void autotest_fft_shift_8()
{
float complex x[] = {
0 + 0*_Complex_I,
1 + 1*_Complex_I,
2 + 2*_Complex_I,
3 + 3*_Complex_I,
4 + 4*_Complex_I,
5 + 5*_Complex_I,
6 + 6*_Complex_I,
7 + 7*_Complex_I
};
float complex test[] = {
4 + 4*_Complex_I,
5 + 5*_Complex_I,
6 + 6*_Complex_I,
7 + 7*_Complex_I,
0 + 0*_Complex_I,
1 + 1*_Complex_I,
2 + 2*_Complex_I,
3 + 3*_Complex_I
};
fft_shift(x,8);
CONTEND_SAME_DATA(x,test,8*sizeof(float complex));
}
void autotest_fft_shift_4()
{
float complex x[] = {
0 + 0*_Complex_I,
1 + 1*_Complex_I,
2 + 2*_Complex_I,
3 + 3*_Complex_I
};
float complex test[] = {
2 + 2*_Complex_I,
3 + 3*_Complex_I,
0 + 0*_Complex_I,
1 + 1*_Complex_I
};
fft_shift(x,4);
CONTEND_SAME_DATA(x,test,4*sizeof(float complex));
}
//
// AUTOTEST : test multi-stage arbitrary resampler
//
void autotest_msresamp_crcf()
{
// options
unsigned int m = 13; // filter semi-length (filter delay)
float r=0.127115323f; // resampling rate (output/input)
float As=60.0f; // resampling filter stop-band attenuation [dB]
unsigned int n=1200; // number of input samples
float fx=0.0254230646f; // complex input sinusoid frequency (0.2*r)
//float bw=0.45f; // resampling filter bandwidth
//unsigned int npfb=64; // number of filters in bank (timing resolution)
unsigned int i;
// number of input samples (zero-padded)
unsigned int nx = n + m;
// output buffer with extra padding for good measure
unsigned int y_len = (unsigned int) ceilf(1.1 * nx * r) + 4;
// arrays
float complex x[nx];
float complex y[y_len];
// create resampler
msresamp_crcf q = msresamp_crcf_create(r,As);
// generate input signal
float wsum = 0.0f;
for (i=0; i<nx; i++) {
// compute window
float w = i < n ? kaiser(i, n, 10.0f, 0.0f) : 0.0f;
// apply window to complex sinusoid
x[i] = cexpf(_Complex_I*2*M_PI*fx*i) * w;
// accumulate window
wsum += w;
}
// resample
unsigned int ny=0;
unsigned int nw;
for (i=0; i<nx; i++) {
// execute resampler, storing in output buffer
msresamp_crcf_execute(q, &x[i], 1, &y[ny], &nw);
// increment output size
ny += nw;
}
// clean up allocated objects
msresamp_crcf_destroy(q);
//
// analyze resulting signal
//
// check that the actual resampling rate is close to the target
float r_actual = (float)ny / (float)nx;
float fy = fx / r; // expected output frequency
// run FFT and ensure that carrier has moved and that image
// frequencies and distortion have been adequately suppressed
unsigned int nfft = 1 << liquid_nextpow2(ny);
float complex yfft[nfft]; // fft input
float complex Yfft[nfft]; // fft output
for (i=0; i<nfft; i++)
yfft[i] = i < ny ? y[i] : 0.0f;
fft_run(nfft, yfft, Yfft, LIQUID_FFT_FORWARD, 0);
fft_shift(Yfft, nfft); // run FFT shift
// find peak frequency
float Ypeak = 0.0f;
float fpeak = 0.0f;
float max_sidelobe = -1e9f; // maximum side-lobe [dB]
float main_lobe_width = 0.07f; // TODO: figure this out from Kaiser's equations
for (i=0; i<nfft; i++) {
// normalized output frequency
float f = (float)i/(float)nfft - 0.5f;
// scale FFT output appropriately
Yfft[i] /= (r * wsum);
float Ymag = 20*log10f( cabsf(Yfft[i]) );
// find frequency location of maximum magnitude
if (Ymag > Ypeak || i==0) {
Ypeak = Ymag;
fpeak = f;
}
// find peak side-lobe value, ignoring frequencies
// within a certain range of signal frequency
if ( fabsf(f-fy) > main_lobe_width )
max_sidelobe = Ymag > max_sidelobe ? Ymag : max_sidelobe;
}
if (liquid_autotest_verbose) {
// print results
printf(" desired resampling rate : %12.8f\n", r);
printf(" measured resampling rate : %12.8f (%u/%u)\n", r_actual, ny, nx);
printf(" peak spectrum : %12.8f dB (expected 0.0 dB)\n", Ypeak);
printf(" peak frequency : %12.8f (expected %-12.8f)\n", fpeak, fy);
printf(" max sidelobe : %12.8f dB (expected at least %.2f dB)\n", max_sidelobe, -As);
}
CONTEND_DELTA( r_actual, r, 0.01f ); // check actual output sample rate
CONTEND_DELTA( Ypeak, 0.0f, 0.25f ); // peak should be about 0 dB
CONTEND_DELTA( fpeak, fy, 0.01f ); // peak frequency should be nearly 0.2
CONTEND_LESS_THAN( max_sidelobe, -As ); // maximum side-lobe should be sufficiently low
#if 0
// export results for debugging
char filename[] = "msresamp_crcf_autotest.m";
FILE*fid = fopen(filename,"w");
