470 lines
15 KiB
Matlab
470 lines
15 KiB
Matlab
% fsk_lib.m
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% David Rowe Oct 2015 - present
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%
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% mFSK modem, started out life as RTTY demodulator for Project
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% Horus High Altitude Ballon (HAB) telemetry, also used for:
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%
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% FreeDV 2400A: 4FSK UHF/UHF digital voice
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% Wenet.......: 100 kbit/s HAB High Def image telemetry
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%
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% Handles frequency offsets, performance right on ideal, C implementation
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% in codec2/src
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1;
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function states = fsk_init(Fs, Rs, M=2, P=8, nsym=50)
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states.M = M;
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states.bitspersymbol = log2(M);
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states.Fs = Fs;
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states.Rs = Rs;
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states.nsym = nsym; % Number of symbols processed by demodulator in each call, also
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% the timing estimator window
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Ts = states.Ts = Fs/Rs; % number of samples per symbol
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assert(Ts == floor(Ts), "Fs/Rs must be an integer");
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N = states.N = Ts*states.nsym; % processing buffer size, nice big window for timing est
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bin_width_Hz = 0.1*Rs; % we want enough DFT bins to get within 10% of the tones centre
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Ndft = Fs/bin_width_Hz;
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states.Ndft = 2.^ceil(log2(Ndft)); % round to nearest power of 2 for efficient FFT
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states.Sf = zeros(states.Ndft,1); % current memory of dft mag samples
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states.tc = 0.1; % average DFT over longtime window, accurate at low Eb/No, but slow
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states.nbit = states.nsym*states.bitspersymbol; % number of bits per processing frame
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Nmem = states.Nmem = N+2*Ts; % two symbol memory in down converted signals to allow for timing adj
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states.f_dc = zeros(M,Nmem);
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states.P = P; % oversample rate out of filter
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assert(Ts/states.P == floor(Ts/states.P), "Ts/P must be an integer");
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states.tx_tone_separation = 2*Rs;
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states.nin = N; % can be N +/- Ts/P samples to adjust for sample clock offsets
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states.verbose = 0;
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states.phi = zeros(1, M); % keep down converter osc phase continuous
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% BER stats
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states.ber_state = 0;
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states.ber_valid_thresh = 0.05; states.ber_invalid_thresh = 0.1;
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states.Tbits = 0;
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states.Terrs = 0;
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states.nerr_log = 0;
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% extra simulation parameters
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states.tx_real = 1;
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states.dA(1:M) = 1;
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states.df(1:M) = 0;
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states.f(1:M) = 0;
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states.norm_rx_timing = 0;
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states.ppm = 0;
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states.prev_pkt = [];
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% Freq. estimator limits
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states.fest_fmax = Fs;
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states.fest_fmin = 0;
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states.fest_min_spacing = 0.75*Rs;
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states.freq_est_type = 'peak';
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%printf("Octave: M: %d Fs: %d Rs: %d Ts: %d nsym: %d nbit: %d N: %d Ndft: %d fmin: %d fmax: %d\n",
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% states.M, states.Fs, states.Rs, states.Ts, states.nsym, states.nbit, states.N, states.Ndft, states.fest_fmin, states.fest_fmax);
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endfunction
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% modulator function
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function tx = fsk_mod(states, tx_bits)
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M = states.M;
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Ts = states.Ts;
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Fs = states.Fs;
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ftx = states.ftx;
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df = states.df; % tone freq change in Hz/s
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dA = states.dA; % amplitude of each tone
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num_bits = length(tx_bits);
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num_symbols = num_bits/states.bitspersymbol;
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tx = zeros(states.Ts*num_symbols,1);
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tx_phase = 0;
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s = 1;
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for i=1:states.bitspersymbol:num_bits
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% map bits to FSK symbol (tone number)
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K = states.bitspersymbol;
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tone = tx_bits(i:i+(K-1)) * (2.^(K-1:-1:0))' + 1;
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tx_phase_vec = tx_phase + (1:Ts)*2*pi*ftx(tone)/Fs;
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tx_phase = tx_phase_vec(Ts) - floor(tx_phase_vec(Ts)/(2*pi))*2*pi;
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if states.tx_real
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tx((s-1)*Ts+1:s*Ts) = dA(tone)*2.0*cos(tx_phase_vec);
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else
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tx((s-1)*Ts+1:s*Ts) = dA(tone)*exp(j*tx_phase_vec);
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end
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s++;
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% freq drift
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ftx += df*Ts/Fs;
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end
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states.ftx = ftx;
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endfunction
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% Estimate the frequency of the FSK tones. In some applications (such
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% as balloon telemetry) these may not be well controlled by the
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% transmitter, so we have to try to estimate them.
