From: drowe67 Date: Sat, 29 Apr 2017 22:40:11 +0000 (+0000) Subject: split rate fs ofdm simulation into multiple files X-Git-Url: http://git.whiteaudio.com/gitweb/?a=commitdiff_plain;h=be9acf2659ac2aee76cee4bb18c20b5c6f2dc72c;p=freetel-svn-tracking.git split rate fs ofdm simulation into multiple files git-svn-id: https://svn.code.sf.net/p/freetel/code@3111 01035d8c-6547-0410-b346-abe4f91aad63 --- diff --git a/codec2-dev/octave/ofdm_dev.m b/codec2-dev/octave/ofdm_dev.m new file mode 100644 index 00000000..2cfed8af --- /dev/null +++ b/codec2-dev/octave/ofdm_dev.m @@ -0,0 +1,516 @@ +% ofdm_dev.m +% David Rowe April 2017 +% +% Simulations used for development and testing of Rate Fs BPSK/QPSK +% OFDM modem. + +ofdm_lib; + +#{ + TODO: + [ ] compute SNR and PAPR + [ ] SSB bandpass filtering + [ ] way to simulate aquisition and demod + [ ] testframe based +#} + +function [sim_out rate_fs_pilot_samples rx] = run_sim(sim_in) + + % set up core modem constants + + states = ofdm_init(sim_in.bps, sim_in.Rs, sim_in.Tcp, sim_in.Ns, sim_in.Nc); + ofdm_load_const; + + % simulation parameters and flags + + woffset = 2*pi*sim_in.foff_hz/Fs; + EbNodB = sim_in.EbNodB; + verbose = states.verbose = sim_in.verbose; + hf_en = sim_in.hf_en; + timing_en = states.timing_en = sim_in.timing_en; + states.foff_est_en = foff_est_en = sim_in.foff_est_en; + states.phase_est_en = phase_est_en = sim_in.phase_est_en; + + if verbose + printf("Rs:..........: %4.2f\n", Rs); + printf("M:...........: %d\n", M); + printf("Ncp:.........: %d\n", Ncp); + printf("bps:.........: %d\n", bps); + printf("Nbitsperframe: %d\n", Nbitsperframe); + printf("Nrowsperframe: %d\n", Nrowsperframe); + printf("Nsamperframe.: %d\n", Nsamperframe); + 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 + + 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 + + % double check if Nbits fit neatly into carriers + + assert(Nbits/(Nc*bps) == floor(Nbits/(Nc*bps)), "Nbits/(Nc*bps) must be an integer"); + + Nrp = Nr + Nframes + 1; % number of rows once pilots inserted + % extra row of pilots at end + + 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); + printf("Nframes: %d\n", Nframes); + printf("Nrp....: %d (number of rows including pilots)\n", Nrp); + end + + % set up HF model --------------------------------------------------------------- + + if hf_en + + % some typical values, or replace with user supplied + + dopplerSpreadHz = 1.0; path_delay_ms = 1; + + if isfield(sim_in, "dopplerSpreadHz") + dopplerSpreadHz = sim_in.dopplerSpreadHz; + end + if isfield(sim_in, "path_delay_ms") + path_delay_ms = sim_in.path_delay_ms; + end + path_delay_samples = path_delay_ms*Fs/1000; + printf("Doppler Spread: %3.2f Hz Path Delay: %3.2f ms %d samples\n", dopplerSpreadHz, path_delay_ms, path_delay_samples); + + % generate same fading pattern for every run + + randn('seed',1); + + spread1 = doppler_spread(dopplerSpreadHz, Fs, (sim_in.Nsec*(M+Ncp)/M+0.2)*Fs); + spread2 = doppler_spread(dopplerSpreadHz, Fs, (sim_in.Nsec*(M+Ncp)/M+0.2)*Fs); + + % sometimes doppler_spread() doesn't return exactly the number of samples we need + + assert(length(spread1) >= Nrp*M, "not enough doppler spreading samples"); + assert(length(spread2) >= Nrp*M, "not enough doppler spreading samples"); + + hf_gain = 1.0/sqrt(var(spread1)+var(spread2)); + % printf("nsymb: %d lspread1: %d\n", nsymb, length(spread1)); + end + + % ------------------------------------------------------------------ + % simulate for each Eb/No point + % ------------------------------------------------------------------ + + for nn=1:length(EbNodB) + rand('seed',1); + randn('seed',1); + + EbNo = bps * (10 .^ (EbNodB(nn)/10)); + variance = 1/(M*EbNo/2); + + Nsam = Nrp*(M+Ncp); + + % generate tx bits and run OFDM modulator + + tx_bits = rand(1,Nbits) > 0.5; + + tx = []; + for f=1:Nframes + tx = [tx ofdm_mod(states, tx_bits((f-1)*Nbitsperframe+1:f*Nbitsperframe))]; + end + + % add extra row of pilots at end, to allow one frame simulations, + % useful for development + + st = Nsamperframe*(Nframes-1)+1; en = st+Ncp+M-1; + tx = [tx tx(st:en)]; + assert(length(tx) == Nsam); + + % channel simulation --------------------------------------------------------------- + + if isfield(sim_in, "sample_clock_offset_ppm") + % todo: this only works for large ppm like 500, runs out of memory + % for small ppm + + if sim_in.sample_clock_offset_ppm + timebase = floor(abs(1E6/sim_in.sample_clock_offset_ppm)); + if sim_in.sample_clock_offset_ppm > 0 + tx = resample(tx, timebase+1, timebase); + else + tx = resample(tx, timebase, timebase+1); + end + + % make sure length is correct for rest of simulation + + tx = [tx zeros(1,Nsam-length(tx))]; + tx = tx(1:Nsam); + end + end + + rx = tx; + + if hf_en + %rx = [zeros(1,path_delay_samples) tx(1:Nsam-path_delay_samples)]; + rx = hf_gain * tx(1:Nsam) .* spread1(1:Nsam); + rx += hf_gain * [zeros(1,path_delay_samples) tx(1:Nsam-path_delay_samples)] .* spread2(1:Nsam); + end + + rx = rx .* exp(j*woffset*(1:Nsam)); + + noise = sqrt(variance)*(0.5*randn(1,Nsam) + j*0.5*randn(1,Nsam)); + rx += noise; + + % some spare samples at end to avoid overflow as est windows may poke into the future a bit + + rx = [rx zeros(1,Nsamperframe)]; + + % bunch of logs + + phase_est_pilot_log = []; + delta_t_log = []; + timing_est_log = []; + foff_est_hz_log = []; + Nerrs_log = []; + rx_bits = []; rx_np = []; + + % reset some states for each EbNo simulation point + + states.sample_point = states.timing_est = 1; + if timing_en == 0 + states.sample_point = Ncp; + end + states.nin = Nsamperframe; + states.foff_est_hz = 0; + + % for this simulation we "prime" buffer to allow one frame runs during development + + prx = 1; + states.rxbuf(M+Ncp+2*Nsamperframe+1:Nrxbuf) = rx(prx:Nsamperframe+2*(M+Ncp)); + prx += Nsamperframe+2*(M+Ncp); + + for f=1:Nframes + + % insert samples at end of