fprintf(fid,"%% %s: auto-generated file\n",filename);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n");
fprintf(fid,"r = %12.8f;\n", r);
fprintf(fid,"nx = %u;\n", nx);
fprintf(fid,"ny = %u;\n", ny);
fprintf(fid,"nfft = %u;\n", nfft);
fprintf(fid,"Y = zeros(1,nfft);\n");
for (i=0; i<nfft; i++)
fprintf(fid,"Y(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(Yfft[i]), cimagf(Yfft[i]));
fprintf(fid,"\n\n");
fprintf(fid,"%% plot frequency-domain result\n");
fprintf(fid,"f=[0:(nfft-1)]/nfft-0.5;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(f,20*log10(abs(Y)),'Color',[0.25 0.5 0.0],'LineWidth',2);\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"xlabel('normalized frequency');\n");
fprintf(fid,"ylabel('PSD [dB]');\n");
fprintf(fid,"axis([-0.5 0.5 -120 20]);\n");
fclose(fid);
printf("results written to %s\n",filename);
#endif
}
int main(int argc, char*argv[])
{
// options
float r = 1.1f; // resampling rate (output/input)
unsigned int m = 13; // resampling filter semi-length (filter delay)
float As = 60.0f; // resampling filter stop-band attenuation [dB]
float bw = 0.45f; // resampling filter bandwidth
unsigned int npfb = 64; // number of filters in bank (timing resolution)
unsigned int n = 400; // number of input samples
float fc = 0.044f; // complex sinusoid frequency
int dopt;
while ((dopt = getopt(argc,argv,"hr:m:b:s:p:n:f:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
case 'r': r = atof(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': bw = atof(optarg); break;
case 's': As = atof(optarg); break;
case 'p': npfb = atoi(optarg); break;
case 'n': n = atoi(optarg); break;
case 'f': fc = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (r <= 0.0f) {
fprintf(stderr,"error: %s, resampling rate must be greater than zero\n", argv[0]);
exit(1);
} else if (m == 0) {
fprintf(stderr,"error: %s, filter semi-length must be greater than zero\n", argv[0]);
exit(1);
} else if (bw == 0.0f || bw >= 0.5f) {
fprintf(stderr,"error: %s, filter bandwidth must be in (0,0.5)\n", argv[0]);
exit(1);
} else if (As < 0.0f) {
fprintf(stderr,"error: %s, filter stop-band attenuation must be greater than zero\n", argv[0]);
exit(1);
} else if (npfb == 0) {
fprintf(stderr,"error: %s, filter bank size must be greater than zero\n", argv[0]);
exit(1);
} else if (n == 0) {
fprintf(stderr,"error: %s, number of input samples must be greater than zero\n", argv[0]);
exit(1);
}
unsigned int i;
// number of input samples (zero-padded)
unsigned int nx = n + m;
// output buffer with extra padding for good measure
unsigned int y_len = (unsigned int) ceilf(1.1 * nx * r) + 4;
// arrays
float complex x[nx];
float complex y[y_len];
// create resampler
resamp_crcf q = resamp_crcf_create(r,m,bw,As,npfb);
// generate input signal
float wsum = 0.0f;
for (i=0; i<nx; i++) {
// compute window
float w = i < n ? kaiser(i, n, 10.0f, 0.0f) : 0.0f;
// apply window to complex sinusoid
x[i] = cexpf(_Complex_I*2*M_PI*fc*i) * w;
// accumulate window
wsum += w;
}
// resample
unsigned int ny=0;
#if 0
// execute one sample at a time
unsigned int nw;
for (i=0; i<nx; i++) {
// execute resampler, storing in output buffer
resamp_crcf_execute(q, x[i], &y[ny], &nw);
// increment output size
ny += nw;
}
#else
// execute on block of samples
resamp_crcf_execute_block(q, x, nx, y, &ny);
#endif
// clean up allocated objects
resamp_crcf_destroy(q);
//
// analyze resulting signal
//
// check that the actual resampling rate is close to the target
float r_actual = (float)ny / (float)nx;
float fy = fc / r; // expected output frequency
// run FFT and ensure that carrier has moved and that image
// frequencies and distortion have been adequately suppressed
unsigned int nfft = 1 << liquid_nextpow2(ny);
float complex yfft[nfft]; // fft input
float complex Yfft[nfft]; // fft output
for (i=0; i<nfft; i++)
yfft[i] = i < ny ? y[i] : 0.0f;
fft_run(nfft, yfft, Yfft, LIQUID_FFT_FORWARD, 0);
fft_shift(Yfft, nfft); // run FFT shift
// find peak frequency
float Ypeak = 0.0f;
float fpeak = 0.0f;
float max_sidelobe = -1e9f; // maximum side-lobe [dB]
float main_lobe_width = 0.07f; // TODO: figure this out from Kaiser's equations
