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21 KiB

% ofdm_rs.m
% David Rowe Mar 2017
%
% Rate Rs BPSK/QPSK simulation to explore techniques for
% phase estimation over multiple carriers in HF channel. Rate
% Rs version of ofdm_fs.m
#{
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
[X] modify for QPSK
#}
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");
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) = 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
% normalise power over HF simulation run
p = sum(var(rx));
rx *= sqrt(Nc/p);
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: %5.4f 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 = 2;
sim_in.Nsec = 60;
sim_in.Nc = 16;
sim_in.Ns = 8;
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.ml_pd = 0;
sim_in.phase_offset = 0;
sim_in.phase_test = 0;
sim_in.hf_en = 1;
sim_in.hf_phase = 1;
sim_in.path_delay = 0;
run_sim(sim_in);
EbNoLin = 10.^(sim_in.EbNodB/10);
hf_theory = 0.5.*(1-sqrt(EbNoLin./(EbNoLin+1)));
printf("HF theory: %5.4f\n", hf_theory);
end
format;
more off;
run_single
%run_curves_hf_bpsk_qpsk
%run_curves_hf_channels
%run_curves_hf_ml