros(Nr,Nc); - for r=1:Nrp - for c=1:Nc+2 - w = 2*pi*c*Rs/Rs; - hf_model(r,c) = hf_gain*(spread1(r) + exp(-j*w*path_delay)*spread2(r)); - end - - if hf_phase - rx(r,:) = rx(r,:) .* hf_model(r,:); - else - rx(r,:) = rx(r,:) .* abs(hf_model(r,:)); - end - end - end - - rx += noise; - - % pilot based phase est, we use known tx symbols as pilots ---------- - - rx_corr = rx; - - if sim_in.pilot_phase_est - - % est phase from pilots either side of data symbols - % adjust phase of data symbol - % demodulate and count errors of just data - - phase_est_pilot_log = 10*ones(Nrp,Nc+2); - phase_est_stripped_log = 10*ones(Nrp,Nc+2); - phase_est_log = 10*ones(Nrp,Nc+2); - for c=2:Nc+1 - for r=1:Ns:Nrp-Ns - - % estimate phase using average of 6 pilots in a rect 2D window centred - % on this carrier - % PPP - % DDD - % DDD - % PPP - - cr = c-1:c+1; - aphase_est_pilot_rect1 = sum(rx(r,cr)*tx(r,cr)'); - aphase_est_pilot_rect2 = sum(rx(r+Ns,cr)*tx(r+Ns,cr)'); - - % optionally use next step of pilots in past and future - - if sim_in.pilot_wide - if r > Ns+1 - aphase_est_pilot_rect1 += sum(rx(r-Ns,cr)*tx(r-Ns,cr)'); - end - if r < Nrp - 2*Ns - aphase_est_pilot_rect2 += sum(rx(r+2*Ns,cr)*tx(r+2*Ns,cr)'); - end - end - - % correct phase offset using phase estimate - - for rr=r+1:r+Ns-1 - a = b = 1; - if sim_in.pilot_interp - b = (rr-r)/Ns; a = 1 - b; - end - %printf("rr: %d a: %4.3f b: %4.3f\n", rr, a, b); - aphase_est_pilot = angle(a*aphase_est_pilot_rect1 + b*aphase_est_pilot_rect2); - phase_est_pilot_log(rr,c) = aphase_est_pilot; - rx_corr(rr,c) = rx(rr,c) * exp(-j*aphase_est_pilot); - end - - if sim_in.stripped_phase_est - % Optional modulation stripping feed fwd phase estimation, to refine - % pilot-based phase estimate. Doing it after pilot based phase estimation - % means we don't need to deal with ambiguity, which is difficult to handle - % in low SNR channels. - - % Use vector of 7 symbols around current data symbol. We could use a 2D - % window if we can work out how best to correct with pilot-est and avoid - % ambiguities - - for rr=r+1:r+Ns-1 - - % extract a matrix of nearby samples with pilot-based offset removed - - amatrix = rx(max(1,rr-3):min(Nrp,rr+3),c) .* exp(-j*aphase_est_pilot); - - % modulation strip and est phase - - stripped = abs(amatrix) .* exp(j*2*angle(amatrix)); - aphase_est_stripped = angle(sum(sum(stripped)))/2; - phase_est_stripped_log(rr,c) = aphase_est_stripped; - - % correct rx symbols based on both phase ests - - phase_est_log(rr,c) = angle(exp(j*(aphase_est_pilot+aphase_est_stripped))); - rx_corr(rr,c) = rx(rr,c) * exp(-j*phase_est_log(rr,c)); - end - end % sim_in.stripped_phase_est - - end % r=1:Ns:Nrp-Ns - - end % c=2:Nc+1 - end % sim_in.pilot_phase_est - - % remove pilots to give us just data symbols - - rx_np = []; - for r=1:Nrp - if mod(r-1,Ns) != 0 - rx_np = [rx_np; rx_corr(r,2:Nc+1)]; - end - end - - %phase_test - %phase_est_log - - % calculate BER stats as a block, after pilots extracted - - rx_bits_np = real(rx_np) > 0; - errors = xor(tx_bits_np, rx_bits_np); - Nerrs = sum(sum(errors)); - - printf("EbNodB: %3.2f BER: %4.3f Nbits: %d Nerrs: %d\n", EbNodB(nn), Nerrs/Nbits, Nbits, Nerrs); - - if verbose - figure(1); clf; - plot(rx_np,'+'); - axis([-2 2 -2 2]); - - if hf_en - figure(2); clf; - plot(abs(hf_model(:,2:Nc+1))); - end - - if sim_in.pilot_phase_est - figure(3); clf; - plot(phase_est_log(:,2:Nc+1),'+', 'markersize', 10); - hold on; - plot(phase_est_pilot_log(:,2:Nc+1),'g+', 'markersize', 5); - if sim_in.stripped_phase_est - plot(phase_est_stripped_log(:,2:Nc+1),'ro', 