for (i=0; i<nfft; i++) {
// normalized output frequency
float f = (float)i/(float)nfft - 0.5f;
// scale FFT output appropriately
float Ymag = 20*log10f( cabsf(Yfft[i] / (r * wsum)) );
// find frequency location of maximum magnitude
if (Ymag > Ypeak || i==0) {
Ypeak = Ymag;
fpeak = f;
}
// find peak side-lobe value, ignoring frequencies
// within a certain range of signal frequency
if ( fabsf(f-fy) > main_lobe_width )
max_sidelobe = Ymag > max_sidelobe ? Ymag : max_sidelobe;
}
// print results and check frequency location
printf(" desired resampling rate : %12.8f\n", r);
printf(" measured resampling rate : %12.8f (%u/%u)\n", r_actual, ny, nx);
printf(" peak spectrum : %12.8f dB (expected 0.0 dB)\n", Ypeak);
printf(" peak frequency : %12.8f (expected %-12.8f)\n", fpeak, fy);
printf(" max sidelobe : %12.8f dB (expected at least %.2f dB)\n", max_sidelobe, -As);
//
// export results
//
FILE * fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s: auto-generated file\n",OUTPUT_FILENAME);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n");
fprintf(fid,"m=%u;\n", m);
fprintf(fid,"npfb=%u;\n", npfb);
fprintf(fid,"r=%12.8f;\n", r);
fprintf(fid,"nx = %u;\n", nx);
fprintf(fid,"x = zeros(1,nx);\n");
for (i=0; i<nx; i++)
fprintf(fid,"x(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"ny = %u;\n", ny);
fprintf(fid,"y = zeros(1,ny);\n");
for (i=0; i<ny; i++)
fprintf(fid,"y(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(y[i]), cimagf(y[i]));
fprintf(fid,"\n\n");
fprintf(fid,"%% plot frequency-domain result\n");
fprintf(fid,"nfft=2^nextpow2(max(nx,ny));\n");
fprintf(fid,"%% estimate PSD, normalize by array length\n");
fprintf(fid,"X=20*log10(abs(fftshift(fft(x,nfft)/length(x))));\n");
fprintf(fid,"Y=20*log10(abs(fftshift(fft(y,nfft)/length(y))));\n");
fprintf(fid,"G=max(X);\n");
fprintf(fid,"X=X-G;\n");
fprintf(fid,"Y=Y-G;\n");
fprintf(fid,"f=[0:(nfft-1)]/nfft-0.5;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"if r>1, fx = f/r; fy = f; %% interpolated\n");
fprintf(fid,"else, fx = f; fy = f*r; %% decimated\n");
fprintf(fid,"end;\n");
fprintf(fid,"plot(fx,X,'Color',[0.5 0.5 0.5],fy,Y,'LineWidth',2);\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"xlabel('normalized frequency');\n");
fprintf(fid,"ylabel('PSD [dB]');\n");
fprintf(fid,"legend('original','resampled','location','northeast');");
fprintf(fid,"axis([-0.5 0.5 -120 20]);\n");
fprintf(fid,"\n\n");
fprintf(fid,"%% plot time-domain result\n");
fprintf(fid,"tx=[0:(length(x)-1)];\n");
fprintf(fid,"ty=[0:(length(y)-1)]/r-m;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid," plot(tx,real(x),'-s','Color',[0.5 0.5 0.5],'MarkerSize',1,...\n");
fprintf(fid," ty,real(y),'-s','Color',[0.5 0 0], 'MarkerSize',1);\n");
fprintf(fid," legend('original','resampled','location','northeast');");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('real');\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid," plot(tx,imag(x),'-s','Color',[0.5 0.5 0.5],'MarkerSize',1,...\n");
fprintf(fid," ty,imag(y),'-s','Color',[0 0.5 0], 'MarkerSize',1);\n");
fprintf(fid," legend('original','resampled','location','northeast');");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('imag');\n");
fclose(fid);
printf("results written to %s\n",OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
int main() {
float r=sqrtf(19); // resampling rate (output/input)
unsigned int n=37; // number of input samples
float As=60.0f; // stop-band attenuation [dB]
unsigned int i;
// derived values: number of input, output samples (adjusted for filter delay)
unsigned int nx = 1.4*n;
unsigned int ny_alloc = (unsigned int) (2*(float)nx * r); // allocation for output
// allocate memory for arrays
float complex x[nx];
float complex y[ny_alloc];
// generate input signal (filter pulse with frequency offset)
float hf[n];
liquid_firdes_kaiser(n, 0.08f, 80.0f, 0, hf);
for (i=0; i<nx; i++)
x[i] = (i < n) ? hf[i]*cexpf(_Complex_I*1.17f*i) : 0.0f;
// create resampler
msresamp_crcf q = msresamp_crcf_create(r,As);
float delay = msresamp_crcf_get_delay(q);
// execute resampler, storing in output buffer
unsigned int ny;
msresamp_crcf_execute(q, x, nx, y, &ny);
