int main(int argc, char*argv[]) {
srand(time(NULL));
// options
unsigned int k = 2; // samples/symbol (input)
unsigned int k_out = 2; // samples/symbol (output)
unsigned int m = 5; // filter delay (symbols)
float beta = 0.5f; // filter excess bandwidth factor
unsigned int num_filters = 32; // number of filters in the bank
unsigned int num_symbols = 400; // number of data symbols
float SNRdB = 30.0f; // signal-to-noise ratio
// transmit/receive filter types
liquid_firfilt_type ftype_tx = LIQUID_FIRFILT_RRC;
liquid_firfilt_type ftype_rx = LIQUID_FIRFILT_RRC;
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,"hT:k:K:m:b:B:s:w:n:t:r:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
case 'T':
if (strcmp(optarg,"gmsk")==0) {
ftype_tx = LIQUID_FIRFILT_GMSKTX;
ftype_rx = LIQUID_FIRFILT_GMSKRX;
} else {
ftype_tx = liquid_getopt_str2firfilt(optarg);
ftype_rx = liquid_getopt_str2firfilt(optarg);
}
if (ftype_tx == LIQUID_FIRFILT_UNKNOWN) {
fprintf(stderr,"error: %s, unknown filter type '%s'\n", argv[0], optarg);
exit(1);
}
break;
case 'k': k = atoi(optarg); break;
case 'K': k_out = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': beta = atof(optarg); break;
case 'B': num_filters = 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");
exit(1);
} else if (m < 1) {
fprintf(stderr,"error: m (filter delay) must be greater than 0\n");
exit(1);
} else if (beta <= 0.0f || beta > 1.0f) {
fprintf(stderr,"error: beta (excess bandwidth factor) must be in (0,1]\n");
exit(1);
} else if (num_filters == 0) {
fprintf(stderr,"error: number of polyphase filters must be greater than 0\n");
exit(1);
} else if (bt <= 0.0f) {
fprintf(stderr,"error: timing PLL bandwidth must be greater than 0\n");
exit(1);
} else if (num_symbols == 0) {
fprintf(stderr,"error: number of symbols must be greater than 0\n");
exit(1);
} else if (tau < -1.0f || tau > 1.0f) {
fprintf(stderr,"error: timing phase offset must be in [-1,1]\n");
exit(1);
} else if (r < 0.5f || r > 2.0f) {
fprintf(stderr,"error: timing frequency offset must be in [0.5,2]\n");
exit(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
if (dt > 0.5f) { // force dt to be in [0.5,0.5]
dt -= 1.0f;
ds++;
}
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[k_out*num_symbols + 64];// synchronized samples
float complex sym_out[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_rnyquist(ftype_tx,k,m,beta,dt,h);
firinterp_crcf q = firinterp_crcf_create(k,h,h_len);
for (i=0; i<num_symbols; i++) {
firinterp_crcf_execute(q, s[i], &x[n]);
n+=k;
}
assert(n == num_samples);
firinterp_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);
for (i=0; i<num_samples_resampled; i++)
y[i] += nstd*(randnf() + _Complex_I*randnf());
//
// create and run symbol synchronizer
//
symsync_crcf d = symsync_crcf_create_rnyquist(ftype_rx, k, m, beta, num_filters);
symsync_crcf_set_lf_bw(d,bt);
symsync_crcf_set_output_rate(d,k_out);
unsigned int num_samples_sync=0;
unsigned int nn;
unsigned int num_symbols_sync = 0;
float tau_hat[num_samples];
for (i=ds; i<num_samples_resampled; i++) {
tau_hat[num_samples_sync] = symsync_crcf_get_tau(d);
symsync_crcf_execute(d, &y[i], 1, &z[num_samples_sync], &nn);
// decimate
unsigned int j;
for (j=0; j<nn; j++) {
if ( (num_samples_sync%k_out)==0 )
sym_out[num_symbols_sync++] = z[num_samples_sync];
num_samples_sync++;
}
}
symsync_crcf_destroy(d);
// print last several symbols to screen
printf("output symbols:\n");
printf(" ...\n");