'markersize', 5); - end - if sim_in.hf_en && sim_in.hf_phase - plot(angle(hf_model(:,2:Nc+1))); - end - if sim_in.phase_test - plot(phase_test(:,2:Nc+1)); - end - axis([1 Nrp -pi pi]); - end - end - - sim_out.ber(nn) = sum(Nerrs)/Nbits; - sim_out.pilot_overhead = 10*log10(Ns/(Ns-1)); - end -endfunction - - -function run_curves_hf - sim_in.Nc = 7; - sim_in.Ns = 5; - sim_in.Nsec = 240; - sim_in.EbNodB = 5:0.5:8; - sim_in.verbose = 0; - sim_in.pilot_phase_est = 0; - sim_in.pilot_wide = 1; - sim_in.pilot_interp = 0; - sim_in.stripped_phase_est = 0; - sim_in.phase_offset = 0; - sim_in.phase_test = 0; - sim_in.hf_en = 1; - sim_in.hf_phase = 0; - - sim_in.Ns = 5; - hf_ref_Ns_5_no_phase = run_sim(sim_in); - sim_in.Ns = 9; - hf_ref_Ns_9_no_phase = run_sim(sim_in); - - sim_in.hf_phase = 1; - sim_in.pilot_phase_est = 1; - - sim_in.Ns = 5; - hf_Ns_5 = run_sim(sim_in); - - sim_in.Ns = 9; - hf_Ns_9 = run_sim(sim_in); - - sim_in.Ns = 17; - hf_Ns_17 = run_sim(sim_in); - - figure(4); clf; - semilogy(sim_in.EbNodB, hf_ref_Ns_5_no_phase.ber,'b+-;Ns=5 HF ref no phase;'); - hold on; - semilogy(sim_in.EbNodB, hf_ref_Ns_9_no_phase.ber,'c+-;Ns=9 HF ref no phase;'); - semilogy(sim_in.EbNodB, hf_Ns_5.ber,'g+--;Ns=5;'); - semilogy(sim_in.EbNodB + hf_Ns_5.pilot_overhead, hf_Ns_5.ber,'go-;Ns=5 with pilot overhead;'); - semilogy(sim_in.EbNodB, hf_Ns_9.ber,'r+--;Ns=9;'); - semilogy(sim_in.EbNodB + hf_Ns_9.pilot_overhead, hf_Ns_9.ber,'ro-;Ns=9 with pilot overhead;'); - semilogy(sim_in.EbNodB, hf_Ns_17.ber,'k+--;Ns=17;'); - semilogy(sim_in.EbNodB + hf_Ns_17.pilot_overhead, hf_Ns_17.ber,'ko-;Ns=17 with pilot overhead;'); - hold off; - axis([5 8 4E-2 1E-1]) - xlabel('Eb/No (dB)'); - ylabel('BER'); - grid; grid minor on; - legend('boxoff'); - title('HF Multipath 1Hz Doppler 1ms delay'); - -end - - -% Some alternative, experimental methods tested during development - -function run_curves_hf_alt - sim_in.Nc = 7; - sim_in.Ns = 5; - sim_in.Nsec = 60; - sim_in.EbNodB = 5:0.5:8; - sim_in.verbose = 0; - sim_in.pilot_phase_est = 0; - sim_in.pilot_wide = 1; - sim_in.pilot_interp = 0; - sim_in.stripped_phase_est = 0; - sim_in.phase_offset = 0; - sim_in.phase_test = 0; - sim_in.hf_en = 1; - sim_in.hf_phase = 0; - - sim_in.Ns = 9; - hf_ref_Ns_9_no_phase = run_sim(sim_in); - - sim_in.hf_phase = 1; - sim_in.pilot_phase_est = 1; - hf_Ns_9 = run_sim(sim_in); - - sim_in.stripped_phase_est = 1; - hf_Ns_9_stripped = run_sim(sim_in); - - sim_in.stripped_phase_est = 0; - sim_in.pilot_wide = 0; - hf_Ns_9_narrow = run_sim(sim_in); - - sim_in.pilot_wide = 1; - sim_in.pilot_interp = 1; - hf_Ns_9_interp = run_sim(sim_in); - - figure(6); clf; - semilogy(sim_in.EbNodB, hf_ref_Ns_9_no_phase.ber,'c+-;Ns=9 HF ref no phase;'); - hold on; - semilogy(sim_in.EbNodB, hf_Ns_9.ber,'r+--;Ns=9;'); - semilogy(sim_in.EbNodB, hf_Ns_9_stripped.ber,'g+--;Ns=9 stripped refinement;'); - semilogy(sim_in.EbNodB, hf_Ns_9_narrow.ber,'b+--;Ns=9 narrow;'); - semilogy(sim_in.EbNodB, hf_Ns_9_interp.ber,'k+--;Ns=9 interp;'); - hold off; - axis([5 8 4E-2 1E-1]) - xlabel('Eb/No (dB)'); - ylabel('BER'); - grid; grid minor on; - legend('boxoff'); - title('HF Multipath 1Hz Doppler 1ms delay'); - -end - - -function run_curves_awgn - sim_in.Nc = 7; - sim_in.Ns = 5; - sim_in.Nsec = 240; - sim_in.verbose = 0; - sim_in.pilot_phase_est = 0; - sim_in.pilot_wide = 1; - sim_in.pilot_interp = 0; - sim_in.stripped_phase_est = 0; - sim_in.phase_offset = 0; - sim_in.phase_test = 0; - sim_in.hf_en = 0; - sim_in.hf_phase = 0; - - sim_in.EbNodB = 0:8; - - ber_awgn_theory = 0.5*erfc(sqrt(10.