// print basic results
printf("input samples : %u\n", nx);
printf("output samples : %u\n", ny);
printf("delay : %f samples\n", delay);
// clean up allocated objects
msresamp_crcf_destroy(q);
//
// export output files
//
FILE * fid;
//
// export time plot
//
fid = fopen(OUTPUT_FILENAME_TIME,"w");
fprintf(fid,"# %s: auto-generated file\n\n", OUTPUT_FILENAME_TIME);
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 [-1.2:1.2]\n");
fprintf(fid,"set size ratio 0.3\n");
fprintf(fid,"set xlabel 'Input 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 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 6 pointsize 0.9 linetype 1 linewidth 1 linecolor rgb '#666666' title 'original',\\\n");
fprintf(fid," '-' using 1:2 with points pointtype 7 pointsize 0.6 linecolor rgb '#008000' title 'resampled'\n");
// export input signal
for (i=0; i<nx; i++)
fprintf(fid,"%12.4e %12.4e %12.4e\n", (float)i, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"e\n");
// export output signal
for (i=0; i<ny; i++)
fprintf(fid,"%12.4e %12.4e %12.4e\n", (float)(i)/r - delay, crealf(y[i]), cimagf(y[i]));
fprintf(fid,"e\n");
fprintf(fid,"# imag\n");
fprintf(fid,"set ylabel 'Imag'\n");
fprintf(fid,"plot '-' using 1:3 with linespoints pointtype 6 pointsize 0.9 linetype 1 linewidth 1 linecolor rgb '#666666' title 'original',\\\n");
fprintf(fid," '-' using 1:3 with points pointtype 7 pointsize 0.6 linecolor rgb '#800000' title 'resampled'\n");
// export input signal
for (i=0; i<nx; i++)
fprintf(fid,"%12.4e %12.4e %12.4e\n", (float)i, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"e\n");
// export output signal
for (i=0; i<ny; i++)
fprintf(fid,"%12.4e %12.4e %12.4e\n", (float)(i)/r - delay, crealf(y[i]), cimagf(y[i]));
fprintf(fid,"e\n");
fprintf(fid,"unset multiplot\n");
// close output file
fclose(fid);
//
// export spectrum plot
//
fid = fopen(OUTPUT_FILENAME_FREQ,"w");
unsigned int nfft = 512;
float complex X[nfft];
float complex Y[nfft];
liquid_doc_compute_psdcf(x, nx, X, nfft, LIQUID_DOC_PSDWINDOW_NONE, 1);
liquid_doc_compute_psdcf(y, ny, Y, nfft, LIQUID_DOC_PSDWINDOW_NONE, 1);
fft_shift(X,nfft);
fft_shift(Y,nfft);
fprintf(fid,"# %s: auto-generated file\n\n", OUTPUT_FILENAME_FREQ);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set xrange [-0.5:0.5];\n");
fprintf(fid,"set yrange [-120:20]\n");
fprintf(fid,"set size ratio 0.6\n");
fprintf(fid,"set xlabel 'Normalized Output Frequency'\n");
fprintf(fid,"set ylabel 'Power Spectral Density [dB]'\n");
fprintf(fid,"set key top right nobox\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,"# real\n");
fprintf(fid,"plot '-' using 1:2 with lines linetype 1 linewidth 4 linecolor rgb '#999999' title 'original',\\\n");
fprintf(fid," '-' using 1:2 with lines linetype 1 linewidth 4 linecolor rgb '#004080' title 'resampled'\n");
// export output
for (i=0; i<nfft; i++) {
float fx = ((float)(i) / (float)nfft - 0.5f) / r;
fprintf(fid,"%12.8f %12.4e\n", fx, 20*log10f(cabsf(X[i])));
}
fprintf(fid,"e\n");
for (i=0; i<nfft; i++) {
float fy = ((float)(i) / (float)nfft - 0.5f);
fprintf(fid,"%12.8f %12.4e\n", fy, 20*log10f(cabsf(Y[i])));
}
fprintf(fid,"e\n");
fclose(fid);
printf("done.\n");
return 0;
}
int main(int argc, char*argv[])
{
// options
unsigned int num_symbols=500; // number of symbols to observe
float SNRdB = 30.0f; // signal-to-noise ratio [dB]
unsigned int hc_len=5; // channel filter length
unsigned int k=2; // matched filter samples/symbol
unsigned int m=3; // matched filter delay (symbols)
float beta=0.3f; // matched filter excess bandwidth factor
unsigned int p=3; // equalizer length (symbols, gr_len = 2*k*p+1)
float mu = 0.09f; // LMS learning rate
// modulation type/depth
modulation_scheme ms = LIQUID_MODEM_QPSK;
// plotting options
unsigned int nfft = 512; // fft size
float gnuplot_version = 4.2;
char filename_base[256] = "figures.gen/eqlms_cccf_blind";
int dopt;
while ((dopt = getopt(argc,argv,"hf:g:n:s:c:k:m:b:p:u:M:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
case 'f': strncpy(filename_base,optarg,256); break;
case 'g': gnuplot_version = atoi(optarg); break;
case 'n': num_symbols = atoi(optarg); break;
