+++ /dev/null
-% 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
-
-
-
-
--- /dev/null
+% 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
+
+
+
+
projects / freetel-svn-tracking.git / commitdiff