^(sim_in.EbNodB/10))); - sim_in.hf_en = 0; - sim_in.Ns = 5; - awgn_Ns_5 = run_sim(sim_in); - sim_in.Ns = 9; - awgn_Ns_9 = run_sim(sim_in); - sim_in.Ns = 17; - awgn_Ns_17 = run_sim(sim_in); - - figure(5); clf; - semilogy(sim_in.EbNodB, ber_awgn_theory,'b+-;AWGN Theory;'); - hold on; - semilogy(sim_in.EbNodB, awgn_Ns_5.ber,'g+-;Ns=5;'); - semilogy(sim_in.EbNodB + awgn_Ns_5.pilot_overhead, awgn_Ns_5.ber,'go-;Ns=5 with pilot overhead;'); - semilogy(sim_in.EbNodB, awgn_Ns_9.ber,'r+--;Ns=9;'); - semilogy(sim_in.EbNodB + awgn_Ns_9.pilot_overhead, awgn_Ns_9.ber,'ro-;Ns=9 with pilot overhead;'); - semilogy(sim_in.EbNodB, awgn_Ns_17.ber,'k+--;Ns=17;'); - semilogy(sim_in.EbNodB + awgn_Ns_17.pilot_overhead, awgn_Ns_17.ber,'ko-;Ns=17 with pilot overhead;'); - hold off; - axis([0 8 1E-3 2E-1]) - xlabel('Eb/No (dB)'); - ylabel('BER'); - grid; grid minor on; - legend('boxoff'); - title('AWGN'); - -end - - -function run_single - sim_in.Nsec = 120; - sim_in.Nc = 7; - sim_in.Ns = 9; - sim_in.EbNodB = 6; - sim_in.verbose = 1; - sim_in.pilot_phase_est = 1; - sim_in.pilot_wide = 1; - sim_in.pilot_interp = 0; - sim_in.stripped_phase_est = 0; - sim_in.phase_offset = 0; - sim_in.phase_test = 0; - sim_in.hf_en = 1; - sim_in.hf_phase = 1; - - run_sim(sim_in); -end - - -format; -more off; - -%run_single -run_curves_hf_alt - - - - diff --git a/codec2-dev/octave/bpsk_hf_rs.m b/codec2-dev/octave/bpsk_hf_rs.m new file mode 100644 index 00000000..8b013fe8 --- /dev/null +++ b/codec2-dev/octave/bpsk_hf_rs.m @@ -0,0 +1,786 @@ +% bpsk_hf_rs.m +% David Rowe Mar 2017 +% +% Rate Rs BPSK simulation to explore techniques for phase estimation +% over multiple carriers in HF channel + +#{ + TODO: + [X] sim pilot based phase est using known symbols + [X] test AWGN BER with averaging pilots from adj carriers + [X] refactor to insert pilot rows + [X] add border cols, not used for data + [X] centre est on current carrier, extend to > 3 + [X] test single points + + 1dB IL @ 6dB HF, 0.4 dB @ 2dB AWGN + [X] try linear interpolation + [X] try longer time windows + [X] try combining mod stripping phase est inside frame + [X] curves taking into account pilot losses + [ ] remove border carriers, interpolate edge carrier + [ ] modify for QPSK + [ ] change name +#} + +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 + + +function sim_out = run_sim(sim_in) + Rs = 100; + + bps = sim_in.bps; + EbNodB = sim_in.EbNodB; + verbose = sim_in.verbose; + hf_en = sim_in.hf_en; + hf_phase = sim_in.hf_phase; + phase_offset = sim_in.phase_offset; + + Ns = sim_in.Ns; % step size for pilots + Nc = sim_in.Nc; % Number of cols, aka number of carriers + + Nbitsperframe = (Ns-1)*Nc*bps; + Nrowsperframe = Nbitsperframe/(Nc*bps); + if verbose + printf("bps:.........: %d\n", bps); + printf("Nbitsperframe: %d\n", Nbitsperframe); + printf("Nrowsperframe: %d\n", Nrowsperframe); + end + + % Important to define run time in seconds so HF model will evolve the same way + % for different pilot insertion rates. So lets work backwards from approx + % seconds in run to get Nbits, the total number of payload data bits + + % frame has Ns-1 data symbols between pilots, e.g. for Ns=3: + % + % PPP + % DDD + % DDD + % PPP + + Nrows = sim_in.Nsec*Rs; + Nframes = floor((Nrows-1)/Ns); + Nbits = Nframes * Nbitsperframe; % number of payload data bits + + Nr = Nbits/(Nc*bps); % Number of data rows to get Nbits total + + if verbose + printf("Nc.....: %d\n", Nc); + printf("Ns.....: %d (step size for pilots, Ns-1 data symbols between pilots)\n", Ns); + printf("Nr.....: %d\n", Nr); + printf("Nbits..: %d\n", Nbits); + end + + % double check if Nbits fit neatly into carriers + + assert(Nbits/(Nc*bps) == floor(Nbits/(Nc*bps)), "Nbits/(Nc*bps) must be an integer"); + + printf("Nframes: %d\n", Nframes); + + Nrp = Nr + Nframes + 1; % number of rows once pilots inserted + % extra row of pilots at end + printf("Nrp....: %d (number of rows including pilots)\n", Nrp); + + % set up HF model + + if hf_en + + % some typical values, or replace with user supplied + + dopplerSpreadHz = 1.0; path_delay = 1E-3*Rs; + + if isfield(sim_in, "dopplerSpreadHz") + dopplerSpreadHz = sim_in.dopplerSpreadHz; + end + if isfield(sim_in, "path_delay") + path_delay = sim_in.path_delay; + end + printf("Doppler Spread: %3.2f Hz Path Delay: %3.2f symbols\n", dopplerSpreadHz, path_delay); + randn('seed',1); + spread1 = doppler_spread(dopplerSpreadHz, Rs, sim_in.Nsec*Rs*1.1); + spread2 = doppler_spread(dopplerSpreadHz, Rs, sim_in.Nsec*Rs*1.1); + + % sometimes doppler_spread() doesn't return exactly the number of samples we need + + assert(length(spread1) >= Nrp, "not enough doppler spreading samples"); + assert(length(spread2) >= Nrp, "not enough doppler spreading samples"); + + hf_gain = 1.0/sqrt(var(spread1)+var(spread2)); + % printf("nsymb: %d lspread1: %d\n", nsymb, length(spread1)); + end + + % construct an artificial phase countour for testing, linear across freq and time + + if sim_in.phase_test + phase_test = ones(Nrp, Nc+2); + for r=1:Nrp + for c=1:Nc+2 + phase_test(r,c) = -pi/2 + c*pi/(Nc+2) + r*0.01*2*pi; + phase_test(r,c) = phase_test(r,c) - 2*pi*floor((phase_test(r,c)+pi)/(2*pi)); + end + end + end + + % simulate for each Eb/No point ------------------------------------ + + for nn=1:length(EbNodB) + rand('seed',1); + randn('seed',1); + + EsNo = bps * (10 .^ (EbNodB(nn)/10)); + variance = 1/(EsNo/2); + noise = sqrt(variance)*(0.5*randn(Nrp,Nc+2) + j*0.5*randn(Nrp,Nc+2)); + + % generate tx bits + + tx_bits = rand(1,Nbits) > 0.5; + + % map to symbols + + if bps == 1 + tx_symb = 2*tx_bits - 1; + end + if bps == 2 + for s=1:Nbits/bps + tx_symb(s) = qpsk_mod(tx_bits(2*(s-1)+1:2*s)); + end + end + + % place symbols in multi-carrier frame with pilots and boundary carriers + + tx = []; s = 1; + for f=1:Nframes + aframe = zeros(Nrowsperframe,Nc+2); + aframe(1,:) = 1; + for r=1:Nrowsperframe + arowofsymbols = tx_symb(s:s+Nc-1); + s += Nc; + aframe(r+1,2:Nc+1) = arowofsymbols; + end + tx = [tx; aframe]; + end + tx = [tx; ones(1,Nc+2)]; % final row of pilots + [nr nc] = size(tx); + assert(nr == Nrp); + + rx = tx * exp(j*phase_offset); + + if sim_in.phase_test + rx = rx .* exp(j*phase_test); + end + + if hf_en + + % simplified rate Rs simulation model that doesn't include + % ISI, just freq filtering. + + % Note Rs carrier spacing, sample rate is Rs + + hf_model = zeros(Nr,Nc+2); phase_est = zeros(Nr,Nc); + for r=1:Nrp + for c=1:Nc+2 + w = 2*pi*c*Rs/Rs; + hf_model(r,c) = hf_gain*(spread1(r) + exp(-j*w*path_delay)*spread2(r)); + end + + if hf_phase + rx(r,:) = rx(r,:) .* hf_model(r,:); + else + rx(r,:) = rx(r,:) .* abs(hf_model(r,:)); + end + end + end + + rx += noise; + + % pilot based phase est, we use known tx symbols as pilots ---------- + + rx_corr = rx; + + if sim_in.pilot_phase_est + + % est phase from pilots either side of data symbols + % adjust phase of data symbol + % demodulate and count errors of just data + + phase_est_pilot_log = 10*ones(Nrp,Nc+2); + phase_est_stripped_log = 10*ones(Nrp,Nc+2); + phase_est_log = 10*ones(Nrp,Nc+2); + for c=2:Nc+1 + for r=1:Ns:Nrp-Ns + + % estimate phase using average of 6 pilots in a rect 2D window centred + % on