case 's': SNRdB = atof(optarg); break;
case 'c': hc_len = atoi(optarg); break;
case 'k': k = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': beta = atof(optarg); break;
case 'p': p = atoi(optarg); break;
case 'u': mu = atof(optarg); break;
case 'M':
ms = liquid_getopt_str2mod(optarg);
if (ms == LIQUID_MODEM_UNKNOWN) {
fprintf(stderr,"error: %s, unknown/unsupported modulation scheme '%s'\n", argv[0], optarg);
return 1;
}
break;
default:
exit(1);
}
}
// validate input
if (num_symbols == 0) {
fprintf(stderr,"error: %s, number of symbols must be greater than zero\n", argv[0]);
exit(1);
} else if (hc_len == 0) {
fprintf(stderr,"error: %s, channel must have at least 1 tap\n", argv[0]);
exit(1);
} else if (k < 2) {
fprintf(stderr,"error: %s, samples/symbol must be at least 2\n", argv[0]);
exit(1);
} else if (m == 0) {
fprintf(stderr,"error: %s, filter semi-length must be at least 1 symbol\n", argv[0]);
exit(1);
} else if (beta < 0.0f || beta > 1.0f) {
fprintf(stderr,"error: %s, filter excess bandwidth must be in [0,1]\n", argv[0]);
exit(1);
} else if (p == 0) {
fprintf(stderr,"error: %s, equalizer semi-length must be at least 1 symbol\n", argv[0]);
exit(1);
} else if (mu < 0.0f || mu > 1.0f) {
fprintf(stderr,"error: %s, equalizer learning rate must be in [0,1]\n", argv[0]);
exit(1);
}
// set 'random' seed on options
srand( hc_len + p + nfft );
// derived values
unsigned int gt_len = 2*k*m+1; // matched filter length
unsigned int gr_len = 2*k*p+1; // equalizer filter length
unsigned int num_samples = k*num_symbols;
// bookkeeping variables
float complex sym_tx[num_symbols]; // transmitted data sequence
float complex x[num_samples]; // interpolated time series
float complex y[num_samples]; // channel output
float complex z[num_samples]; // equalized output
// least mean-squares (LMS) equalizer
float mse[num_symbols]; // equalizer mean-squared error
float complex gr[gr_len]; // equalizer filter coefficients
unsigned int i;
// generate matched filter response
float gtf[gt_len]; // matched filter response
liquid_firdes_rnyquist(LIQUID_RNYQUIST_RRC, k, m, beta, 0.0f, gtf);
// convert to complex coefficients
float complex gt[gt_len];
for (i=0; i<gt_len; i++)
gt[i] = gtf[i]; //+ 0.1f*(randnf() + _Complex_I*randnf());
// create interpolator
interp_cccf interp = interp_cccf_create(k, gt, gt_len);
// create the modem objects
modem mod = modem_create(ms);
modem demod = modem_create(ms);
unsigned int bps = modem_get_bps(mod);
unsigned int M = 1 << bps;
// generate channel impulse response, filter
#if 0
float complex hc[hc_len]; // channel filter coefficients
hc[0] = 1.0f;
for (i=1; i<hc_len; i++)
hc[i] = 0.09f*(randnf() + randnf()*_Complex_I);
#else
// use fixed channel
hc_len = 8;
float complex hc[hc_len]; // channel filter coefficients
hc[0] = 1.00000000+ 0.00000000*_Complex_I;
hc[1] = 0.08077553+ -0.00247592*_Complex_I;
hc[2] = 0.03625883+ -0.09219734*_Complex_I;
hc[3] = 0.05764082+ 0.03277601*_Complex_I;
hc[4] = -0.04773349+ -0.18766306*_Complex_I;
hc[5] = -0.00101735+ -0.00270737*_Complex_I;
hc[6] = -0.05796884+ -0.12665297*_Complex_I;
hc[7] = 0.03805391+ -0.07609370*_Complex_I;
#endif
firfilt_cccf fchannel = firfilt_cccf_create(hc, hc_len);
firfilt_cccf_print(fchannel);
// generate random symbols
for (i=0; i<num_symbols; i++)
modem_modulate(mod, rand()%M, &sym_tx[i]);
// interpolate
for (i=0; i<num_symbols; i++)
interp_cccf_execute(interp, sym_tx[i], &x[i*k]);
// push through channel
float nstd = powf(10.0f, -SNRdB/20.0f);
for (i=0; i<num_samples; i++) {
firfilt_cccf_push(fchannel, x[i]);
firfilt_cccf_execute(fchannel, &y[i]);
// add noise
y[i] += nstd*(randnf() + randnf()*_Complex_I)*M_SQRT1_2;
}
// push through equalizers
float grf[gr_len];
liquid_firdes_rnyquist(LIQUID_RNYQUIST_RRC, k, p, beta, 0.0f, grf);
for (i=0; i<gr_len; i++) {
gr[i] = grf[i] / (float)k;
}
// create LMS equalizer
eqlms_cccf eq = eqlms_cccf_create(gr, gr_len);
eqlms_cccf_set_bw(eq, mu);
// filtered error vector magnitude (emperical MSE)
//float zeta=0.05f; // smoothing factor (small zeta -> smooth MSE)
float complex d_hat = 0.0f;
unsigned int num_symbols_rx=0;
for (i=0; i<num_samples; i++) {