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function states = est_freq(states, sf, ntones)
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N = states.N;
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Ndft = states.Ndft;
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Fs = states.Fs;
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% This assumption is OK for balloon telemetry but may not be true in
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% general
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min_tone_spacing = states.fest_min_spacing;
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% set some limits to search range, which will mean some manual re-tuning
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fmin = states.fest_fmin;
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fmax = states.fest_fmax;
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% note 0 Hz is mapped to Ndft/2+1 via fftshift
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st = floor(fmin*Ndft/Fs) + Ndft/2; st = max(1,st);
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en = floor(fmax*Ndft/Fs) + Ndft/2; en = min(Ndft,en);
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#printf("Fs: %f Ndft: %d fmin: %f fmax: %f st: %d en: %d\n",Fs, Ndft, fmin, fmax, st, en)
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% Update mag DFT ---------------------------------------------
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% we break up input buffer to a series of overlapping Ndft sequences
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numffts = floor(length(sf)/(Ndft/2)) - 1;
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h = hanning(Ndft);
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for i=1:numffts
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a = (i-1)*Ndft/2+1; b = a + Ndft - 1;
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Sf = abs(fftshift(fft(sf(a:b) .* h, Ndft)));
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% Smooth DFT mag spectrum, slower to respond to changes but more
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% accurate. Single order IIR filter is an exponentially weighted
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% moving average. This means the freq est window is wider than
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% timing est window
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tc = states.tc; states.Sf = (1-tc)*states.Sf + tc*Sf;
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end
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% Search for each tone method 1 - peak pick each tone location ----------------------------------
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f = []; a = [];
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Sf = states.Sf;
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for m=1:ntones
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[tone_amp tone_index] = max(Sf(st:en));
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tone_index += st - 1;
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f = [f (tone_index-1-Ndft/2)*Fs/Ndft];
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a = [a tone_amp];
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% zero out region min_tone_spacing either side of max so we can find next highest peak
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% closest spacing for non-coh mFSK is Rs
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stz = tone_index - floor((min_tone_spacing)*Ndft/Fs);
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stz = max(1,stz);
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enz = tone_index + floor((min_tone_spacing)*Ndft/Fs);
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enz = min(Ndft,enz);
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Sf(stz:enz) = 0;
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end
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states.f = sort(f);
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% Search for each tone method 2 - correlate with mask with non-zero entries at tone spacings -----
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% Create a mask with non-zero entries at tone spacing. Might be
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% smarter to use the DFT of a hanning window as mask
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mask = zeros(1,Ndft);
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mask(1:3) = 1;
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for m=1:ntones-1
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bin = round(m*states.tx_tone_separation*Ndft/Fs);
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mask(bin:bin+2) = 1;
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end
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mask = mask(1:bin+2);
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states.mask = mask;
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% drag mask over Sf, looking for peak in correlation
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b_max = st; corr_max = 0;
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Sf = states.Sf; corr_log = [];
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for b=st:en-length(mask)
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corr = mask * Sf(b:b+length(mask)-1);
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corr_log = [corr_log corr];
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if corr > corr_max
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corr_max = corr;
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b_max = b;
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end
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end
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foff = ((b_max-1)-Ndft/2)*Fs/Ndft;
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if bitand(states.verbose, 0x8)
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% enable this to single step through frames
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figure(1); clf; subplot(211); plot(Sf,'b;sf;');
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hold on; plot(max(Sf)*[zeros(1,b_max) mask],'g;mask;'); hold off;
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subplot(212); plot(corr_log); ylabel('corr against f');
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printf("foff: %4.0f\n", foff);
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kbhit;
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end
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states.f2 = foff + (0:ntones-1)*states.tx_tone_separation;
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end
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% ------------------------------------------------------------------------------------
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% Given a buffer of nin input Rs baud FSK samples, returns nsym bits.
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%
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% nin is the number of input samples required by demodulator. This is
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% time varying. It will nominally be N (8000), and occasionally N +/-
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% Ts/2 (e.g. 8080 or 7920). This is how we compensate for differences between the
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% remote tx sample clock and our sample clock. This function always returns
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% N/Ts (e.g. 50) demodulated bits. Variable number of input samples, constant number
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% of output bits.