this carrier + % PPP + % DDD + % DDD + % PPP + + cr = c-1:c+1; + aphase_est_pilot_rect1 = sum(rx(r,cr)*tx(r,cr)'); + aphase_est_pilot_rect2 = sum(rx(r+Ns,cr)*tx(r+Ns,cr)'); + + % optionally use next step of pilots in past and future + + if sim_in.pilot_wide + if r > Ns+1 + aphase_est_pilot_rect1 += sum(rx(r-Ns,cr)*tx(r-Ns,cr)'); + end + if r < Nrp - 2*Ns + aphase_est_pilot_rect2 += sum(rx(r+2*Ns,cr)*tx(r+2*Ns,cr)'); + end + end + + % correct phase offset using phase estimate + + for rr=r+1:r+Ns-1 + a = b = 1; + if sim_in.pilot_interp + b = (rr-r)/Ns; a = 1 - b; + end + %printf("rr: %d a: %4.3f b: %4.3f\n", rr, a, b); + aphase_est_pilot = angle(a*aphase_est_pilot_rect1 + b*aphase_est_pilot_rect2); + phase_est_pilot_log(rr,c) = aphase_est_pilot; + rx_corr(rr,c) = rx(rr,c) * exp(-j*aphase_est_pilot); + end + + if sim_in.stripped_phase_est + % Optional modulation stripping feed fwd phase estimation, to refine + % pilot-based phase estimate. Doing it after pilot based phase estimation + % means we don't need to deal with ambiguity, which is difficult to handle + % in low SNR channels. + + % Use vector of 7 symbols around current data symbol. We could use a 2D + % window if we can work out how best to correct with pilot-est and avoid + % ambiguities + + for rr=r+1:r+Ns-1 + + % extract a matrix of nearby samples with pilot-based offset removed + + amatrix = rx(max(1,rr-3):min(Nrp,rr+3),c) .* exp(-j*aphase_est_pilot); + + % modulation strip and est phase + + stripped = abs(amatrix) .* exp(j*2*angle(amatrix)); + aphase_est_stripped = angle(sum(sum(stripped)))/2; + phase_est_stripped_log(rr,c) = aphase_est_stripped; + + % correct rx symbols based on both phase ests + + phase_est_log(rr,c) = angle(exp(j*(aphase_est_pilot+aphase_est_stripped))); + rx_corr(rr,c) = rx(rr,c) * exp(-j*phase_est_log(rr,c)); + end + end % sim_in.stripped_phase_est + + end % r=1:Ns:Nrp-Ns + + end % c=2:Nc+1 + end % sim_in.pilot_phase_est + + + if isfield(sim_in, "ml_pd") && sim_in.ml_pd + + % Bill's ML with pilots phase detector, does phase est and demodulation + + rx_bits = []; rx_np = []; + aframeofbits = zeros(Ns-1, Nc); + for r=1:Ns:Nrp-Ns + + % demodulate this frame, ML operates carrier by carrier + + for c=2:Nc+1 + arxcol = rx(r:r+Ns, c); + arxcol(1) = rx(r, c-1) + rx(r, c+1); + arxcol(Ns+1) = rx(r+Ns, c-1) + rx(r+Ns, c+1); + [acolofbits aphase_est] = ml_pd(rot90(arxcol), bps, [1 Ns+1]); + aframeofbits(:,c-1) = xor(acolofbits, ones(1,Ns-1)); + rx_np = [rx_np rot90(arxcol) .* exp(-j*aphase_est)]; + end + + % unpack from frame into linear array of bits + + for rr=1:Ns-1 + rx_bits = [rx_bits aframeofbits(rr,:)]; + end + + end + else + + % remove pilots to give us just data symbols and demodulate + + rx_bits = []; rx_np = []; + for r=1:Nrp + if mod(r-1,Ns) != 0 + arowofsymbols = rx_corr(r,2:Nc+1); + rx_np = [rx_np arowofsymbols]; + if bps == 1 + arowofbits = real(arowofsymbols) > 0; + end + if bps == 2 + arowofbits = zeros(1,Nc); + for c=1:Nc + arowofbits((c-1)*2+1:c*2) = qpsk_demod(arowofsymbols(c)); + end + end + rx_bits = [rx_bits arowofbits]; + end + end + end + %tx_bits + %rx_bits + assert(length(rx_bits) == Nbits); + + %phase_test + %phase_est_log + + % calculate BER stats as a block, after pilots extracted + + errors = xor(tx_bits, rx_bits); + Nerrs = sum(errors); + + printf("EbNodB: %3.2f BER: %4.3f Nbits: %d Nerrs: %d\n", EbNodB(nn), Nerrs/Nbits, Nbits, Nerrs); + + if verbose + figure(1); clf; + plot(rx_np,'+'); + axis([-2 2 -2 2]); + + if hf_en + figure(2); clf; + plot(abs(hf_model(:,2:Nc+1))); + end + + if sim_in.pilot_phase_est + figure(3); clf; + plot(phase_est_log(:,2:Nc+1),'+', 'markersize', 10); + hold on; + plot(phase_est_pilot_log(:,2:Nc+1),'g+', 'markersize', 5); + if sim_in.stripped_phase_est + plot(phase_est_stripped_log(:,2:Nc+1),'ro', 'markersize', 5); + end + if sim_in.hf_en && sim_in.hf_phase + plot(angle(hf_model(:,2:Nc+1))); + end + if sim_in.phase_test + plot(phase_test(:,2:Nc+1)); + end + axis([1 Nrp -pi pi]); + end + end + + sim_out.ber(nn) = sum(Nerrs)/Nbits; + sim_out.pilot_overhead = 10*log10(Ns/(Ns-1)); + end +endfunction + + +% Plot BER against Eb/No curves at various pilot insertion rates Ns +% using the HF multipath channel. Second set of curves includes Eb/No +% loss for pilot insertion, so small Ns means better tracking of phase +% but large pilot insertion loss + +% Target operating point Eb/No is 6dB, as this is where our rate 1/2 +% LDPC code gives good results (10% PER, 1% BER). However this means +% the Eb/No at the input is 10*log(1/2) or 3dB less, so we need to +% make sure phase est works at Eb/No = 6 - 3 = 3dB + +function run_curves_hf + sim_in.Nc = 7; + sim_in.Ns = 5; + sim_in.Nsec = 240; + sim_in.EbNodB = 1:8; + sim_in.verbose = 0; + sim_in.pilot_phase_est = 0; + sim_in.pilot_wide = 1; + sim_in.pilot_interp = 0; + sim_in.stripped_phase_est = 0; + sim_in.phase_offset = 0; + sim_in.phase_test = 0; + sim_in.hf_en = 1; + sim_in.hf_phase = 0; + + sim_in.Ns = 5; + hf_ref_Ns_5_no_phase = run_sim(sim_in); + sim_in.Ns = 9; + hf_ref_Ns_9_no_phase = run_sim(sim_in); + + sim_in.hf_phase = 1; + sim_in.pilot_phase_est = 1; + + sim_in.Ns = 5; + hf_Ns_5 = run_sim(sim_in); + + sim_in.Ns = 9; + hf_Ns_9 = run_sim(sim_in); + + sim_in.Ns = 17; + hf_Ns_17 = run_sim(sim_in); + + figure(4); clf; + semilogy(sim_in.EbNodB, hf_ref_Ns_5_no_phase.ber,'b+-;Ns=5 HF ref no phase;'); + hold on; + semilogy(sim_in.EbNodB, hf_ref_Ns_9_no_phase.ber,'c+-;Ns=9 HF ref no phase;'); + semilogy(sim_in.EbNodB, hf_Ns_5.ber,'g+--;Ns=5;'); + semilogy(sim_in.EbNodB + hf_Ns_5.pilot_overhead, hf_Ns_5.ber,'go-;Ns=5 with pilot overhead;'); + semilogy(sim_in.EbNodB, hf_Ns_9.ber,'r+--;Ns=9;'); + semilogy(sim_in.EbNodB + hf_Ns_9.pilot_overhead, hf_Ns_9.ber,'ro-;Ns=9 with pilot overhead;'); + semilogy(sim_in.EbNodB, hf_Ns_17.ber,'k+--;Ns=17;'); + semilogy(sim_in.EbNodB + hf_Ns_17.pilot_overhead, hf_Ns_17.ber,'ko-;Ns=17 with pilot overhead;'); + hold off; + axis([1 8 4E-2 2E-1]) + xlabel('Eb/No (dB)'); + ylabel('BER'); + grid; grid minor on; + legend('boxoff'); + title('HF Multipath 1Hz Doppler 1ms delay'); + +end + + +% Generate HF curves for some alternative, experimental methods tested +% during development, such as interpolation, refinements using +% modulation stripping, narrow window. + +function run_curves_hf_alt + sim_in.Nc = 7; + sim_in.Ns = 5; + sim_in.Nsec = 60; + sim_in.EbNodB = 1:8; + sim_in.verbose = 0; + sim_in.pilot_phase_est = 0; + sim_in.pilot_wide = 1; + sim_in.pilot_interp = 0; + sim_in.stripped_phase_est = 0; + sim_in.phase_offset = 0; + sim_in.phase_test = 0; + sim_in.hf_en = 1; + sim_in.hf_phase = 0; + + sim_in.Ns = 9; + hf_ref_Ns_9_no_phase = run_sim(sim_in); + + sim_in.hf_phase = 1; + sim_in.pilot_phase_est = 1; + hf_Ns_9 = run_sim(sim_in); + + sim_in.stripped_phase_est = 1; + hf_Ns_9_stripped = run_sim(sim_in); + + sim_in.stripped_phase_est = 0; + sim_in.pilot_wide = 0; + hf_Ns_9_narrow = run_sim(sim_in); + + sim_in.pilot_wide = 1; + sim_in.pilot_interp = 1; + hf_Ns_9_interp = run_sim(sim_in); + + figure(6); clf; + semilogy(sim_in.EbNodB, hf_ref_Ns_9_no_phase.ber,'c+-;Ns=9 HF ref no phase;'); + hold