// push samples into equalizers
eqlms_cccf_push(eq, y[i]);
// compute outputs
eqlms_cccf_execute(eq, &d_hat);
// store outputs
z[i] = d_hat;
// check to see if buffer is full
if ( i < gr_len) continue;
// decimate by k
if ( (i%k) != 0 ) continue;
// estimate transmitted signal
unsigned int sym_out; // output symbol
float complex d_prime; // estimated input sample
// LMS
modem_demodulate(demod, d_hat, &sym_out);
modem_get_demodulator_sample(demod, &d_prime);
// update equalizers
eqlms_cccf_step(eq, d_prime, d_hat);
#if 0
// update filtered evm estimate
float evm = crealf( (d_prime-d_hat)*conjf(d_prime-d_hat) );
if (num_symbols_rx == 0) {
mse[num_symbols_rx] = evm;
} else {
mse[num_symbols_rx] = mse[num_symbols_rx-1]*(1-zeta) + evm*zeta;
}
#else
// compute ISI for entire system
eqlms_cccf_get_weights(eq, gr);
mse[num_symbols_rx] = eqlms_cccf_isi(k, gt, gt_len, hc, hc_len, gr, gr_len);
#endif
// print filtered evm (emperical rms error)
if ( ((num_symbols_rx+1)%100) == 0 )
printf("%4u : mse = %12.8f dB\n",
num_symbols_rx+1,
20*log10f(mse[num_symbols_rx]));
// increment output symbol counter
num_symbols_rx++;
}
// get equalizer weights
eqlms_cccf_get_weights(eq, gr);
// destroy objects
eqlms_cccf_destroy(eq);
interp_cccf_destroy(interp);
firfilt_cccf_destroy(fchannel);
modem_destroy(mod);
modem_destroy(demod);
//
// export output
//
FILE * fid = NULL;
char filename[300];
//
// const: constellation
//
strncpy(filename, filename_base, 256);
strcat(filename, "_const.gnu");
fid = fopen(filename,"w");
if (!fid) {
fprintf(stderr,"error: %s, could not open file '%s' for writing\n", argv[0], filename);
return 1;
}
fprintf(fid,"# %s: auto-generated file\n\n", filename);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set size ratio 1\n");
fprintf(fid,"set xrange [-1.5:1.5];\n");
fprintf(fid,"set yrange [-1.5:1.5];\n");
fprintf(fid,"set xlabel 'In-phase'\n");
fprintf(fid,"set ylabel 'Quadrature phase'\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' linewidth 1\n",LIQUID_DOC_COLOR_GRID);
fprintf(fid,"plot '-' using 1:2 with points pointtype 7 pointsize 0.5 linecolor rgb '%s' title 'first 50%%',\\\n", LIQUID_DOC_COLOR_GRAY);
fprintf(fid," '-' using 1:2 with points pointtype 7 pointsize 0.7 linecolor rgb '%s' title 'last 50%%'\n", LIQUID_DOC_COLOR_RED);
// first half of symbols
for (i=2*p; i<num_symbols/2; i+=k)
fprintf(fid," %12.4e %12.4e\n", crealf(y[i]), cimagf(y[i]));
fprintf(fid,"e\n");
// second half of symbols
for ( ; i<num_symbols; i+=k)
fprintf(fid," %12.4e %12.4e\n", crealf(z[i]), cimagf(z[i]));
fprintf(fid,"e\n");
fclose(fid);
printf("results written to '%s'\n", filename);
//
// mse : mean-squared error
//
strncpy(filename, filename_base, 256);
strcat(filename, "_mse.gnu");
fid = fopen(filename,"w");
if (!fid) {
fprintf(stderr,"error: %s, could not open file '%s' for writing\n", argv[0], filename);
return 1;
}
fprintf(fid,"# %s: auto-generated file\n\n", filename);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set size ratio 0.3\n");
fprintf(fid,"set xrange [0:%u];\n", num_symbols);
fprintf(fid,"set yrange [1e-3:1e-1];\n");
fprintf(fid,"set format y '10^{%%L}'\n");
fprintf(fid,"set log y\n");
fprintf(fid,"set xlabel 'symbol index'\n");
fprintf(fid,"set ylabel 'mean-squared error'\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' linewidth 1\n",LIQUID_DOC_COLOR_GRID);
fprintf(fid,"plot '-' using 1:2 with lines linewidth 4 linetype 1 linecolor rgb '%s' title 'LMS MSE'\n", LIQUID_DOC_COLOR_RED);
// LMS
for (i=0; i<num_symbols_rx; i++)
fprintf(fid," %4u %16.8e\n", i, mse[i]);
fprintf(fid,"e\n");
fclose(fid);
printf("results written to '%s'\n", filename);
//
// psd : power spectral density
//
// scale transmit filter appropriately
for (i=0; i<gt_len; i++) gt[i] /= (float)k;
float complex Gt[nfft]; // transmit matched filter
float complex Hc[nfft]; // channel response
float complex Gr[nfft]; // equalizer response
liquid_doc_compute_psdcf(gt, gt_len, Gt, nfft, LIQUID_DOC_PSDWINDOW_NONE, 0);
liquid_doc_compute_psdcf(hc, hc_len, Hc, nfft, LIQUID_DOC_PSDWINDOW_NONE, 0);
liquid_doc_compute_psdcf(gr, gr_len, Gr, nfft, LIQUID_DOC_PSDWINDOW_NONE, 0);
fft_shift(Gt, nfft);
