// Design (root-)Nyquist filter from prototype
// _type : filter type (e.g. LIQUID_FIRFILT_RRRC)
// _k : samples/symbol
// _m : symbol delay
// _beta : excess bandwidth factor, _beta in [0,1]
// _dt : fractional sample delay
// _h : output coefficient buffer (length: 2*k*m+1)
void liquid_firdes_prototype(liquid_firfilt_type _type,
unsigned int _k,
unsigned int _m,
float _beta,
float _dt,
float * _h)
{
// compute filter parameters
unsigned int h_len = 2*_k*_m + 1; // length
float fc = 0.5f / (float)_k; // cut-off frequency
float df = _beta / (float)_k; // transition bandwidth
float As = estimate_req_filter_As(df,h_len); // stop-band attenuation
// Parks-McClellan algorithm parameters
float bands[6] = { 0.0f, fc-0.5f*df,
fc, fc,
fc+0.5f*df, 0.5f};
float des[3] = { (float)_k, 0.5f*_k, 0.0f };
float weights[3] = {1.0f, 1.0f, 1.0f};
liquid_firdespm_wtype wtype[3] = { LIQUID_FIRDESPM_FLATWEIGHT,
LIQUID_FIRDESPM_FLATWEIGHT,
LIQUID_FIRDESPM_FLATWEIGHT};
switch (_type) {
// Nyquist filter prototypes
case LIQUID_FIRFILT_KAISER:
liquid_firdes_kaiser(h_len, fc, As, _dt, _h);
break;
case LIQUID_FIRFILT_PM:
// WARNING: input timing offset is ignored here
firdespm_run(h_len, 3, bands, des, weights, wtype, LIQUID_FIRDESPM_BANDPASS, _h);
break;
case LIQUID_FIRFILT_RCOS:
liquid_firdes_rcos(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_FEXP:
liquid_firdes_fexp(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_FSECH:
liquid_firdes_fsech(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_FARCSECH:
liquid_firdes_farcsech(_k, _m, _beta, _dt, _h);
break;
// root-Nyquist filter prototypes
case LIQUID_FIRFILT_ARKAISER:
liquid_firdes_arkaiser(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RKAISER:
liquid_firdes_rkaiser(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RRC:
liquid_firdes_rrcos(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_hM3:
liquid_firdes_hM3(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_GMSKTX:
liquid_firdes_gmsktx(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_GMSKRX:
liquid_firdes_gmskrx(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RFEXP:
liquid_firdes_rfexp(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RFSECH:
liquid_firdes_rfsech(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RFARCSECH:
liquid_firdes_rfarcsech(_k, _m, _beta, _dt, _h);
break;
default:
fprintf(stderr,"error: liquid_firdes_prototype(), invalid root-Nyquist filter type '%d'\n", _type);
exit(1);
}
}
int main(int argc, char*argv[]) {
srand(time(NULL));
// options
unsigned int k=2; // samples/symbol
unsigned int m=3; // filter delay (symbols)
float beta=0.9f; // filter excess bandwidth factor
unsigned int order=2;
unsigned int num_symbols=1024;
float SNRdB = 30.0f;
float bt=0.02f; // loop filter bandwidth
float tau=0.2f; // fractional symbol offset
float r = 1.00f; // resampled rate
// use random data or 101010 phasing pattern
int random_data=1;
int dopt;
while ((dopt = getopt(argc,argv,"uhk:m:b:o:s:w:n:t:r:")) != EOF) {
switch (dopt) {
case 'u':
case 'h': usage(); return 0;
case 'k': k = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': beta = atof(optarg); break;
case 'o': order = atoi(optarg); break;
case 's': SNRdB = atof(optarg); break;
case 'w': bt = atof(optarg); break;
case 'n': num_symbols = atoi(optarg); break;
case 't': tau = atof(optarg); break;
case 'r': r = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (k < 2) {
fprintf(stderr,"error: k (samples/symbol) must be at least 2\n");
return 1;
} else if (m < 1) {
fprintf(stderr,"error: m (filter delay) must be greater than 0\n");
return 1;
} else if (beta <= 0.0f || beta > 1.0f) {
fprintf(stderr,"error: beta (excess bandwidth factor) must be in (0,1]\n");
return 1;
} else if (order == 0) {
fprintf(stderr,"error: number of polyphase filters must be greater than 0\n");
return 1;
} else if (bt <= 0.0f) {
fprintf(stderr,"error: timing PLL bandwidth must be greater than 0\n");
return 1;
} else if (num_symbols == 0) {
fprintf(stderr,"error: number of symbols must be greater than 0\n");
return 1;