on; + semilogy(sim_in.EbNodB, hf_Ns_9.ber,'r+--;Ns=9;'); + semilogy(sim_in.EbNodB, hf_Ns_9_stripped.ber,'g+--;Ns=9 stripped refinement;'); + semilogy(sim_in.EbNodB, hf_Ns_9_narrow.ber,'b+--;Ns=9 narrow;'); + semilogy(sim_in.EbNodB, hf_Ns_9_interp.ber,'k+--;Ns=9 interp;'); + hold off; + axis([1 8 4E-2 2E-1]) + xlabel('Eb/No (dB)'); + ylabel('BER'); + grid; grid minor on; + legend('boxoff'); + title('HF Multipath 1Hz Doppler 1ms delay'); + +end + + +% Generate HF curves for fixed Ns but different HF channels. + +function run_curves_hf_channels + sim_in.Nc = 7; + sim_in.Ns = 9; + sim_in.Nsec = 240; + sim_in.EbNodB = 1:8; + sim_in.verbose = 0; + sim_in.pilot_phase_est = 0; + sim_in.pilot_wide = 1; + sim_in.pilot_interp = 0; + sim_in.stripped_phase_est = 0; + sim_in.phase_offset = 0; + sim_in.phase_test = 0; + sim_in.hf_en = 1; + sim_in.hf_phase = 0; + + hf_Ns_9_1hz_1ms_no_phase = run_sim(sim_in); + + sim_in.hf_phase = 1; + sim_in.pilot_phase_est = 1; + hf_Ns_9_1hz_1ms = run_sim(sim_in); + + Rs = 100; + + sim_in.dopplerSpreadHz = 1.0; + sim_in.path_delay = 500E-6*Rs; + hf_Ns_9_1hz_500us = run_sim(sim_in); + + sim_in.dopplerSpreadHz = 1.0; + sim_in.path_delay = 2E-3*Rs; + hf_Ns_9_1hz_2ms = run_sim(sim_in); + + sim_in.dopplerSpreadHz = 2.0; + sim_in.path_delay = 1E-3*Rs; + hf_Ns_9_2hz_1ms = run_sim(sim_in); + + sim_in.dopplerSpreadHz = 2.0; + sim_in.path_delay = 1E-3*Rs; + hf_Ns_9_2hz_2ms = run_sim(sim_in); + + sim_in.dopplerSpreadHz = 2.0; + sim_in.path_delay = 2E-3*Rs; + hf_Ns_9_2hz_2ms = run_sim(sim_in); + + sim_in.dopplerSpreadHz = 4.0; + sim_in.path_delay = 1E-3*Rs; + hf_Ns_9_4hz_1ms = run_sim(sim_in); + + figure(6); clf; + semilogy(sim_in.EbNodB, hf_Ns_9_1hz_1ms_no_phase.ber,'c+-;Ns=9 1Hz 1ms ref no phase;'); + hold on; + semilogy(sim_in.EbNodB, hf_Ns_9_1hz_500us.ber,'k+-;Ns=9 1Hz 500us;'); + semilogy(sim_in.EbNodB, hf_Ns_9_1hz_1ms.ber,'r+-;Ns=9 1Hz 1ms;'); + semilogy(sim_in.EbNodB, hf_Ns_9_1hz_2ms.ber,'bo-;Ns=9 1Hz 2ms;'); + semilogy(sim_in.EbNodB, hf_Ns_9_2hz_1ms.ber,'g+-;Ns=9 2Hz 1ms;'); + semilogy(sim_in.EbNodB, hf_Ns_9_2hz_2ms.ber,'mo-;Ns=9 2Hz 2ms;'); + semilogy(sim_in.EbNodB, hf_Ns_9_4hz_1ms.ber,'c+-;Ns=9 4Hz 1ms;'); + hold off; + axis([1 8 4E-2 2E-1]) + xlabel('Eb/No (dB)'); + ylabel('BER'); + grid; grid minor on; + legend('boxoff'); + title('HF Multipath Ns = 9'); + +end + + +% AWGN curves for BPSK and QPSK. Coded Eb/No operating point is 2dB, +% so raw BER for rate 1/2 will be -1dB + +function run_curves_awgn_bpsk_qpsk + sim_in.Nc = 7; + sim_in.Ns = 7; + sim_in.Nsec = 30; + sim_in.verbose = 0; + sim_in.pilot_phase_est = 0; + sim_in.pilot_wide = 1; + sim_in.pilot_interp = 0; + sim_in.stripped_phase_est = 1; + sim_in.phase_offset = 0; + sim_in.phase_test = 0; + sim_in.hf_en = 0; + sim_in.hf_phase = 0; + + sim_in.EbNodB = -3:5; + + ber_awgn_theory = 0.5*erfc(sqrt(10.^(sim_in.EbNodB/10))); + + sim_in.bps = 1; + awgn_bpsk = run_sim(sim_in); + sim_in.bps = 2; + awgn_qpsk = run_sim(sim_in); + + figure(5); clf; + semilogy(sim_in.EbNodB, ber_awgn_theory,'b+-;AWGN Theory;'); + hold on; + semilogy(sim_in.EbNodB, awgn_bpsk.ber,'g+-;Ns=7 BPSK;'); + semilogy(sim_in.EbNodB + awgn_bpsk.pilot_overhead, awgn_bpsk.ber,'go-;Ns=7 BPSK with pilot overhead;'); + semilogy(sim_in.EbNodB, awgn_qpsk.ber,'r+-;Ns=7 QPSK;'); + semilogy(sim_in.EbNodB + awgn_qpsk.pilot_overhead, awgn_qpsk.ber,'ro-;Ns=7 QPSK with pilot overhead;'); + hold off; + axis([-3 5 4E-3 2E-1]) + xlabel('Eb/No (dB)'); + ylabel('BER'); + grid; grid minor on; + legend('boxoff'); + title('AWGN'); +end + + +% HF multipath curves for BPSK and QPSK. Coded operating point is about 3dB + +function run_curves_hf_bpsk_qpsk + sim_in.Nc = 7; + sim_in.Ns = 7; + sim_in.Nsec = 120; + sim_in.verbose = 0; + sim_in.pilot_phase_est = 1; + sim_in.pilot_wide = 1; + sim_in.pilot_interp = 0; + sim_in.stripped_phase_est = 0; + sim_in.phase_offset = 0; + sim_in.phase_test = 0; + sim_in.hf_en = 1; + sim_in.hf_phase = 1; + + sim_in.EbNodB = 1:8; + + EbNoLin = 10.