fft_shift(Hc, nfft);
fft_shift(Gr, nfft);
float freq[nfft];
for (i=0; i<nfft; i++)
freq[i] = (float)(i) / (float)nfft - 0.5f;
strncpy(filename, filename_base, 256);
strcat(filename, "_freq.gnu");
fid = fopen(filename,"w");
if (!fid) {
fprintf(stderr,"error: %s, could not open file '%s' for writing\n", argv[0], filename);
return 1;
}
fprintf(fid,"# %s: auto-generated file\n\n", filename);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set size ratio 0.6\n");
fprintf(fid,"set xrange [-0.5:0.5];\n");
fprintf(fid,"set yrange [-10:6]\n");
fprintf(fid,"set xlabel 'Normalized Frequency'\n");
fprintf(fid,"set ylabel 'Power Spectral Density [dB]'\n");
fprintf(fid,"set key top right nobox\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' lw 1\n",LIQUID_DOC_COLOR_GRID);
fprintf(fid,"plot '-' using 1:2 with lines linetype 1 linewidth 1.5 linecolor rgb '%s' title 'transmit',\\\n", LIQUID_DOC_COLOR_GRAY);
fprintf(fid," '-' using 1:2 with lines linetype 1 linewidth 1.5 linecolor rgb '%s' title 'channel',\\\n", LIQUID_DOC_COLOR_RED);
fprintf(fid," '-' using 1:2 with lines linetype 1 linewidth 1.5 linecolor rgb '%s' title 'equalizer',\\\n", LIQUID_DOC_COLOR_GREEN);
fprintf(fid," '-' using 1:2 with lines linetype 1 linewidth 4.0 linecolor rgb '%s' title 'composite',\\\n", LIQUID_DOC_COLOR_BLUE);
fprintf(fid," '-' using 1:2 with points pointtype 7 pointsize 0.6 linecolor rgb '%s' notitle\n", LIQUID_DOC_COLOR_BLUE);
// received signal
for (i=0; i<nfft; i++)
fprintf(fid,"%12.8f %12.4e\n", freq[i], 20*log10f(cabsf(Gt[i])) );
fprintf(fid,"e\n");
// channel
for (i=0; i<nfft; i++)
fprintf(fid,"%12.8f %12.4e\n", freq[i], 20*log10f(cabsf(Hc[i])) );
fprintf(fid,"e\n");
// equalizer
for (i=0; i<nfft; i++)
fprintf(fid,"%12.8f %12.4e\n", freq[i], 20*log10f(cabsf(Gr[i])) );
fprintf(fid,"e\n");
// composite
for (i=0; i<nfft; i++)
fprintf(fid,"%12.8f %12.4e\n", freq[i], 20*log10f( cabsf(Gt[i])*cabsf(Hc[i])*cabsf(Gr[i])) );
fprintf(fid,"e\n");
// composite
fprintf(fid,"%12.8f %12.4e\n", -0.5f/(float)k, 20*log10f(0.5f));
fprintf(fid,"%12.8f %12.4e\n", 0.5f/(float)k, 20*log10f(0.5f));
fprintf(fid,"e\n");
fclose(fid);
printf("results written to '%s'\n", filename);
//
// time...
//
strncpy(filename, filename_base, 256);
strcat(filename, "_time.gnu");
fid = fopen(filename,"w");
if (!fid) {
fprintf(stderr,"error: %s, could not open file '%s' for writing\n", argv[0], filename);
return 1;
}
fprintf(fid,"# %s: auto-generated file\n\n", filename);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set xrange [0:%u];\n",num_symbols);
fprintf(fid,"set yrange [-1.5:1.5]\n");
fprintf(fid,"set size ratio 0.3\n");
fprintf(fid,"set xlabel 'Symbol 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");
// real
fprintf(fid,"# real\n");
fprintf(fid,"set ylabel 'Real'\n");
fprintf(fid,"plot '-' using 1:2 with lines linetype 1 linewidth 1 linecolor rgb '#999999' notitle,\\\n");
fprintf(fid," '-' using 1:2 with points pointtype 7 linecolor rgb '%s' notitle'\n", LIQUID_DOC_COLOR_BLUE);
//
for (i=0; i<num_samples; i++)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k, crealf(z[i]));
fprintf(fid,"e\n");
//
for (i=0; i<num_samples; i+=k)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k, crealf(z[i]));
fprintf(fid,"e\n");
// imag
fprintf(fid,"# imag\n");
fprintf(fid,"set ylabel 'Imag'\n");
fprintf(fid,"plot '-' using 1:2 with lines linetype 1 linewidth 1 linecolor rgb '#999999' notitle,\\\n");
fprintf(fid," '-' using 1:2 with points pointtype 7 linecolor rgb '%s' notitle'\n", LIQUID_DOC_COLOR_GREEN);
//
for (i=0; i<num_samples; i++)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k, cimagf(z[i]));
fprintf(fid,"e\n");
//
for (i=0; i<num_samples; i+=k)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k, cimagf(z[i]));
fprintf(fid,"e\n");
fprintf(fid,"unset multiplot\n");
// close output file
fclose(fid);
printf("results written to '%s'\n", filename);
return 0;
}
int main() {
// options
unsigned int h_len = 7; // filter semi-length (filter delay)
float r=1/sqrtf(2); // resampling rate (output/input)
float bw=0.25f; // resampling filter bandwidth
float As=60.0f; // resampling filter stop-band attenuation [dB]