} else if (tau < -1.0f || tau > 1.0f) {
fprintf(stderr,"error: timing phase offset must be in [-1,1]\n");
return 1;
} else if (r < 0.5f || r > 2.0f) {
fprintf(stderr,"error: timing frequency offset must be in [0.5,2]\n");
return 1;
}
// compute delay
while (tau < 0) tau += 1.0f; // ensure positive tau
float g = k*tau; // number of samples offset
int ds=floorf(g); // additional symbol delay
float dt = (g - (float)ds); // fractional sample offset
unsigned int i, n=0;
unsigned int num_samples = k*num_symbols;
unsigned int num_samples_resamp = (unsigned int) ceilf(num_samples*r*1.1f) + 4;
float complex s[num_symbols]; // data symbols
float complex x[num_samples]; // interpolated samples
float complex y[num_samples_resamp]; // resampled data (resamp_crcf)
float complex z[num_symbols + 64]; // synchronized symbols
for (i=0; i<num_symbols; i++) {
if (random_data) {
// random signal (QPSK)
s[i] = cexpf(_Complex_I*0.5f*M_PI*((rand() % 4) + 0.5f));
} else {
s[i] = (i%2) ? 1.0f : -1.0f; // 101010 phasing pattern
}
}
//
// create and run interpolator
//
// design interpolating filter
unsigned int h_len = 2*k*m + 1;
float h[h_len];
liquid_firdes_rcos(k,m,beta,dt,h);
interp_crcf q = interp_crcf_create(k,h,h_len);
for (i=0; i<num_symbols; i++) {
interp_crcf_execute(q, s[i], &x[n]);
n+=k;
}
assert(n == num_samples);
interp_crcf_destroy(q);
//
// run resampler
//
unsigned int resamp_len = 10*k; // resampling filter semi-length (filter delay)
float resamp_bw = 0.45f; // resampling filter bandwidth
float resamp_As = 60.0f; // resampling filter stop-band attenuation
unsigned int resamp_npfb = 64; // number of filters in bank
resamp_crcf f = resamp_crcf_create(r, resamp_len, resamp_bw, resamp_As, resamp_npfb);
unsigned int num_samples_resampled = 0;
unsigned int num_written;
for (i=0; i<num_samples; i++) {
#if 0
// bypass arbitrary resampler
y[i] = x[i];
num_samples_resampled = num_samples;
#else
// TODO : compensate for resampler filter delay
resamp_crcf_execute(f, x[i], &y[num_samples_resampled], &num_written);
num_samples_resampled += num_written;
#endif
}
resamp_crcf_destroy(f);
//
// add noise
//
float nstd = powf(10.0f, -SNRdB/20.0f) / sqrtf(2.0f);
for (i=0; i<num_samples_resampled; i++)
y[i] += nstd*(randnf() + _Complex_I*randnf());
//
// create and run symbol synchronizer
//
// create symbol synchronizer
symsynclp_crcf d = symsynclp_crcf_create(k, order);
symsynclp_crcf_set_lf_bw(d,bt);
unsigned int num_symbols_sync=0;
unsigned int nn;
float tau_hat[num_samples];
for (i=ds; i<num_samples_resampled; i++) {
tau_hat[num_symbols_sync] = symsynclp_crcf_get_tau(d);
symsynclp_crcf_execute(d, &y[i], 1, &z[num_symbols_sync], &nn);
num_symbols_sync += nn;
}
symsynclp_crcf_destroy(d);
// print last several symbols to screen
printf("z(t) :\n");
for (i=num_symbols_sync-10; i<num_symbols_sync; i++)
printf(" z(%2u) = %8.4f + j*%8.4f;\n", i+1, crealf(z[i]), cimagf(z[i]));
//
// export output file
//
FILE* fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s, auto-generated file\n\n", OUTPUT_FILENAME);
fprintf(fid,"close all;\nclear all;\n\n");
fprintf(fid,"k=%u;\n",k);
fprintf(fid,"m=%u;\n",m);
fprintf(fid,"beta=%12.8f;\n",beta);
fprintf(fid,"order=%u;\n",order);
fprintf(fid,"num_symbols=%u;\n",num_symbols);
for (i=0; i<h_len; i++)
fprintf(fid,"h(%3u) = %12.5f;\n", i+1, h[i]);
for (i=0; i<num_symbols; i++)
fprintf(fid,"s(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(s[i]), cimagf(s[i]));
for (i=0; i<num_samples; i++)
fprintf(fid,"x(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(x[i]), cimagf(x[i]));
for (i=0; i<num_samples_resampled; i++)
fprintf(fid,"y(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(y[i]), cimagf(y[i]));
for (i=0; i<num_symbols_sync; i++)
fprintf(fid,"z(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(z[i]), cimagf(z[i]));
for (i=0; i<num_symbols_sync; i++)
fprintf(fid,"tau_hat(%3u) = %12.8f;\n", i+1, tau_hat[i]);
fprintf(fid,"\n\n");
fprintf(fid,"ms = 8; %% marker size\n");
fprintf(fid,"zp = filter(h,1,y);\n");
fprintf(fid,"figure;\nhold on;\n");
fprintf(fid,"plot([0:length(s)-1], real(s), 'ob', 'MarkerSize',ms);\n");