buffer, set to zero if no samples + % available to disable phase estimation on future pilots on last + % frame of simulation + + lnew = min(Nsam-prx,states.nin); + rxbuf_in = zeros(1,states.nin); + + if lnew + rxbuf_in(1:lnew) = rx(prx:prx+lnew-1); + end + prx += states.nin; + + [arx_bits states aphase_est_pilot_log arx_np] = ofdm_demod(states, rxbuf_in); + + rx_bits = [rx_bits arx_bits]; rx_np = [rx_np arx_np]; + timing_est_log = [timing_est_log states.timing_est]; + delta_t_log = [delta_t_log states.delta_t]; + foff_est_hz_log = [foff_est_hz_log states.foff_est_hz]; + phase_est_pilot_log = [phase_est_pilot_log; aphase_est_pilot_log]; + end + + assert(length(rx_bits) == Nbits); + + % calculate BER stats as a block, after pilots extracted + + errors = xor(tx_bits, rx_bits); + Nerrs = sum(errors); + for f=1:Nframes + st = (f-1)*Nbitsperframe+1; en = st + Nbitsperframe-1; + Nerrs_log(f) = sum(xor(tx_bits(st:en), rx_bits(st:en))); + end + + 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]); + title('Scatter'); + + figure(2); clf; + plot(phase_est_pilot_log(:,2:Nc+1),'g+', 'markersize', 5); + title('Phase est'); + axis([1 Nrp -pi pi]); + + figure(3); clf; + subplot(211) + stem(delta_t_log) + title('delta t'); + subplot(212) + plot(timing_est_log); + title('timing est'); + + figure(4); clf; + plot(foff_est_hz_log) + axis([1 max(Nframes,2) -3 3]); + title('Fine Freq'); + + figure(5); clf; + plot(Nerrs_log); + +#{ + figure(2) + Tx = abs(fft(tx(1:Nsam).*hanning(Nsam)')); + Tx_dB = 20*log10(Tx); + dF = Fs/Nsam; + plot((1:Nsam)*dF, Tx_dB); + mx = max(Tx_dB); + axis([0 Fs/2 mx-60 mx]) +#} + +#{ + if hf_en + figure(4); clf; + subplot(211) + plot(abs(spread1(1:Nsam))); + %hold on; plot(abs(spread2(1:Nsam)),'g'); hold off; + subplot(212) + plot(angle(spread1(1:Nsam))); + title('spread1 amp and phase'); + end +#} + +#{ + % todo, work out a way to plot rate Fs hf model phase + if sim_in.hf_en + plot(angle(hf_model(:,2:Nc+1))); + end +#} + + + end + + sim_out.ber(nn) = sum(Nerrs)/Nbits; + sim_out.pilot_overhead = 10*log10(Ns/(Ns-1)); + sim_out.M = M; sim_out.Fs = Fs; sim_out.Ncp = Ncp; + sim_out.Nrowsperframe = Nrowsperframe; sim_out.Nsamperframe = Nsamperframe; + end +endfunction + + +function run_single + Ts = 0.018; + sim_in.Tcp = 0.002; + sim_in.Rs = 1/Ts; sim_in.bps = 2; sim_in.Nc = 16; sim_in.Ns = 8; + + %sim_in.Nsec = 5*(sim_in.Ns+1)/sim_in.Rs; % one frame + sim_in.Nsec = 30; + + sim_in.EbNodB = 3; + sim_in.verbose = 1; + sim_in.hf_en = 1; + sim_in.foff_hz = 0; + sim_in.timing_en = 1; + sim_in.sample_clock_offset_ppm = 0; + sim_in.foff_est_en = 1; + sim_in.phase_est_en = 1; + + run_sim(sim_in); +end + + +% Plot BER against Eb/No curves for AWGN and HF + +% Target operating point Eb/No for HF 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 +% +% For AWGN target is 2dB so -1dB op point. + +function run_curves + Ts = 0.010; + sim_in.Rs = 1/Ts; + sim_in.Tcp = 0.002; + sim_in.bps = 2; sim_in.Ns = 8; sim_in.Nc = 8; sim_in.verbose = 0; + sim_in.foff_hz = 0; + + pilot_overhead = (sim_in.Ns-1)/sim_in.Ns; + cp_overhead = Ts/(Ts+sim_in.Tcp); + overhead_dB = -10*log10(pilot_overhead*cp_overhead); + + sim_in.hf_en = 0; + sim_in.Nsec = 30; + sim_in.EbNodB = -3:5; + awgn_EbNodB = sim_in.EbNodB; + + awgn_theory = 0.5*erfc(sqrt(10.^(sim_in.EbNodB/10))); + awgn = run_sim(sim_in); + + sim_in.hf_en = 1; + sim_in.Nsec = 120; + sim_in.EbNodB = 1:8; + + EbNoLin = 10.^(sim_in.EbNodB/10); + hf_theory = 0.5.*(1-sqrt(EbNoLin./(EbNoLin+1))); + + hf = run_sim(sim_in); + + figure(4); clf; + semilogy(awgn_EbNodB, awgn_theory,'b+-;AWGN theory;'); + hold on; + semilogy(sim_in.EbNodB, hf_theory,'b+-;HF theory;'); + semilogy(awgn_EbNodB+overhead_dB, awgn_theory,'g+-;AWGN lower bound with pilot + CP overhead;'); + semilogy(sim_in.EbNodB+overhead_dB, hf_theory,'g+-;HF lower bound with pilot + CP overhead;'); + semilogy(awgn_EbNodB+overhead_dB, awgn.ber,'r+-;AWGN sim;'); + semilogy(sim_in.EbNodB+overhead_dB, hf.ber,'r+-;HF sim;'); + hold off; + axis([-3 8 1E-2 2E-1]) + xlabel('Eb/No (dB)'); + ylabel('BER'); + grid; grid minor on; + legend('boxoff'); +end + + +% Run an acquisition test, returning vectors of estimation errors + +function [delta_t delta_foff] = acquisition_test(Ntests=10, EbNodB=100, foff_hz=0, hf_en=0, fine_en=0) + + % generate test signal at a given Eb/No and frequency offset + + Ts = 0.016; + sim_in.Tcp = 0.002; + sim_in.Rs = 1/Ts; sim_in.bps = 2; sim_in.Nc = 16; sim_in.Ns = 8; + + sim_in.Nsec = Ntests*(sim_in.Ns+1)/sim_in.Rs; + + sim_in.EbNodB = EbNodB; + sim_in.verbose = 0; + sim_in.hf_en = hf_en; + sim_in.foff_hz = foff_hz; sim_in.timing_en = 0; + + % set up acquistion + + Nsamperframe = states.Nsamperframe = sim_out.Nsamperframe; + states.M = sim_out.M; states.Ncp = sim_out.Ncp; + states.verbose = 0; + states.Fs = sim_out.Fs; + + % test fine or acquisition over test signal + #{ + fine: - start with coarse timing instant + - on each frame est timing a few samples about that point + - update timing instant + + corr: - where is best plcase to sample + - just before end of symbol? + - how long should sequence be? + - add extra? + - aim for last possible moment? + - man I hope IL isn't too big..... + #} + + delta_t = []; delta_t = []; delta_foff = []; + + if fine_en + + window_width = 5; % search +/-2 samples from current timing instant + timing_instant = Nsamperframe+1; % start at correct instant for AWGN + % start at second frame so we can search -2 ... +2 + + while timing_instant < (length(rx) - (Nsamperframe + length(rate_fs_pilot_samples) + window_width)) + st = timing_instant - ceil(window_width/2); + en = st + Nsamperframe-1 + length(rate_fs_pilot_samples) + window_width-1; + [ft_est foff_est] = coarse_sync(states, rx(st:en), rate_fs_pilot_samples); + printf("ft_est: %d timing_instant %d %d\n", ft_est, timing_instant, mod(timing_instant, Nsamperframe)); + timing_instant += Nsamperframe + ft_est - ceil(window_width/2); + delta_t = [delta_ft ft_est - ceil(window_width/2)]; + end + else + % for coarse simulation we just use contant window shifts + + st = 0.5*Nsamperframe; + en = 2.5*Nsamperframe - 1; + ct_target = Nsamperframe/2; + + for w=1:Nsamperframe:length(rx)-3*Nsamperframe + %st = w+0.5*Nsamperframe; en = st+2*Nsamperframe-1; + %[ct_est foff_est] = coarse_sync(states, rx(st:en), rate_fs_pilot_samples); + [ct_est foff_est] = coarse_sync(states, rx(w+st:w+en), rate_fs_pilot_samples); + printf("ct_est: %4d foff_est: %3.1f\n", ct_est, foff_est); + + % valid coarse timing ests are modulo Nsamperframe + + delta_t = [delta_ct ct_est-ct_target]; + delta_foff = [delta_foff (foff_est-foff_hz)]; + end + end + +endfunction + + +% Run some tests for various acquisition conditions. Probability of +% acquistion is what matters, e.g. if it's 50% we can expect sync +% within 2 frames +% P(t)/P(f) P(t)/P(f) +% Eb/No AWGN HF +% +/- 25Hz -1/3 1.0/0.3 0.96/0.3 +% +/- 5Hz -1/3 1.0/0.347 0.96/0.55 +% +/- 25Hz 10/10 1.00/0.92 0.99/0.77 + +function acquisition_histograms(fine_en = 0) + Fs = 8000; + Ntests = 100; + + % allowable tolerance for acquistion + + ftol_hz = 2.0; + ttol_samples = 0.002*Fs; + + % AWGN channel operating point + + [dct dfoff] = acquisition_test(Ntests, -1, 25, 0, fine_en); + + % Probability of acquistion is what matters, e.g. if it's 50% we can + % expect sync within 2 frames + + printf("AWGN P(time offset acq) = %3.2f\n", length(find (abs(dct) < ttol_samples))/length(dct)); + if fine_en == 0 + printf("AWGN P(freq offset acq) = %3.2f\n", length(find (abs(dfoff) < ftol_hz))/length(dfoff)); + end + + figure(1) + hist(dct(find (abs(dct) < ttol_samples))) + if fine_en == 0 + figure(2) + hist(dfoff) + end + + % HF channel operating point + + [dct dfoff] = acquisition_test(Ntests, 3, 25, 1, fine_en); + + printf("HF P(time offset acq) = %3.2f\n", length(find (abs(dct) < ttol_samples))/length(dct)); + if fine_en == 0 + printf("HF P(freq offset acq) = %3.2f\n", length(find (abs(dfoff) < ftol_hz))/length(dfoff)); + end + + figure(3) + hist(dct(find (abs(dct) < ttol_samples))) + if fine_en == 0 + figure(4) + hist(dfoff) + end + +endfunction + + +% --------------------------------------------------------- +% choose simulation to run here +% --------------------------------------------------------- + +format; +more off; + +run_single +%run_curves +%acquisition_histograms(1) + diff --git a/codec2-dev/octave/ofdm_fs.m b/codec2-dev/octave/ofdm_fs.m deleted file mode 100644 index 821f9842..00000000 --- a/codec2-dev/octave/ofdm_fs.m +++ /dev/null @@ -1,896 +0,0 @@ -% ofdm_fs.m -% David Rowe Mar 2017 -% -% Rate Fs BPSK/QPSK OFDM simulation, rate Fs verison of ofdm_rs.m with -% OFDM based up and down conversion. - -#{ - TODO: - [X] strip back experimental stuff to just features we need - [X] ZOH/integrator - [X] OFDM up and down conversion - [X] rate Fs HF model and HF results - [X] add QPSK - [X] add CP - [X] fine timing estimator and sample clock offset tracking - [X] acquisition coarse timing & freq offset estimation - [ ] adjust waveform parameters for real world - [ ] Nsec run time take into account CP - [ ] plot phase ests - [ ] handle border carriers - [ ] start with phantom carriers - + but unhappy with 1800Hz bandwidth - [ ] also try interpolation or just single row - [ ] compute SNR and PAPR - [ ] SSB bandpass filtering -#} - -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 - - -% Correlates the OFDM pilot symbol samples with a window of received -% samples to determine the most likely timing offset. Combines two -% frames pilots so we need at least Nsamperframe+M+Ncp samples in rx. -% Also determines frequency offset at maximimum correlation. Can be -% used for acquisition (coarse timing a freq offset), and fine timing - -function [t_est foff_est] = coarse_sync(states, rx, rate_fs_pilot_samples) - Nsamperframe = states.Nsamperframe; Fs = states.Fs; - Npsam = length(rate_fs_pilot_samples); - verbose = states.verbose; - - Ncorr = length(rx) - (Nsamperframe+Npsam) + 1; - assert(Ncorr > 0); - corr = zeros(1,Ncorr); - for i=1:Ncorr - corr(i) = abs(rx(i:i+Npsam-1) * rate_fs_pilot_samples'); - corr(i) += abs(rx(i+Nsamperframe:i+Nsamperframe+Npsam-1) * rate_fs_pilot_samples'); - end - - [mx t_est] = max(abs(corr)); - - C = abs(fft(rx(t_est:t_est+Npsam-1) .* conj(rate_fs_pilot_samples), Fs)); - C += abs(fft(rx(t_est+Nsamperframe:t_est+Nsamperframe+Npsam-1) .* conj(rate_fs_pilot_samples), Fs)); - - fmax = 30; - [mx_pos foff_est_pos] = max(C(1:fmax)); - [mx_neg foff_est_neg] = max(C(Fs-fmax+1:Fs)); - - if mx_pos > mx_neg - foff_est = foff_est_pos - 1; - else - foff_est = foff_est_neg - fmax - 1; - end - - if verbose > 1 - %printf("t_est: %d\n", t_est); - figure(7); clf; - plot(abs(corr)) - figure(8) - plot(C) - axis([0 200 0 0.4]) - end -endfunction - - -#{ - Frame has Ns-1 data symbols between pilots, e.g. for Ns=3: - - PPP - DDD - DDD - PPP -#} - -function states = ofdm_init(bps, Rs, Tcp, Ns, Nc) - states.Fs = 8000; - states.bps = bps; - states.Rs = Rs; - states.Tcp = Tcp; - states.Ns = Ns; % step size for pilots - states.Nc = Nc; % Number of cols, aka number of carriers - states.M = states.Fs/Rs; - states.Ncp = Tcp*states.Fs; - states.Nbitsperframe = (Ns-1)*Nc*bps; - states.Nrowsperframe = states.Nbitsperframe/(Nc*bps); - states.Nsamperframe = (states.Nrowsperframe+1)*(states.M+states.Ncp); - - % generate same pilots each time - - rand('seed',1); - states.pilots = 1 - 2*(rand(1,Nc+2) > 0.5); - - % carrier tables for up and down conversion - - w = (0:Nc+1)*2*pi*Rs/states.Fs; - W = zeros(Nc+2,states.M); - for c=1:Nc+2 - W(c,:) = exp(j*w(c)*(0:states.M-1)); - end - states.w = w; - states.W = W; - - % fine timing search +/- window_width/2 from current timing instant - - states.window_width = 11; - - % Receive