for (i=num_symbols_sync-10; i<num_symbols_sync; i++)
printf(" sym_out(%2u) = %8.4f + j*%8.4f;\n", i+1, crealf(sym_out[i]), cimagf(sym_out[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,"k_out=%u;\n",k_out);
fprintf(fid,"num_filters=%u;\n",num_filters);
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_samples_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,"sym_out(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(sym_out[i]), cimagf(sym_out[i]));
for (i=0; i<num_samples_sync; i++)
fprintf(fid,"tau_hat(%3u) = %12.8f;\n", i+1, tau_hat[i]);
fprintf(fid,"\n\n");
fprintf(fid,"%% scale QPSK in-phase by sqrt(2)\n");
fprintf(fid,"z = z*sqrt(2);\n");
fprintf(fid,"\n\n");
fprintf(fid,"tz = [0:length(z)-1]/k_out;\n");
fprintf(fid,"iz = 1:k_out:length(z);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(tz, real(z), '-',...\n");
fprintf(fid," tz(iz), real(z(iz)),'or');\n");
fprintf(fid,"xlabel('Time');\n");
fprintf(fid,"ylabel('Output Signal (real)');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"legend('output time series','optimum timing','location','northeast');\n");
fprintf(fid,"iz0 = iz( 1:round(length(iz)*0.5) );\n");
fprintf(fid,"iz1 = iz( round(length(iz)*0.5):length(iz) );\n");
fprintf(fid,"figure;\n");
fprintf(fid,"hold on;\n");
fprintf(fid,"plot(real(z(iz0)),imag(z(iz0)),'x','MarkerSize',4,'Color',[0.6 0.6 0.6]);\n");
fprintf(fid,"plot(real(z(iz1)),imag(z(iz1)),'o','MarkerSize',4,'Color',[0 0.25 0.5]);\n");
fprintf(fid,"hold off;\n");
fprintf(fid,"axis square;\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"axis([-1 1 -1 1]*2.0);\n");
fprintf(fid,"xlabel('In-phase');\n");
fprintf(fid,"ylabel('Quadrature');\n");
fprintf(fid,"legend(['first 50%%'],['last 50%%'],'location','northeast');\n");
fprintf(fid,"figure;\n");
fprintf(fid,"tt = 0:(length(tau_hat)-1);\n");
fprintf(fid,"b = floor(num_filters*tau_hat + 0.5);\n");
fprintf(fid,"stairs(tt,tau_hat*num_filters);\n");
fprintf(fid,"hold on;\n");
fprintf(fid,"plot(tt,b,'-k','Color',[0 0 0]);\n");
fprintf(fid,"hold off;\n");
fprintf(fid,"xlabel('time');\n");
fprintf(fid,"ylabel('filterbank index');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"axis([0 length(tau_hat) -1 num_filters]);\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
// clean it up
printf("done.\n");
return 0;
}
int main(int argc, char*argv[]) {
// options
unsigned int k=2; // samples/symbol
unsigned int m=2; // filter delay
float beta = 0.5f; // filter excess bandwidth
unsigned int num_data_symbols=8; // number of data symbols
int dopt;
while ((dopt = getopt(argc,argv,"uhk:m:b:n:")) != 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 'n': num_data_symbols = atoi(optarg); break;
default:
usage();
return 1;
}
}
// validate options
if (k < 2) {
fprintf(stderr,"error: %s, interp factor must be greater than 1\n", argv[0]);
return 1;
} else if (m < 1) {
fprintf(stderr,"error: %s, filter delay must be greater than 0\n", argv[0]);
return 1;
} else if (beta <= 0.0 || beta > 1.0f) {
fprintf(stderr,"error: %s, beta (excess bandwidth factor) must be in (0,1]\n", argv[0]);
return 1;
} else if (num_data_symbols < 1) {
fprintf(stderr,"error: %s, must have at least one data symbol\n", argv[0]);
return 1;
}
// derived values
unsigned int h_len = 2*k*m+1;
unsigned int num_symbols = num_data_symbols + 2*m;
unsigned int num_samples = k*num_symbols;
// design filter and create interpolator and decimator objects
float h[h_len]; // transmit filter
float g[h_len]; // receive filter (reverse of h)