^(sim_in.EbNodB/10); + hf_theory = 0.5.*(1-sqrt(EbNoLin./(EbNoLin+1))); + + sim_in.bps = 1; + hf_bpsk = run_sim(sim_in); + sim_in.bps = 2; + hf_qpsk = run_sim(sim_in); + + figure(5); clf; + semilogy(sim_in.EbNodB, hf_theory,'b+-;HF Theory;'); + hold on; + semilogy(sim_in.EbNodB, hf_bpsk.ber,'g+-;Ns=7 BPSK;'); + semilogy(sim_in.EbNodB + hf_bpsk.pilot_overhead, hf_bpsk.ber,'go-;Ns=7 BPSK with pilot overhead;'); + semilogy(sim_in.EbNodB, hf_qpsk.ber,'r+-;Ns=7 QPSK;'); + semilogy(sim_in.EbNodB + hf_qpsk.pilot_overhead, hf_qpsk.ber,'ro-;Ns=7 QPSK with pilot overhead;'); + hold off; + axis([1 8 4E-3 2E-1]) + xlabel('Eb/No (dB)'); + ylabel('BER'); + grid; grid minor on; + legend('boxoff'); + title('HF Multipath'); +end + + +% AWGN curves for BPSK using 3 carrier 2D matrix pilot and ML pilot + +function run_curves_awgn_ml + sim_in.bps = 1; + sim_in.Nc = 7; + sim_in.Ns = 7; + sim_in.Nsec = 10; + sim_in.verbose = 0; + sim_in.pilot_phase_est = 1; + sim_in.pilot_wide = 1; + sim_in.pilot_interp = 0; + sim_in.stripped_phase_est = 1; + sim_in.phase_offset = 0; + sim_in.phase_test = 0; + sim_in.hf_en = 0; + sim_in.hf_phase = 0; + + sim_in.EbNodB = -3:5; + + ber_awgn_theory = 0.5*erfc(sqrt(10.^(sim_in.EbNodB/10))); + + awgn_2d = run_sim(sim_in); + sim_in.pilot_phase_est = 0; + sim_in.ml_pd = 1; + awgn_ml = run_sim(sim_in); + + figure(5); clf; + semilogy(sim_in.EbNodB, ber_awgn_theory,'b+-;AWGN Theory;'); + hold on; + semilogy(sim_in.EbNodB, awgn_2d.ber,'g+-;Ns=7 3 carrier pilot BPSK;'); + semilogy(sim_in.EbNodB, awgn_ml.ber,'ro-;Ns=7 ML pilot BPSK;'); + hold off; + axis([-3 5 4E-3 5E-1]) + xlabel('Eb/No (dB)'); + ylabel('BER'); + grid; grid minor on; + legend('boxoff'); + title('AWGN'); +end + + +% HF multipath curves for ML + +function run_curves_hf_ml + sim_in.bps = 1; + sim_in.Nc = 7; + sim_in.Ns = 14; + sim_in.Nsec = 120; + sim_in.verbose = 0; + sim_in.pilot_phase_est = 1; + sim_in.pilot_wide = 1; + sim_in.pilot_interp = 0; + sim_in.stripped_phase_est = 0; + sim_in.phase_offset = 0; + sim_in.phase_test = 0; + sim_in.hf_en = 1; + sim_in.hf_phase = 1; + + sim_in.EbNodB = 1:8; + + EbNoLin = 10.^(sim_in.EbNodB/10); + hf_theory = 0.5.*(1-sqrt(EbNoLin./(EbNoLin+1))); + + hf_2d = run_sim(sim_in); + sim_in.pilot_phase_est = 0; + sim_in.ml_pd = 1; + hf_ml = run_sim(sim_in); + + figure(7); clf; + semilogy(sim_in.EbNodB, hf_theory,'b+-;HF Theory;'); + hold on; + semilogy(sim_in.EbNodB, hf_2d.ber,'g+-;Ns=7 3 carrier pilot BPSK;'); + semilogy(sim_in.EbNodB, hf_ml.ber,'ro-;Ns=7 ML pilot BPSK;'); + hold off; + axis([1 8 4E-3 2E-1]) + xlabel('Eb/No (dB)'); + ylabel('BER'); + grid; grid minor on; + legend('boxoff'); + title('HF Multipath'); +end + + + +function run_single + sim_in.bps = 1; + sim_in.Nsec = 30; + sim_in.Nc = 3; + sim_in.Ns = 9; + sim_in.EbNodB = -1; + sim_in.verbose = 1; + sim_in.pilot_phase_est = 1; + sim_in.pilot_wide = 1; + sim_in.pilot_interp = 0; + sim_in.stripped_phase_est = 0; + sim_in.phase_offset = 0; + sim_in.phase_test = 0; + sim_in.hf_en = 0; + sim_in.hf_phase = 0; + sim_in.ml_pd = 1; + + run_sim(sim_in); +end + + +format; +more off; + +%run_single +%run_curves_hf_bpsk_qpsk +%run_curves_hf_channels +run_curves_hf_ml + + + +