buffer: D P DDD P DDD P DDD P D - % ^ - % also see ofdm_demod() ... - - states.Nrxbuf = 3*states.Nsamperframe+states.M+states.Ncp + 2*(states.M + states.Ncp); - states.rxbuf = zeros(1, states.Nrxbuf); - - % default settings on a bunch of options and states - - states.verbose = 0; - states.timing_en = 1; - states.foff_est_en = 1; - states.phase_est_en = 1; - - states.foff_est_gain = 0.1; - states.foff_est_hz = 0; - states.sample_point = states.timing_est = 1; - states.nin = states.Nsamperframe; - -endfunction - - -% --------------------------- -% Modulates one frame of bits -% --------------------------- - -function tx = ofdm_mod(states, tx_bits) - ofdm_load_const; - - assert(length(tx_bits) == Nbitsperframe); - - % map to symbols in linear array - - if bps == 1 - tx_sym_lin = 2*tx_bits - 1; - end - if bps == 2 - for s=1:Nbitsperframe/bps - tx_sym_lin(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_sym = []; s = 1; - aframe = zeros(Ns,Nc+2); - aframe(1,:) = pilots; - for r=1:Nrowsperframe - arowofsymbols = tx_sym_lin(s:s+Nc-1); - s += Nc; - aframe(r+1,2:Nc+1) = arowofsymbols; - end - tx_sym = [tx_sym; aframe]; - - % OFDM upconvert symbol by symbol so we can add CP - - tx = []; - for r=1:Ns - asymbol = tx_sym(r,:) * W/M; - asymbol_cp = [asymbol(M-Ncp+1:M) asymbol]; - tx = [tx asymbol_cp]; - end -endfunction - - -% ----------------------------- -% Demodulates one frame of bits -% ----------------------------- - -#{ - - For phase estimation we need to maintain buffer of 3 frames plus - one pilot, so we have 4 pilots total. '^' is the start of current - frame that we are demodulating. - - P DDD P DDD P DDD P - ^ - - Then add one symbol either side to account for movement in - sampling instant due to sample clock differences: - - D P DDD P DDD P DDD P D - ^ -#} - -function [rx_bits states aphase_est_pilot_log rx_np] = ofdm_demod(states, rxbuf_in) - ofdm_load_const; - - % extra states that are st up at run time rather than init time - - timing_est = states.timing_est; - timing_en = states.timing_en; - foff_est_hz = states.foff_est_hz; - foff_est_gain = states.foff_est_gain; - foff_est_en = states.foff_est_en; - sample_point = states.sample_point; - rate_fs_pilot_samples = states.rate_fs_pilot_samples; - verbose = states.verbose; - phase_est_en = states.phase_est_en; - - % insert latest input samples into rxbuf - - rxbuf(1:Nrxbuf-states.nin) = rxbuf(states.nin+1:Nrxbuf); - rxbuf(Nrxbuf-states.nin+1:Nrxbuf) = rxbuf_in; - - woff_est = 2*pi*foff_est_hz/Fs; - - % update timing estimate -------------------------------------------------- - - delta_t = sample_point = 0; - if timing_en - % update timing at start of every frame - - st = M+Ncp + Nsamperframe + 1 - floor(window_width/2) + (timing_est-1); - en = st + Nsamperframe-1 + M+Ncp + window_width-1; - - ft_est = coarse_sync(states, rxbuf(st:en) .* exp(-j*woff_est*(st:en)), rate_fs_pilot_samples); - timing_est += ft_est - ceil(window_width/2); - - if verbose > 1 - printf(" ft_est: %2d timing_est: %2d sample_point: %2d\n", ft_est, timing_est, sample_point); - end - - % Black magic to keep sample_point inside cyclic prefix. Or something like that. - - delta_t = ft_est - ceil(window_width/2); - sample_point = max(timing_est+Ncp/4, sample_point); - sample_point = min(timing_est+Ncp, sample_point); - end - - % down convert at current timing instant---------------------------------- - - % todo: this cld be more efficent, as pilot r becomes r-Ns on next frame - - rx_sym = zeros(1+Ns+1+1, Nc+2); - - % previous pilot - - st = M+Ncp + Nsamperframe + (-Ns)*(M+Ncp) + 1 + sample_point; en = st + M - 1; - - for c=1:Nc+2 - acarrier = rxbuf(st:en) .* exp(-j*woff_est*(st:en)) .* conj(W(c,:)); - rx_sym(1,c) = sum(acarrier); - end - - % pilot - this frame - pilot - - for rr=1:Ns+1 - st = M+Ncp + Nsamperframe + (rr-1)*(M+Ncp) + 1 + sample_point; en = st + M - 1; - for c=1:Nc+2 - acarrier = rxbuf(st:en) .* exp(-j*woff_est*(st:en)) .* conj(W(c,:)); - rx_sym(rr+1,c) = sum(acarrier); - end - end - - % next pilot - - st = M+Ncp + Nsamperframe + (2*Ns)*(M+Ncp) + 1 + sample_point; en = st + M - 1; - for c=1:Nc+2 - acarrier = rxbuf(st:en) .* exp(-j*woff_est*(st:en)) .* conj(W(c,:)); - rx_sym(Ns+3,c) = sum(acarrier); - end - - % est freq err based on all carriers ------------------------------------ - - if foff_est_en - freq_err_rect = sum(rx_sym(2,:))' * sum(rx_sym(2+Ns,:)); - freq_err_hz = angle(freq_err_rect)*Rs/(2*pi*Ns); - foff_est_hz += foff_est_gain*freq_err_hz; - end - - % OK - now estimate and correct phase ---------------------------------- - - aphase_est_pilot = 10*ones(1,Nc+2); - for c=2:Nc+1 - - % 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_rect = sum(rx_sym(2,cr)*pilots(cr)') + sum(rx_sym(2+Ns,cr)*pilots(cr)'); - - % use next step of pilots in past and future - - aphase_est_pilot_rect += sum(rx_sym(1,cr)*pilots(cr)'); - aphase_est_pilot_rect += sum(rx_sym(2+Ns+1,cr)*pilots(cr)'); - - aphase_est_pilot(c) = angle(aphase_est_pilot_rect); - end - - % correct phase offset using phase estimate, and demodulate - % bits, separate loop as it runs across cols (carriers) to get - % frame bit ordering correct - - aphase_est_pilot_log = []; - rx_bits = []; rx_np = []; - for rr=1:Ns-1 - for c=2:Nc+1 - if phase_est_en - rx_corr = rx_sym(rr+2,c) * exp(-j*aphase_est_pilot(c)); - else - rx_corr = rx_sym(rr+2,c); - end - rx_np = [rx_np rx_corr]; - if bps == 1 - abit = real(rx_corr) > 0; - end - if bps == 2 - abit = qpsk_demod(rx_corr); - end - rx_bits = [rx_bits abit]; - end % c=2:Nc+1 - aphase_est_pilot_log = [aphase_est_pilot_log; aphase_est_pilot]; - end - - % Adjust nin to take care of sample clock offset - - nin = Nsamperframe; - if timing_en - thresh = (M+Ncp)/8; - tshift = (M+Ncp)/4; - if timing_est > thresh - nin = Nsamperframe+tshift; - timing_est -= tshift; - sample_point -= tshift; - end - if timing_est < -thresh - nin = Nsamperframe-tshift; - timing_est += tshift; - sample_point += tshift; - end - end - - states.rxbuf = rxbuf; - states.nin = nin; - states.timing_est = timing_est; - states.sample_point = sample_point; - states.delta_t = delta_t; - states.foff_est_hz = foff_est_hz; -endfunction - - -#{ - TODO: - [ ] Some states need warm rest at the start of each simulation point - [ ] rate_fs_pilot_samples generated in init - [ ] move buffer shift into demod - [ ] way to simulate aquisition and demod - [ ] testframe based -#} - -function [sim_out rate_fs_pilot_samples rx] = run_sim(sim_in) - - % set up core modem constants - - states = ofdm_init(sim_in.bps, sim_in.Rs, sim_in.Tcp, sim_in.Ns, sim_in.Nc); - ofdm_load_const; - - % simulation parameters and flags - - woffset = 2*pi*sim_in.foff_hz/Fs; - EbNodB = sim_in.EbNodB; - verbose = states.verbose = sim_in.verbose; - hf_en = sim_in.hf_en; - timing_en = states.timing_en = sim_in.timing_en; - states.foff_est_en = foff_est_en = sim_in.foff_est_en; - states.phase_est_en = phase_est_en = sim_in.phase_est_en; - - if verbose - printf("Rs:..........: %4.2f\n", Rs); - printf("M:...........: %d\n", M); - printf("Ncp:.........: %d\n", Ncp); - printf("bps:.........: %d\n", bps); - printf("Nbitsperframe: %d\n", Nbitsperframe); - printf("Nrowsperframe: %d\n", Nrowsperframe); - printf("Nsamperframe.: %d\n", Nsamperframe); - 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 - - 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 - - % double check if Nbits fit neatly into carriers - - assert(Nbits/(Nc*bps) == floor(Nbits/(Nc*bps)), "Nbits/(Nc*bps) must be an integer"); - - Nrp = Nr + Nframes + 1; % number of rows once pilots inserted - % extra row of pilots at end - - 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); - printf("Nframes: %d\n", Nframes); - printf("Nrp....: %d (number of rows including pilots)\n", Nrp); - end - - % set up HF model --------------------------------------------------------------- - - if hf_en - - % some typical values, or replace with user supplied - - dopplerSpreadHz = 1.0; path_delay_ms = 1; - - if isfield(sim_in, "dopplerSpreadHz") - dopplerSpreadHz = sim_in.dopplerSpreadHz; - end - if isfield(sim_in, "path_delay_ms") - path_delay_ms = sim_in.path_delay_ms; - end - path_delay_samples = path_delay_ms*Fs/1000; - printf("Doppler Spread: %3.2f Hz Path Delay: %3.2f ms %d samples\n", dopplerSpreadHz, path_delay_ms, path_delay_samples); - - % generate same fading pattern for every run - - randn('seed',1); - - spread1 = doppler_spread(dopplerSpreadHz, Fs, (sim_in.Nsec*(M+Ncp)/M+0.2)*Fs); - spread2 = doppler_spread(dopplerSpreadHz, Fs, (sim_in.Nsec*(M+Ncp)/M+0.2)*Fs); - - % sometimes doppler_spread() doesn't return exactly the number of samples we need - - assert(length(spread1) >= Nrp*M, "not enough doppler spreading samples"); - assert(length(spread2) >= Nrp*M, "not enough doppler spreading samples"); - - hf_gain = 1.0/sqrt(var(spread1)+var(spread2)); - % printf("nsymb: %d lspread1: %d\n", nsymb, length(spread1)); - end - - % ------------------------------------------------------------------ - % simulate for each Eb/No point - % ------------------------------------------------------------------ - - for nn=1:length(EbNodB) - rand('seed',1); - randn('seed',1); - - EbNo = bps * (10 .^ (EbNodB(nn)/10)); - variance = 1/(M*EbNo/2); - - Nsam = Nrp*(M+Ncp); - - % generate tx bits and run OFDM modulator - - tx_bits = rand(1,Nbits) > 0.5; - - tx = []; - for f=1:Nframes - tx = [tx ofdm_mod(states, tx_bits((f-1)*Nbitsperframe+1:f*Nbitsperframe))]; - end - - % add extra row of pilots at end, to allow one frame simulations, - % useful for development - - st = Nsamperframe*(Nframes-1)+1; en = st+Ncp+M-1; - tx = [tx tx(st:en)]; - assert(length(tx) == Nsam); - - % OFDM symbol of pilots is used for coarse timing and freq during acquisition, and fine timing - % TODO: put this in init code - - states.rate_fs_pilot_samples = tx(1:M+Ncp); - - % channel simulation --------------------------------------------------------------- - - if isfield(sim_in, "sample_clock_offset_ppm") - % todo: this only works for large ppm like 500, runs out of memory - % for small ppm - - if sim_in.sample_clock_offset_ppm - timebase = floor(abs(1E6/sim_in.sample_clock_offset_ppm)); - if sim_in.sample_clock_offset_ppm > 0 - tx = resample(tx, timebase+1, timebase); - else - tx = resample(tx, timebase, timebase+1); - end - - % make sure length is correct for rest of simulation - - tx = [tx zeros(1,Nsam-length(tx))]; - tx = tx(1:Nsam); - end - end - - rx = tx; - - if hf_en - %rx = [zeros(1,path_delay_samples) tx(1:Nsam-path_delay_samples)]; - rx = hf_gain * tx(1:Nsam) .* spread1(1:Nsam); - rx += hf_gain * [zeros(1,path_delay_samples) tx(1:Nsam-path_delay_samples)] .* spread2(1:Nsam); - end - - rx = rx .* exp(j*woffset*(1:Nsam)); - - noise = sqrt(variance)*(0.5*randn(1,Nsam) + j*0.5*randn(1,Nsam)); - rx += noise; - - % some spare samples at end to avoid overflow as est windows may poke into the future a bit - - rx = [rx zeros(1,Nsamperframe)]; - - % bunch of logs - - phase_est_pilot_log = []; - delta_t_log = []; - timing_est_log = []; - foff_est_hz_log = []; - Nerrs_log = []; - rx_bits = []; rx_np = []; - - % reset some states for each EbNo simulation point - - states.sample_point = states.timing_est = 1; - if timing_en == 0 - states.sample_point = Ncp; - end - states.nin = Nsamperframe; - states.foff_est_hz = 0; - - % for this simulation we "prime" buffer to allow one frame runs during development - - prx = 1; - states.rxbuf(M+Ncp+2*Nsamperframe+1:Nrxbuf) = rx(prx:Nsamperframe+2*(M+Ncp)); - prx += Nsamperframe+2*(M+Ncp); - - for f=1:Nframes - - % insert samples at end of buffer, set to zero if no samples - % available to disable phase estimation on future pilots on last - % frame of simulation - - lnew = min(Nsam-prx,states.nin); - rxbuf_in = zeros(1,states.nin); - - if lnew - rxbuf_in(1:lnew) = rx(prx:prx+lnew-1); - end - prx += states.nin; - - [arx_bits states aphase_est_pilot_log arx_np] = ofdm_demod(states, rxbuf_in); - - rx_bits = [rx_bits arx_bits]; rx_np = [rx_np arx_np]; - timing_est_log = [timing_est_log states.timing_est]; - delta_t_log = [delta_t_log states.delta_t]; - foff_est_hz_log = [foff_est_hz_log states.foff_est_hz]; - phase_est_pilot_log = [phase_est_pilot_log; aphase_est_pilot_log]; - end - - assert(length(rx_bits) == Nbits); - - % calculate BER stats as a block, after pilots extracted - - errors = xor(tx_bits, rx_bits); - Nerrs = sum(errors); - for f=1:Nframes - st = (f-1)*Nbitsperframe+1; en = st + Nbitsperframe-1; - Nerrs_log(f) = sum(xor(tx_bits(st:en), rx_bits(st:en))); - end - - 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]); - title('Scatter'); - - figure(2); clf; - plot(phase_est_pilot_log(:,2:Nc+1),'g+', 'markersize', 5); - title('Phase est'); - axis([1 Nrp -pi pi]); - - figure(3); clf; - subplot(211) - stem(delta_t_log) - title('delta t'); - subplot(212) - plot(timing_est_log); - title('timing est'); - - figure(4); clf; - plot(foff_est_hz_log) - axis([1 max(Nframes,2) -3 3]); - title('Fine Freq'); - - figure(5); clf; - plot(Nerrs log); - -#{ - figure(2) - Tx = abs(fft(tx(1:Nsam).*hanning(Nsam)')); - Tx_dB = 20*log10(Tx); - dF = Fs/Nsam; - plot((1:Nsam)*dF, Tx_dB); - mx = max(Tx_dB); - axis([0 Fs/2 mx-60 mx]) -#} - -#{ - if hf_en - figure(4); clf; - subplot(211) - plot(abs(spread1(1:Nsam))); - %hold on; plot(abs(spread2(1:Nsam)),'g'); hold off; - subplot(212) - plot(angle(spread1(1:Nsam))); - title('spread1 amp and phase'); - end -#} - -#{ - % todo, work out a way to plot rate Fs hf model phase - if sim_in.hf_en - plot(angle(hf_model(:,2:Nc+1))); - end -#} - - - end - - sim_out.ber(nn) = sum(Nerrs)/Nbits; - sim_out.pilot_overhead = 10*log10(Ns/(Ns-1)); - sim_out.M = M; sim_out.Fs = Fs; sim_out.Ncp = Ncp; - sim_out.Nrowsperframe = Nrowsperframe; sim_out.Nsamperframe = Nsamperframe; - end -endfunction - - -function run_single - Ts = 0.018; - sim_in.Tcp = 0.002; - sim_in.Rs = 1/Ts; sim_in.bps = 2; sim_in.Nc = 16; sim_in.Ns = 8; - - %sim_in.Nsec = 5*(sim_in.Ns+1)/sim_in.Rs; % one frame - sim_in.Nsec = 30; - - sim_in.EbNodB = 3; - sim_in.verbose = 1; - sim_in.hf_en = 1; - sim_in.foff_hz = 0; - sim_in.timing_en = 1; - sim_in.sample_clock_offset_ppm = 0; - sim_in.foff_est_en = 1; - sim_in.phase_est_en = 1; - - run_sim(sim_in); -end - - -% Plot BER against Eb/No curves for AWGN and HF - -% Target operating point Eb/No for HF 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 -% -% For AWGN target is 2dB so -1dB op point. - -function run_curves - Ts = 0.010; - sim_in.Rs = 1/Ts; - sim_in.Tcp = 0.002; - sim_in.bps = 2; sim_in.Ns = 8; sim_in.Nc = 8; sim_in.verbose = 0; - sim_in.foff_hz = 0; - - pilot_overhead = (sim_in.Ns-1)/sim_in.Ns; - cp_overhead = Ts/(Ts+sim_in.Tcp); - overhead_dB = -10*log10(pilot_overhead*cp_overhead); - - sim_in.hf_en = 0; - sim_in.Nsec = 30; - sim_in.EbNodB = -3:5; - awgn_EbNodB = sim_in.EbNodB; - - awgn_theory = 0.5*erfc(sqrt(10.^(sim_in.EbNodB/10))); - awgn = run_sim(sim_in); - - sim_in.hf_en = 1; - sim_in.Nsec = 120; - sim_in.EbNodB = 1:8; - - EbNoLin = 10.^(sim_in.EbNodB/10); - hf_theory = 0.5.*(1-sqrt(EbNoLin./(EbNoLin+1))); - - hf = run_sim(sim_in); - - figure(4); clf; - semilogy(awgn_EbNodB, awgn_theory,'b+-;AWGN theory;'); - hold on; - semilogy(sim_in.EbNodB, hf_theory,'b+-;HF theory;'); - semilogy(awgn_EbNodB+overhead_dB, awgn_theory,'g+-;AWGN lower bound with pilot + CP overhead;'); - semilogy(sim_in.EbNodB+overhead_dB, hf_theory,'g+-;HF lower bound with pilot + CP overhead;'); - semilogy(awgn_EbNodB+overhead_dB, awgn.ber,'r+-;AWGN sim;'); - semilogy(sim_in.EbNodB+overhead_dB, hf.ber,'r+-;HF sim;'); - hold off; - axis([-3 8 1E-2 2E-1]) - xlabel('Eb/No (dB)'); - ylabel('BER'); - grid; grid minor on; - legend('boxoff'); -end - - -% Run an acquisition test, returning vectors of estimation errors - -function [delta_t delta_foff] = acquisition_test(Ntests=10, EbNodB=100, foff_hz=0, hf_en=0, fine_en=0) - - % generate test signal at a given Eb/No and frequency offset - - Ts = 0.016; - sim_in.Tcp = 0.002; - sim_in.Rs = 1/Ts; sim_in.bps = 2; sim_in.Nc = 16; sim_in.Ns = 8; - - sim_in.Nsec = Ntests*(sim_in.Ns+1)/sim_in.Rs; - - sim_in.EbNodB = EbNodB; - sim_in.verbose = 0; - sim_in.hf_en = hf_en; - sim_in.foff_hz = foff_hz; sim_in.timing_en = 0; - - % set up acquistion - - Nsamperframe = states.Nsamperframe = sim_out.Nsamperframe; - states.M = sim_out.M; states.Ncp = sim_out.Ncp; - states.verbose = 0; - states.Fs = sim_out.Fs; - - % test fine or acquisition over test signal - #{ - fine: - start with coarse timing instant - - on each frame est timing a few samples about that point - - update timing instant - - corr: - where is best plcase to sample - - just before end of symbol? - - how long should sequence be? - - add extra? - - aim for last possible moment? - - man I hope IL isn't too big..... - #} - - delta_t = []; delta_t = []; delta_foff = []; - - if fine_en - - window_width = 5; % search +/-2 samples from current timing instant - timing_instant = Nsamperframe+1; % start at correct instant for AWGN - % start at second frame so we can search -2 ... +2 - - while timing_instant < (length(rx) - (Nsamperframe + length(rate_fs_pilot_samples) + window_width)) - st = timing_instant - ceil(window_width/2); - en = st + Nsamperframe-1 + length(rate_fs_pilot_samples) + window_width-1; - [ft_est foff_est] = coarse_sync(states, rx(st:en), rate_fs_pilot_samples); - printf("ft_est: %d timing_instant %d %d\n", ft_est, timing_instant, mod(timing_instant, Nsamperframe)); - timing_instant += Nsamperframe + ft_est - ceil(window_width/2); - delta_t = [delta_ft ft_est - ceil(window_width/2)]; - end - else - % for coarse