liquid_firdes_rrcos(k,m,beta,0.3f,h);
unsigned int i;
for (i=0; i<h_len; i++)
g[i] = h[h_len-i-1];
firinterp_crcf interp = firinterp_crcf_create(k,h,h_len);
firdecim_crcf decim = firdecim_crcf_create(k,g,h_len);
// allocate memory for buffers
float complex x[num_symbols]; // input symbols
float complex y[num_samples]; // interpolated sequence
float complex z[num_symbols]; // decimated (received) symbols
// generate input symbols, padded with zeros at the end
for (i=0; i<num_data_symbols; i++) {
x[i] = (rand() % 2 ? 1.0f : -1.0f) +
(rand() % 2 ? 1.0f : -1.0f) * _Complex_I;
}
for ( ; i<num_symbols; i++)
x[i] = 0.0f;
// run interpolator
for (i=0; i<num_symbols; i++) {
firinterp_crcf_execute(interp, x[i], &y[k*i]);
}
// run decimator
for (i=0; i<num_symbols; i++) {
firdecim_crcf_execute(decim, &y[k*i], &z[i]);
// normalize output by samples/symbol
z[i] /= k;
}
// destroy objects
firinterp_crcf_destroy(interp);
firdecim_crcf_destroy(decim);
// print results to screen
printf("filter impulse response :\n");
for (i=0; i<h_len; i++)
printf(" [%4u] : %8.4f\n", i, h[i]);
printf("input symbols\n");
for (i=0; i<num_symbols; i++) {
printf(" [%4u] : %8.4f + j*%8.4f", i, crealf(x[i]), cimagf(x[i]));
// highlight actual data symbols
if (i < num_data_symbols) printf(" *\n");
else printf("\n");
}
printf("interpolator output samples:\n");
for (i=0; i<num_samples; i++) {
printf(" [%4u] : %8.4f + j*%8.4f", i, crealf(y[i]), cimagf(y[i]));
if ( (i >= k*m) && ((i%k)==0)) printf(" **\n");
else printf("\n");
}
printf("output symbols:\n");
for (i=0; i<num_symbols; i++) {
printf(" [%4u] : %8.4f + j*%8.4f", i, crealf(z[i]), cimagf(z[i]));
// highlight symbols (compensate for filter delay)
if ( i < 2*m ) printf("\n");
else printf(" *\n");
}
// open output file
FILE * fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s: auto-generated file\n\n", OUTPUT_FILENAME);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n");
fprintf(fid,"k = %u;\n", k);
fprintf(fid,"m = %u;\n", m);
fprintf(fid,"h_len=%u;\n",h_len);
fprintf(fid,"num_symbols = %u;\n", num_symbols);
fprintf(fid,"num_samples = k*num_symbols;\n");
fprintf(fid,"h = zeros(1,h_len);\n");
fprintf(fid,"x = zeros(1,num_symbols);\n");
fprintf(fid,"y = zeros(1,num_samples);\n");
for (i=0; i<h_len; i++)
fprintf(fid,"h(%4u) = %12.4e;\n", i+1, h[i]);
for (i=0; i<num_symbols; i++)
fprintf(fid,"x(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(x[i]), cimagf(x[i]));
for (i=0; i<num_samples; i++)
fprintf(fid,"y(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(y[i]), cimagf(y[i]));
for (i=0; i<num_symbols; i++)
fprintf(fid,"z(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(z[i]), cimagf(z[i]));
fprintf(fid,"\n\n");
fprintf(fid,"tx = [0:(num_symbols-1)];\n");
fprintf(fid,"ty = [0:(num_samples-1)]/k - m;\n");
fprintf(fid,"tz = [0:(num_symbols-1)] - 2*m;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid," plot(ty,real(y),'-',tx,real(x),'s',tz,real(z),'x');\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('real');\n");
fprintf(fid," grid on;\n");
fprintf(fid," legend('interp','data in','data out',0);\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid," plot(ty,imag(y),'-',tx,imag(x),'s',tz,imag(z),'x');\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('imag');\n");
fprintf(fid," grid on;\n");
fclose(fid);
printf("results written to %s.\n",OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
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);