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function [rx_bits states] = fsk_demod(states, sf)
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M = states.M;
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N = states.N;
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Ndft = states.Ndft;
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Fs = states.Fs;
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Rs = states.Rs;
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Ts = states.Ts;
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nsym = states.nsym;
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P = states.P;
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nin = states.nin;
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verbose = states.verbose;
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Nmem = states.Nmem;
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f = states.f;
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assert(length(sf) == nin);
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% down convert and filter at rate P ------------------------------
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% update filter (integrator) memory by shifting in nin samples
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nold = Nmem-nin; % number of old samples we retain
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f_dc = states.f_dc;
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f_dc(:,1:nold) = f_dc(:,Nmem-nold+1:Nmem);
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% freq shift down to around DC, ensuring continuous phase from last frame, as nin may vary
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for m=1:M
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phi_vec = states.phi(m) + (1:nin)*2*pi*f(m)/Fs;
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f_dc(m,nold+1:Nmem) = sf .* exp(j*phi_vec)';
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states.phi(m) = phi_vec(nin);
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states.phi(m) -= 2*pi*floor(states.phi(m)/(2*pi));
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end
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% save filter (integrator) memory for next time
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states.f_dc = f_dc;
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% integrate over symbol period, which is effectively a LPF, removing
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% the -2Fc frequency image. Can also be interpreted as an ideal
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% integrate and dump, non-coherent demod. We run the integrator at
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% rate P*Rs (1/P symbol offsets) to get outputs at a range of
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% different fine timing offsets. We calculate integrator output
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% over nsym+1 symbols so we have extra samples for the fine timing
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% re-sampler at either end of the array.
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f_int = zeros(M,(nsym+1)*P);
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for i=1:(nsym+1)*P
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st = 1 + (i-1)*Ts/P;
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en = st+Ts-1;
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for m=1:M
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f_int(m,i) = sum(f_dc(m,st:en));
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end
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end
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states.f_int = f_int;
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% fine timing estimation -----------------------------------------------
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% Non linearity has a spectral line at Rs, with a phase
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% related to the fine timing offset. See:
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% http://www.rowetel.com/blog/?p=3573
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% We have sampled the integrator output at Fs=P samples/symbol, so
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% lets do a single point DFT at w = 2*pi*f/Fs = 2*pi*Rs/(P*Rs)
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%
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% Note timing non-linearity derived by experiment. Not quite sure what I'm doing here.....
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% but it gives 0dB impl loss for 2FSK Eb/No=9dB, testmode 1:
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% Fs: 8000 Rs: 50 Ts: 160 nsym: 50
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% frames: 200 Tbits: 9700 Terrs: 93 BER 0.010
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Np = length(f_int(1,:));
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w = 2*pi*(Rs)/(P*Rs);
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timing_nl = sum(abs(f_int(:,:)).^2);
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x = timing_nl * exp(-j*w*(0:Np-1))';
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norm_rx_timing = angle(x)/(2*pi);
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rx_timing = norm_rx_timing*P;
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states.x = x;
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states.timing_nl = timing_nl;
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states.rx_timing = rx_timing;
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prev_norm_rx_timing = states.norm_rx_timing;
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states.norm_rx_timing = norm_rx_timing;
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% estimate sample clock offset in ppm
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% d_norm_timing is fraction of symbol period shift over nsym symbols
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d_norm_rx_timing = norm_rx_timing - prev_norm_rx_timing;
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% filter out big jumps due to nin changes
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if abs(d_norm_rx_timing) < 0.2
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appm = 1E6*d_norm_rx_timing/nsym;
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states.ppm = 0.9*states.ppm + 0.1*appm;
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end
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% work out how many input samples we need on the next call. The aim
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% is to keep angle(x) away from the -pi/pi (+/- 0.5 fine timing
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% offset) discontinuity. The side effect is to track sample clock
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% offsets
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next_nin = N;
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if norm_rx_timing > 0.25
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next_nin += Ts/4;
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end
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if norm_rx_timing < -0.25;
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next_nin -= Ts/4;
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end
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states.nin = next_nin;
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% Now we know the correct fine timing offset, Re-sample integrator
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% outputs using fine timing estimate and linear interpolation, then
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% extract the demodulated bits
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low_sample = floor(rx_timing);
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fract = rx_timing - low_sample;
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high_sample = ceil(rx_timing);
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if bitand(verbose,0x2)
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printf("rx_timing: %3.2f low_sample: %d high_sample: %d fract: %3.3f nin_next: %d\n", rx_timing, low_sample, high_sample, fract, next_nin);
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end
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f_int_resample = zeros(M,nsym);
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rx_bits = zeros(1,nsym*states.bitspersymbol);
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tone_max = zeros(1,nsym);
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rx_nse_pow = 1E-12; rx_sig_pow = 0.0;
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for i=1:nsym
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st = i*P+1;
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f_int_resample(:,i) = f_int(:,st+low_sample)*(1-fract) + f_int(:,st+high_sample)*fract;
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% Hard decision decoding, Largest amplitude tone is the winner.
