% function ofdm_sync(x, nsym, ngrd)
% Example: ofdm_sync(x, 1152, 128)
function ofdm_rx(x, offset, nsym_soll, ngrd)

% Init
fa = 48000;
fc = fa/4;
F1 = 750;
F2 = 2250;
F3 = 3000;
close all;
do_evaluate = 1;
alpha = 0.05;

x = real(x);
% Detection
display('Sync detection');
nsym_ist = nsym_soll;
xi = zeros(ngrd, 1);
range_max = 24;
range_min = 4;
range_forget = 0.5;
range = range_max;
err = 0;
k = 0;
kk = 1;
remain = length(x);
progress_ival = 1;
progress_last = -1;
nfft = nsym_soll-ngrd

bin_c = fix(nfft*fc/fa)+1
bin_f1 = fix(nfft*(fc+F1)/fa)+1
bin_f2 = fix(nfft*(fc+F2)/fa)+1
bin_f3 = fix(nfft*(fc+F3)/fa)+1
k_fft = 3/sqrt(nfft);

phi_c_last = 0;
phi_f1_last = 0;
phi_f2_last = 0;
phi_f3_last = 0;

while remain > 2*nsym_ist,
    xsym = x(offset+k*nsym_ist+1:offset+k*nsym_ist+nsym_ist+range);
    [xcor, imax, jmax, xi] = xcc(xsym, nsym_ist, ngrd, -range, range, -range, range, xi);
    remain = remain - (length(offset+k*nsym_ist+1:offset+k*nsym_ist+nsym_ist+range));
    err = -imax + jmax;
    offset = offset + imax;
    nsym_ist = max(round(nsym_ist + err), ngrd)
    sl_offset(kk) = offset;
    sl_err(kk) = err;
    sl_nsym_ist(kk) = nsym_ist;
    range = min(max(fix(range + abs(err) - range_forget), range_min), range_max);
    progress = round(100*(length(x)-remain)/length(x));
    if (progress ~= progress_last)
       progress_last = progress_last + progress_ival;
       progress = progress
    end;
    if (do_evaluate == 1)
      X0 = k_fft*fft(xsym(1:nsym_ist-ngrd), nfft);
      phi_c(kk) = (1-alpha)*phi_c_last + alpha*angle(X0(bin_c));
      phi_f1(kk) = (1-alpha)*phi_f1_last + alpha*angle(X0(bin_f1));
      phi_f2(kk) = (1-alpha)*phi_f2_last + alpha*angle(X0(bin_f2));
      phi_f3(kk) = (1-alpha)*phi_f3_last + alpha*angle(X0(bin_f3));
      phi_c_last = phi_c(kk);
      phi_f1_last = phi_f1(kk);
      phi_f2_last = phi_f2(kk);
      phi_f3_last = phi_f3(kk);
      %pause;
    end;  
    k = k + 1;
    kk = kk + 1;
end;

% Result
display('Results:');

offset_stddev = sqrt(var(sl_offset))
err_mean = mean(sl_err)
nsym_ist_mean = mean(nsym_ist)

% Diagrams
figure;
plot(1:length(sl_offset), sl_offset); title('offset'); legend('offset'); grid;

figure;
subplot(2,1,1)
plot(1:length(sl_err), sl_err); title('error'); legend('error'); grid;
subplot(2,1,2)
plot(1:length(sl_nsym_ist), sl_nsym_ist, 1:length(sl_nsym_ist), nsym_soll*ones(size(sl_nsym_ist))); title('Tracking'); legend('nsym_{ist}', 'nsym_{soll}'); grid;

figure
plot(1:length(phi_c), phi_c, 1:length(phi_f1), phi_f1, 1:length(phi_f2), phi_f2, 1:length(phi_f3), phi_f3); grid; legend('phi_{c}', 'phi_{f1}', 'phi_{f2}', 'phi_{f3}'); title('Phase');

% custom function
% Correlation
function [ccm, imax, jmax, xo] = xcc(x, Ns, Ng, i_low, i_high, j_low, j_high, xi)

Nu = Ns - Ng;
off = length(xi);

xo = x(length(x)-off+1:length(x));
xs = [xi' x']';

ccm = 0;
imax = 0;
jmax = 0;
for i_off=i_low:i_high,
    ii = off+i_off+1:off+Ng+i_off;
    xm_i = mean(xs(ii));
    xi = xs(ii)-xm_i;
    var_i = var(xi);
    for j_off=j_low:j_high,
        jj = off+Nu+j_off+1:off+Nu+Ng+j_off;
        xm_j = mean(xs(jj));
        xj = xs(jj) - xm_j;
        var_j = var(xj);
        cc = sum(xi.*xj)./sqrt(var_i*var_j);
        if (cc > ccm)
            imax = i_off;
            jmax = j_off;
            ccm = cc;
        end;    
    end;
end;