firinterp_crcf q = firinterp_crcf_create(k,h,h_len);
for (i=0; i<num_symbols; i++) {
firinterp_crcf_execute(q, s[i], &x[n]);
n+=k;
}
assert(n == num_samples);
firinterp_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(int argc, char*argv[])
{
srand(time(NULL));
// 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, hp_len = 2*k*p+1)
float mu = 0.08f; // learning rate
// modulation type/depth
modulation_scheme ms = LIQUID_MODEM_QPSK;
int dopt;
while ((dopt = getopt(argc,argv,"hn:s:c:k:m:b:p:u:M:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
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);
}
// derived values
unsigned int hm_len = 2*k*m+1; // matched filter length
unsigned int hp_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
float hm[hm_len]; // matched filter response
float complex hc[hc_len]; // channel filter coefficients
float complex hp[hp_len]; // equalizer filter coefficients
unsigned int i;
// generate matched filter response
liquid_firdes_rnyquist(LIQUID_FIRFILT_RRC, k, m, beta, 0.0f, hm);
firinterp_crcf interp = firinterp_crcf_create(k, hm, hm_len);
// create the modem objects
modem mod = modem_create(ms);
modem demod = modem_create(ms);
unsigned int M = 1 << modem_get_bps(mod);
// generate channel impulse response, filter
hc[0] = 1.0f;
for (i=1; i<hc_len; i++)
hc[i] = 0.09f*(randnf() + randnf()*_Complex_I);
firfilt_cccf fchannel = firfilt_cccf_create(hc, hc_len);
// 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++)
firinterp_crcf_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 equalizer
// create equalizer, intialized with square-root Nyquist filter
eqlms_cccf eq = eqlms_cccf_create_rnyquist(LIQUID_FIRFILT_RRC, k, p, beta, 0.0f);
eqlms_cccf_set_bw(eq, mu);
// get initialized weights
eqlms_cccf_get_weights(eq, hp);
// filtered error vector magnitude (emperical RMS error)
float evm_hat = 0.03f;
float complex d_hat = 0.0f;
for (i=0; i<num_samples; i++) {
// print filtered evm (emperical rms error)
if ( ((i+1)%50)==0 )
printf("%4u : rms error = %12.8f dB\n", i+1, 10*log10(evm_hat));
eqlms_cccf_push(eq, y[i]);
eqlms_cccf_execute(eq, &d_hat);
// store output
z[i] = d_hat;
// decimate by k
if ( (i%k) != 0 ) continue;
// estimate transmitted signal
unsigned int sym_out; // output symbol
float complex d_prime; // estimated input sample
modem_demodulate(demod, d_hat, &sym_out);
modem_get_demodulator_sample(demod, &d_prime);
// update equalizer
eqlms_cccf_step(eq, d_prime, d_hat);
// update filtered evm estimate
float evm = crealf( (d_prime-d_hat)*conjf(d_prime-d_hat) );
evm_hat = 0.98f*evm_hat + 0.02f*evm;
}
// get equalizer weights
eqlms_cccf_get_weights(eq, hp);
// destroy objects
eqlms_cccf_destroy(eq);
firinterp_crcf_destroy(interp);
firfilt_cccf_destroy(fchannel);
modem_destroy(mod);
modem_destroy(demod);
//
// export output
//
FILE * fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s : auto-generated file\n\n", OUTPUT_FILENAME);
fprintf(fid,"clear all\n");
fprintf(fid,"close all\n");
fprintf(fid,"k = %u;\n", k);
fprintf(fid,"m = %u;\n", m);
fprintf(fid,"num_symbols = %u;\n", num_symbols);
fprintf(fid,"num_samples = num_symbols*k;\n");
// save transmit matched-filter response
fprintf(fid,"hm_len = 2*k*m+1;\n");
fprintf(fid,"hm = zeros(1,hm_len);\n");
for (i=0; i<hm_len; i++)
fprintf(fid,"hm(%4u) = %12.4e;\n", i+1, hm[i]);
// save channel impulse response
fprintf(fid,"hc_len = %u;\n", hc_len);
fprintf(fid,"hc = zeros(1,hc_len);\n");