unsigned int npfb=32; // number of filters in bank (timing resolution)
unsigned int n=180; // number of input samples
// number of input samples (adjusted for filter delay)
unsigned int nx = n + h_len;
// generate input sequence : windowed sum of complex sinusoids
unsigned int i;
float complex x[nx];
for (i=0; i<nx; i++) {
float complex jphi = _Complex_I*2.0f*M_PI*i;
x[i] = cexpf(jphi*0.02f) + 1.4f*cexpf(jphi*0.07f);
// window edge size
unsigned int t = (unsigned int)(0.1*n);
if (i < n) {
// edge-rounded window
if (i < t) x[i] *= blackmanharris(i,2*t);
else if (i >= n-t) x[i] *= blackmanharris(n-i-1,2*t);
} else {
x[i] = 0.;
}
}
// output buffer with extra padding for good measure
unsigned int y_len = (unsigned int) ceilf(1.1*r*nx) + 16;
float complex y[y_len];
// create resampler
resamp_crcf f = resamp_crcf_create(r,h_len,bw,As,npfb);
unsigned int num_written;
unsigned int ny=0;
for (i=0; i<nx; i++) {
// execute resampler, storing in output buffer
resamp_crcf_execute(f, x[i], &y[ny], &num_written);
ny += num_written;
}
printf(" %u / %u\n", ny, nx);
// clean up allocated objects
resamp_crcf_destroy(f);
// open/initialize output file
FILE*fid = fopen(OUTPUT_FILENAME_TIME,"w");
fprintf(fid,"# %s: auto-generated file\n\n", OUTPUT_FILENAME_TIME);
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 [-3:3]\n");
fprintf(fid,"set size ratio 0.3\n");
fprintf(fid,"set xlabel 'Input 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 linetype 1 linewidth 1 linecolor rgb '#999999' title 'original',\\\n");
fprintf(fid," '-' using 1:2 with points pointtype 7 linecolor rgb '#008000' title 'resampled'\n");
// export output
for (i=0; i<nx; i++) {
//fprintf(fid,"%6u %12.4e %12.4e\n", i, cos(2*M_PI*0.04*i), sin(2*M_PI*0.04*i));
fprintf(fid,"%6u %12.4e %12.4e\n", i, crealf(x[i]), cimagf(x[i]));
}
fprintf(fid,"e\n");
float t;
for (i=0; i<ny; i++) {
t = (float)(i) / r - (float)(h_len);
fprintf(fid,"%12.4e %12.4e %12.4e\n", t, crealf(y[i]), cimagf(y[i]));
}
fprintf(fid,"e\n");
fprintf(fid,"# imag\n");
fprintf(fid,"set ylabel 'Imag'\n");
fprintf(fid,"plot '-' using 1:3 with linespoints pointtype 7 linetype 1 linewidth 1 linecolor rgb '#999999' title 'original',\\\n");
fprintf(fid," '-' using 1:3 with points pointtype 7 linecolor rgb '#800000' title 'resampled'\n");
// export output
for (i=0; i<nx; i++) {
//fprintf(fid,"%6u %12.4e %12.4e\n", i, cos(2*M_PI*0.04*i), sin(2*M_PI*0.04*i));
fprintf(fid,"%6u %12.4e %12.4e\n", i, crealf(x[i]), cimagf(x[i]));
}
fprintf(fid,"e\n");
for (i=0; i<ny; i++) {
t = (float)(i) / r - (float)(h_len);
fprintf(fid,"%12.4e %12.4e %12.4e\n", t, crealf(y[i]), cimagf(y[i]));
}
fprintf(fid,"e\n");
fprintf(fid,"unset multiplot\n");
// close output file
fclose(fid);
fid = fopen(OUTPUT_FILENAME_FREQ,"w");
unsigned int nfft = 512;
float complex X[nfft];
float complex Y[nfft];
liquid_doc_compute_psdcf(x,nx,X,nfft,LIQUID_DOC_PSDWINDOW_HANN,0);
liquid_doc_compute_psdcf(y,ny,Y,nfft,LIQUID_DOC_PSDWINDOW_HANN,0);
fft_shift(X,nfft);
fft_shift(Y,nfft);
float scaling_factor = 20*log10f(nfft);
fprintf(fid,"# %s: auto-generated file\n\n", OUTPUT_FILENAME_FREQ);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set xrange [-0.5:0.5];\n");
fprintf(fid,"set yrange [-120:20]\n");
fprintf(fid,"set size ratio 0.6\n");
fprintf(fid,"set xlabel 'Normalized Input Frequency'\n");
fprintf(fid,"set ylabel 'Power Spectral Density [dB]'\n");
fprintf(fid,"set key top right nobox\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,"# real\n");
fprintf(fid,"plot '-' using 1:2 with lines linetype 1 linewidth 4 linecolor rgb '#999999' title 'original',\\\n");
fprintf(fid," '-' using 1:2 with lines linetype 1 linewidth 4 linecolor rgb '#004080' title 'resampled'\n");
// export output
for (i=0; i<nfft; i++) {
float fx = (float)(i) / (float)nfft - 0.5f;
fprintf(fid,"%12.8f %12.4e\n", fx, 20*log10f(cabsf(X[i])) - scaling_factor);
}
fprintf(fid,"e\n");
for (i=0; i<nfft; i++) {
float fy = ((float)(i) / (float)nfft - 0.5f)*r;
fprintf(fid,"%12.8f %12.4e\n", fy, 20*log10f(cabsf(Y[i])) - scaling_factor - 20*log10(r));
}
fprintf(fid,"e\n");
fclose(fid);
printf("done.\n");
return 0;
}