simulation we just use contant window shifts - - st = 0.5*Nsamperframe; - en = 2.5*Nsamperframe - 1; - ct_target = Nsamperframe/2; - - for w=1:Nsamperframe:length(rx)-3*Nsamperframe - %st = w+0.5*Nsamperframe; en = st+2*Nsamperframe-1; - %[ct_est foff_est] = coarse_sync(states, rx(st:en), rate_fs_pilot_samples); - [ct_est foff_est] = coarse_sync(states, rx(w+st:w+en), rate_fs_pilot_samples); - printf("ct_est: %4d foff_est: %3.1f\n", ct_est, foff_est); - - % valid coarse timing ests are modulo Nsamperframe - - delta_t = [delta_ct ct_est-ct_target]; - delta_foff = [delta_foff (foff_est-foff_hz)]; - end - end - -endfunction - - -% Run some tests for various acquisition conditions. Probability of -% acquistion is what matters, e.g. if it's 50% we can expect sync -% within 2 frames -% P(t)/P(f) P(t)/P(f) -% Eb/No AWGN HF -% +/- 25Hz -1/3 1.0/0.3 0.96/0.3 -% +/- 5Hz -1/3 1.0/0.347 0.96/0.55 -% +/- 25Hz 10/10 1.00/0.92 0.99/0.77 - -function acquisition_histograms(fine_en = 0) - Fs = 8000; - Ntests = 100; - - % allowable tolerance for acquistion - - ftol_hz = 2.0; - ttol_samples = 0.002*Fs; - - % AWGN channel operating point - - [dct dfoff] = acquisition_test(Ntests, -1, 25, 0, fine_en); - - % Probability of acquistion is what matters, e.g. if it's 50% we can - % expect sync within 2 frames - - printf("AWGN P(time offset acq) = %3.2f\n", length(find (abs(dct) < ttol_samples))/length(dct)); - if fine_en == 0 - printf("AWGN P(freq offset acq) = %3.2f\n", length(find (abs(dfoff) < ftol_hz))/length(dfoff)); - end - - figure(1) - hist(dct(find (abs(dct) < ttol_samples))) - if fine_en == 0 - figure(2) - hist(dfoff) - end - - % HF channel operating point - - [dct dfoff] = acquisition_test(Ntests, 3, 25, 1, fine_en); - - printf("HF P(time offset acq) = %3.2f\n", length(find (abs(dct) < ttol_samples))/length(dct)); - if fine_en == 0 - printf("HF P(freq offset acq) = %3.2f\n", length(find (abs(dfoff) < ftol_hz))/length(dfoff)); - end - - figure(3) - hist(dct(find (abs(dct) < ttol_samples))) - if fine_en == 0 - figure(4) - hist(dfoff) - end - -endfunction - - - -% choose simulation to run here ------------------------------------------------------- - -format; -more off; - -run_single -%run_curves -%acquisition_histograms(1) - diff --git a/codec2-dev/octave/ofdm_lib.m b/codec2-dev/octave/ofdm_lib.m new file mode 100644 index 00000000..1004ddbb --- /dev/null +++ b/codec2-dev/octave/ofdm_lib.m @@ -0,0 +1,373 @@ +% ofdm_lib.m +% David Rowe Mar 2017 +% + +% Library of functions that implement a BPSK/QPSK OFDM modem. Rate Fs +% verison of ofdm_rs.m with OFDM based up and down conversion, and all +% those nasty real-world details like fine freq, timing. + +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 + + +% Correlates the OFDM pilot symbol samples with a window of received +% samples to determine the most likely timing offset. Combines two +% frames pilots so we need at least Nsamperframe+M+Ncp samples in rx. +% Also determines frequency offset at maximimum correlation. Can be +% used for acquisition (coarse timing a freq offset), and fine timing + +function [t_est foff_est] = coarse_sync(states, rx, rate_fs_pilot_samples) + Nsamperframe = states.Nsamperframe; Fs = states.Fs; + Npsam = length(rate_fs_pilot_samples); + verbose = states.verbose; + + Ncorr = length(rx) - (Nsamperframe+Npsam) + 1; + assert(Ncorr > 0); + corr = zeros(1,Ncorr); + for i=1:Ncorr + corr(i) = abs(rx(i:i+Npsam-1) * rate_fs_pilot_samples'); + corr(i) += abs(rx(i+Nsamperframe:i+Nsamperframe+Npsam-1) * rate_fs_pilot_samples'); + end + + [mx t_est] = max(abs(corr)); + + C = abs(fft(rx(t_est:t_est+Npsam-1) .* conj(rate_fs_pilot_samples), Fs)); + C += abs(fft(rx(t_est+Nsamperframe:t_est+Nsamperframe+Npsam-1) .* conj(rate_fs_pilot_samples), Fs)); + + fmax = 30; + [mx_pos foff_est_pos] = max(C(1:fmax)); + [mx_neg foff_est_neg] = max(C(Fs-fmax+1:Fs)); + + if mx_pos > mx_neg + foff_est = foff_est_pos - 1; + else + foff_est = foff_est_neg - fmax - 1; + end + + if verbose > 1 + %printf("t_est: %d\n", t_est); + figure(7); clf; + plot(abs(corr)) + figure(8) + plot(C) + axis([0 200 0 0.4]) + end +endfunction + + +%------------------------------------------------------------- +% ofdm_init +%------------------------------------------------------------- + +#{ + Frame has Ns-1 data symbols between pilots, e.g. for Ns=3: + + PPP + DDD + DDD + PPP +#} + +function states = ofdm_init(bps, Rs, Tcp, Ns, Nc) + states.Fs = 8000; + states.bps = bps; + states.Rs = Rs; + states.Tcp = Tcp; + states.Ns = Ns; % step size for pilots + states.Nc = Nc; % Number of cols, aka number of carriers + states.M = states.Fs/Rs; + states.Ncp = Tcp*states.Fs; + states.Nbitsperframe = (Ns-1)*Nc*bps; + states.Nrowsperframe = states.Nbitsperframe/(Nc*bps); + states.Nsamperframe = (states.Nrowsperframe+1)*(states.M+states.Ncp); + + % generate same pilots each time + + rand('seed',1); + states.pilots = 1 - 2*(rand(1,Nc+2) > 0.5); + + % carrier tables for up and down conversion + + w = (0:Nc+1)*2*pi*Rs/states.Fs; + W = zeros(Nc+2,states.M); + for c=1:Nc+2 + W(c,:) = exp(j*w(c)*(0:states.M-1)); + end + states.w = w; + states.W = W; + + % fine timing search +/- window_width/2 from current timing instant + + states.window_width = 11; + + % Receive buffer: D P DDD P DDD P DDD P D + % ^ + % also see ofdm_demod() ... + + states.Nrxbuf = 3*states.Nsamperframe+states.M+states.Ncp + 2*(states.M + states.Ncp); + states.rxbuf = zeros(1, states.Nrxbuf); + + % default settings on a bunch of options and states + + states.verbose = 0; + states.timing_en = 1; + states.foff_est_en = 1; + states.phase_est_en = 1; + + states.foff_est_gain = 0.1; + states.foff_est_hz = 0; + states.sample_point = states.timing_est = 1; + states.nin = states.Nsamperframe; + + % generate OFDM pilot symbol, used for timing and freq offset est + + rate_fs_pilot_samples = states.pilots * W/states.M; + states.rate_fs_pilot_samples = [rate_fs_pilot_samples(states.M-states.Ncp+1:states.M) rate_fs_pilot_samples]; + +endfunction + + +% -------------------------------------- +% ofdm_mod - modulates one frame of bits +% -------------------------------------- + +function tx = ofdm_mod(states, tx_bits) + ofdm_load_const; + + assert(length(tx_bits) == Nbitsperframe); + + % map to symbols in linear array + + if bps == 1 + tx_sym_lin = 2*tx_bits - 1; + end + if bps == 2 + for s=1:Nbitsperframe/bps + tx_sym_lin(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_sym = []; s = 1; + aframe = zeros(Ns,Nc+2); + aframe(1,:) = pilots; + for r=1:Nrowsperframe + arowofsymbols = tx_sym_lin(s:s+Nc-1); + s += Nc; + aframe(r+1,2:Nc+1) = arowofsymbols; + end + tx_sym = [tx_sym; aframe]; + + % OFDM upconvert symbol by symbol so we can add CP + + tx = []; + for r=1:Ns + asymbol = tx_sym(r,:) * W/M; + asymbol_cp = [asymbol(M-Ncp+1:M) asymbol]; + tx = [tx asymbol_cp]; + end +endfunction + + +% ------------------------------------------ +% ofdm_demod - Demodulates one frame of bits +% ------------------------------------------ + +#{ + + For phase estimation we need to maintain buffer of 3 frames plus + one pilot, so we have 4 pilots total. '^' is the start of current + frame that we are demodulating. + + P DDD P DDD P DDD P + ^ + + Then add one symbol either side to account for movement in + sampling instant due to sample clock differences: + + D P DDD P DDD P DDD P D + ^ +#} + +function [rx_bits states aphase_est_pilot_log rx_np] = ofdm_demod(states, rxbuf_in) + ofdm_load_const; + + % extra states that are st up at run time rather than init time + + timing_est = states.timing_est; + timing_en = states.timing_en; + foff_est_hz = states.foff_est_hz; + foff_est_gain = states.foff_est_gain; + foff_est_en = states.foff_est_en; + sample_point = states.sample_point; + rate_fs_pilot_samples = states.rate_fs_pilot_samples; + verbose = states.verbose; + phase_est_en = states.phase_est_en; + + % insert latest input samples into rxbuf + + rxbuf(1:Nrxbuf-states.nin) = rxbuf(states.nin+1:Nrxbuf); + rxbuf(Nrxbuf-states.nin+1:Nrxbuf) = rxbuf_in; + + woff_est = 2*pi*foff_est_hz/Fs; + + % update timing estimate -------------------------------------------------- + + delta_t = sample_point = 0; + if timing_en + % update timing at start of every frame + + st = M+Ncp + Nsamperframe + 1 - floor(window_width/2) + (timing_est-1); + en = st + Nsamperframe-1 + M+Ncp + window_width-1; + + ft_est = coarse_sync(states, rxbuf(st:en) .* exp(-j*woff_est*(st:en)), rate_fs_pilot_samples); + timing_est += ft_est - ceil(window_width/2); + + if verbose > 1 + printf(" ft_est: %2d timing_est: %2d sample_point: %2d\n", ft_est, timing_est, sample_point); + end + + % Black magic to keep sample_point inside cyclic prefix. Or something like that. + + delta_t = ft_est - ceil(window_width/2); + sample_point = max(timing_est+Ncp/4, sample_point); + sample_point = min(timing_est+Ncp, sample_point); + end + + % down convert at current timing instant---------------------------------- + + % todo: this cld be more efficent, as pilot r becomes r-Ns on next frame + + rx_sym = zeros(1+Ns+1+1, Nc+2); + + % previous pilot + + st = M+Ncp + Nsamperframe + (-Ns)*(M+Ncp) + 1 + sample_point; en = st + M - 1; + + for c=1:Nc+2 + acarrier = rxbuf(st:en) .* exp(-j*woff_est*(st:en)) .* conj(W(c,:)); + rx_sym(1,c) = sum(acarrier); + end + + % pilot - this frame - pilot + + for rr=1:Ns+1 + st = M+Ncp + Nsamperframe + (rr-1)*(M+Ncp) + 1 + sample_point; en = st + M - 1; + for c=1:Nc+2 + acarrier = rxbuf(st:en) .* exp(-j*woff_est*(st:en)) .* conj(W(c,:)); + rx_sym(rr+1,c) = sum(acarrier); + end + end + + % next pilot + + st = M+Ncp + Nsamperframe + (2*Ns)*(M+Ncp) + 1 + sample_point; en = st + M - 1; + for c=1:Nc+2 + acarrier = rxbuf(st:en) .* exp(-j*woff_est*(st:en)) .* conj(W(c,:)); + rx_sym(Ns+3,c) = sum(acarrier); + end + + % est freq err based on all carriers ------------------------------------ + + if foff_est_en + freq_err_rect = sum(rx_sym(2,:))' * sum(rx_sym(2+Ns,:)); + freq_err_hz = angle(freq_err_rect)*Rs/(2*pi*Ns); + foff_est_hz += foff_est_gain*freq_err_hz; + end + + % OK - now estimate and correct phase ---------------------------------- + + aphase_est_pilot = 10*ones(1,Nc+2); + for c=2:Nc+1 + + % 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_rect = sum(rx_sym(2,cr)*pilots(cr)') + sum(rx_sym(2+Ns,cr)*pilots(cr)'); + + % use next step of pilots in past and future + + aphase_est_pilot_rect += sum(rx_sym(1,cr)*pilots(cr)'); + aphase_est_pilot_rect += sum(rx_sym(2+Ns+1,cr)*pilots(cr)'); + + aphase_est_pilot(c) = angle(aphase_est_pilot_rect); + end + + % correct phase offset using phase estimate, and demodulate + % bits, separate loop as it runs across cols (carriers) to get + % frame bit ordering correct + + aphase_est_pilot_log = []; + rx_bits = []; rx_np = []; + for rr=1:Ns-1 + for c=2:Nc+1 + if phase_est_en + rx_corr = rx_sym(rr+2,c) * exp(-j*aphase_est_pilot(c)); + else + rx_corr = rx_sym(rr+2,c); + end + rx_np = [rx_np rx_corr]; + if bps == 1 + abit = real(rx_corr) > 0; + end + if bps == 2 + abit = qpsk_demod(rx_corr); + end + rx_bits = [rx_bits abit]; + end % c=2:Nc+1 + aphase_est_pilot_log = [aphase_est_pilot_log; aphase_est_pilot]; + end + + % Adjust nin to take care of sample clock offset + + nin = Nsamperframe; + if timing_en + thresh = (M+Ncp)/8; + tshift = (M+Ncp)/4; + if timing_est > thresh + nin = Nsamperframe+tshift; + timing_est -= tshift; + sample_point -= tshift; + end + if timing_est < -thresh + nin = Nsamperframe-tshift; + timing_est += tshift; + sample_point += tshift; + end + end + + states.rxbuf = rxbuf; + states.nin = nin; + states.timing_est = timing_est; + states.sample_point = sample_point; + states.delta_t = delta_t; + states.foff_est_hz = foff_est_hz; +endfunction + +