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% Map this FSK "symbol" back to bits, depending on M
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[tone_max(i) tone_index] = max(f_int_resample(:,i));
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st = (i-1)*states.bitspersymbol + 1;
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en = st + states.bitspersymbol-1;
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arx_bits = dec2bin(tone_index - 1, states.bitspersymbol) - '0';
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rx_bits(st:en) = arx_bits;
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% each filter is the DFT of a chunk of spectrum. If there is no tone in the
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% filter it can be considered an estimate of noise in that bandwidth
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rx_pows = f_int_resample(:,i) .* conj(f_int_resample(:,i));
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rx_sig_pow += rx_pows(tone_index);
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rx_nse_pow += (sum(rx_pows) - rx_pows(tone_index))/(M-1);
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end
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states.f_int_resample = f_int_resample;
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% Eb/No estimation (todo: this needs some work, like calibration, low Eb/No perf, work for all M)
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tone_max = abs(tone_max);
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states.EbNodB = -6 + 20*log10(1E-6+mean(tone_max)/(1E-6+std(tone_max)));
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% Estimators for LDPC decoder, might be a bit rough if nsym is small
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rx_sig_pow = rx_sig_pow/nsym;
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rx_nse_pow = rx_nse_pow/nsym;
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states.v_est = sqrt(rx_sig_pow-rx_nse_pow);
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states.SNRest = rx_sig_pow/rx_nse_pow;
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endfunction
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% BER counter and test frame sync logic -------------------------------------------
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% We look for test_frame in rx_bits_buf, rx_bits_buf must be twice as long as test_frame
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function states = ber_counter(states, test_frame, rx_bits_buf)
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nbit = length(test_frame);
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assert (length(rx_bits_buf) == 2*nbit);
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state = states.ber_state;
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next_state = state;
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if state == 0
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% try to sync up with test frame
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nerrs_min = nbit;
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for i=1:nbit
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error_positions = xor(rx_bits_buf(i:nbit+i-1), test_frame);
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nerrs = sum(error_positions);
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if nerrs < nerrs_min
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nerrs_min = nerrs;
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states.coarse_offset = i;
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end
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end
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if nerrs_min/nbit < states.ber_valid_thresh
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next_state = 1;
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end
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if bitand(states.verbose,0x4)
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printf("coarse offset: %d nerrs_min: %d next_state: %d\n", states.coarse_offset, nerrs_min, next_state);
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end
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states.nerr = nerrs_min;
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end
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if state == 1
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% we're synced up, lets measure bit errors
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error_positions = xor(rx_bits_buf(states.coarse_offset:states.coarse_offset+nbit-1), test_frame);
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nerrs = sum(error_positions);
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if nerrs/nbit > states.ber_invalid_thresh
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next_state = 0;
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if bitand(states.verbose,0x4)
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printf("coarse offset: %d nerrs: %d next_state: %d\n", states.coarse_offset, nerrs, next_state);
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end
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else
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states.Terrs += nerrs;
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states.Tbits += nbit;
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states.nerr_log = [states.nerr_log nerrs];
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end
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states.nerr = nerrs;
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end
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states.ber_state = next_state;
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endfunction
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% Alternative stateless BER counter that works on packets that may have gaps between them
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function states = ber_counter_packet(states, test_frame, rx_bits_buf)
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ntestframebits = states.ntestframebits;
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nbit = states.nbit;
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% look for offset with min errors
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nerrs_min = ntestframebits; coarse_offset = 1;
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for i=1:nbit
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error_positions = xor(rx_bits_buf(i:ntestframebits+i-1), test_frame);
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nerrs = sum(error_positions);
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%printf("i: %d nerrs: %d\n", i, nerrs);
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if nerrs < nerrs_min
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nerrs_min = nerrs;
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coarse_offset = i;
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end
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end
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% if less than threshold count errors
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if nerrs_min/ntestframebits < 0.05
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states.Terrs += nerrs_min;
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states.Tbits += ntestframebits;
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states.nerr_log = [states.nerr_log nerrs_min];
|
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if bitand(states.verbose, 0x4)
|
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printf("coarse_offset: %d nerrs_min: %d\n", coarse_offset, nerrs_min);
|
|
end
|
|
end
|
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endfunction
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