fprintf(fid,"plot([0:length(y)-1]/k -m, real(y), '-', 'MarkerSize',ms, 'Color',[0.8 0.8 0.8]);\n");
fprintf(fid,"plot([0:length(zp)-1]/k -k*m, real(zp/k), '-b', 'MarkerSize',ms);\n");
fprintf(fid,"plot([0:length(z)-1] -k*m+1,real(z), 'xr', 'MarkerSize',ms);\n");
fprintf(fid,"hold off;\n");
fprintf(fid,"xlabel('Symbol Index');\n");
fprintf(fid,"ylabel('Output Signal');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"legend('sym in','interp','mf','sym out',0);\n");
fprintf(fid,"t0=1:floor(0.25*length(z));\n");
fprintf(fid,"t1=ceil(0.25*length(z)):length(z);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"hold on;\n");
fprintf(fid,"plot(real(z(t0)),imag(z(t0)),'x','MarkerSize',ms,'Color',[0.6 0.6 0.6]);\n");
fprintf(fid,"plot(real(z(t1)),imag(z(t1)),'x','MarkerSize',ms,'Color',[0 0.25 0.5]);\n");
fprintf(fid,"hold off;\n");
fprintf(fid,"axis square; grid on;\n");
fprintf(fid,"axis([-1 1 -1 1]*1.2);\n");
fprintf(fid,"xlabel('In-phase');\n");
fprintf(fid,"ylabel('Quadrature');\n");
fprintf(fid,"legend(['first 25%%'],['last 75%%'],1);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"tt = 0:(length(tau_hat)-1);\n");
fprintf(fid,"plot(tt,tau_hat,'-k','Color',[0 0 0]);\n");
fprintf(fid,"xlabel('time');\n");
fprintf(fid,"ylabel('tau-hat');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"axis([0 length(tau_hat) 0 1]);\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
// clean it up
printf("done.\n");
return 0;
}
int main() {
// options
unsigned int D=4; // samples/symbol
unsigned int m=3; // filter delay
float beta = 0.3f; // filter excess bandwidth
unsigned int num_data_symbols=32; // number of data symbols
// derived values
unsigned int h_len = 2*D*m+1;
unsigned int num_symbols = num_data_symbols + 2*m;
unsigned int num_samples = D*num_symbols;
// design filter and create interpolator
float h[h_len];
liquid_firdes_rcos(D,m,beta,0.0f,h);
decim_crcf q = decim_crcf_create(D,h,h_len);
// generate input signal and interpolate
float complex x[num_samples];
float complex y[num_symbols];
unsigned int i;
for (i=0; i<num_samples; i++)
x[i] = 1.0f * hann(i,num_samples) * cexpf(_Complex_I * 2 * M_PI * i * 0.057f);
for (i=0; i<num_symbols; i++)
decim_crcf_execute(q, &x[D*i], &y[i], 0);
decim_crcf_destroy(q);
// open output file
FILE * fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"# %s: auto-generated file\n\n", OUTPUT_FILENAME);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
//fprintf(fid,"set xrange [0:%u];\n",n);
fprintf(fid,"set yrange [-1.5:1.5]\n");
fprintf(fid,"set size ratio 0.3\n");
fprintf(fid,"set xlabel 'Sample Index'\n");
fprintf(fid,"set key top right nobox\n");
fprintf(fid,"set ytics -5,1,5\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set pointsize 0.6\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' lw 1\n", LIQUID_DOC_COLOR_GRID);
fprintf(fid,"set multiplot layout 2,1 scale 1.0,1.0\n");
fprintf(fid,"# real\n");
fprintf(fid,"set ylabel 'Real'\n");
fprintf(fid,"plot '-' using 1:2 with linespoints pointtype 7 pointsize 0.3 linecolor rgb '%s' linewidth 1 title 'input',\\\n",LIQUID_DOC_COLOR_GRAY);
fprintf(fid," '-' using 1:2 with points pointtype 7 linecolor rgb '%s' title 'decimated'\n",LIQUID_DOC_COLOR_GREEN);
for (i=0; i<num_samples; i++)
fprintf(fid,"%4u %12.4e\n", i, crealf(x[i]));
fprintf(fid,"e\n");
for (i=0; i<num_symbols; i++)
fprintf(fid,"%12.4e %12.4e\n", (float)(i*D) - (float)(D*m), crealf(y[i])/D);
fprintf(fid,"e\n");
fprintf(fid,"# imag\n");
fprintf(fid,"set ylabel 'Imag'\n");
fprintf(fid,"plot '-' using 1:2 with linespoints pointtype 7 pointsize 0.3 linecolor rgb '%s' linewidth 1 title 'input',\\\n",LIQUID_DOC_COLOR_GRAY);
fprintf(fid," '-' using 1:2 with points pointtype 7 linecolor rgb '%s' title 'decimated'\n", LIQUID_DOC_COLOR_RED);
for (i=0; i<num_samples; i++)
fprintf(fid,"%4u %12.4e\n", i, cimagf(x[i]));
fprintf(fid,"e\n");
for (i=0; i<num_symbols; i++)
fprintf(fid,"%12.4e %12.4e\n", (float)(i*D) - (float)(D*m), cimagf(y[i])/D);
fprintf(fid,"e\n");
// close output file
fclose(fid);
return 0;
}