for (i=0; i<hc_len; i++)
fprintf(fid,"hc(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(hc[i]), cimagf(hc[i]));
// save equalizer response
fprintf(fid,"hp_len = %u;\n", hp_len);
fprintf(fid,"hp = zeros(1,hp_len);\n");
for (i=0; i<hp_len; i++)
fprintf(fid,"hp(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(hp[i]), cimagf(hp[i]));
// save sample sets
fprintf(fid,"x = zeros(1,num_samples);\n");
fprintf(fid,"y = zeros(1,num_samples);\n");
fprintf(fid,"z = zeros(1,num_samples);\n");
for (i=0; i<num_samples; i++) {
fprintf(fid,"x(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"y(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(y[i]), cimagf(y[i]));
fprintf(fid,"z(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(z[i]), cimagf(z[i]));
}
// plot time response
fprintf(fid,"t = 0:(num_samples-1);\n");
fprintf(fid,"tsym = 1:k:num_samples;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(t,real(z),...\n");
fprintf(fid," t(tsym),real(z(tsym)),'x');\n");
// plot constellation
fprintf(fid,"tsym0 = tsym(1:(length(tsym)/2));\n");
fprintf(fid,"tsym1 = tsym((length(tsym)/2):end);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(real(z(tsym0)),imag(z(tsym0)),'x','Color',[1 1 1]*0.7,...\n");
fprintf(fid," real(z(tsym1)),imag(z(tsym1)),'x','Color',[1 1 1]*0.0);\n");
fprintf(fid,"xlabel('In-Phase');\n");
fprintf(fid,"ylabel('Quadrature');\n");
fprintf(fid,"axis([-1 1 -1 1]*1.5);\n");
fprintf(fid,"axis square;\n");
fprintf(fid,"grid on;\n");
// compute composite response
fprintf(fid,"g = real(conv(conv(hm,hc),hp));\n");
// plot responses
fprintf(fid,"nfft = 1024;\n");
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"Hm = 20*log10(abs(fftshift(fft(hm/k,nfft))));\n");
fprintf(fid,"Hc = 20*log10(abs(fftshift(fft(hc, nfft))));\n");
fprintf(fid,"Hp = 20*log10(abs(fftshift(fft(hp, nfft))));\n");
fprintf(fid,"G = 20*log10(abs(fftshift(fft(g/k, nfft))));\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(f,Hm, f,Hc, f,Hp, f,G,'-k','LineWidth',2, [-0.5/k 0.5/k],[-6.026 -6.026],'or');\n");
fprintf(fid,"xlabel('Normalized Frequency');\n");
fprintf(fid,"ylabel('Power Spectral Density');\n");
fprintf(fid,"legend('transmit','channel','equalizer','composite','half-power points',1);\n");
fprintf(fid,"axis([-0.5 0.5 -12 8]);\n");
fprintf(fid,"grid on;\n");
fclose(fid);
printf("results written to '%s'\n", OUTPUT_FILENAME);
return 0;
}
void autotest_firinterp_crcf_generic()
{
// h = [0, 0.25, 0.5, 0.75, 1.0, 0.75, 0.5, 0.25, 0];
float h[9] = {
-0.7393353832652201,
0.1909821993029451,
-1.7013834621383086,
-0.6157406339062349,
0.5806218191269317,
0.0576963976148674,
-1.0958217797368455,
-0.6379821629743743,
0.7019489165905530};
unsigned int M = 4; // firinterp factor
firinterp_crcf q = firinterp_crcf_create(M,h,9);
// x = [1+j*0.2, -0.2+j*1.3, 0.5+j*0.3, 1.1-j*0.2]
float complex x[4] = {
1.0000e+00+ 2.0000e-01*_Complex_I,
-2.0000e-01+ 1.3000e+00*_Complex_I,
5.0000e-01+ 3.0000e-01*_Complex_I,
1.1000e+00+ -2.0000e-01*_Complex_I
};
float complex y[16];
// z = [x(1) 0 0 0 x(2) 0 0 0 x(3) 0 0 0 x(4) 0 0 0];
// test = filter(h,1,z)
float complex test[16] = {
-0.7393353832652201 - 0.1478670766530440*_Complex_I,
0.1909821993029451 + 0.0381964398605890*_Complex_I,
-1.7013834621383086 - 0.3402766924276617*_Complex_I,
-0.6157406339062349 - 0.1231481267812470*_Complex_I,
0.7284888957799757 - 0.8450116344193997*_Complex_I,
0.0194999577542784 + 0.2598161386168021*_Complex_I,
-0.7555450873091838 - 2.4309628567271702*_Complex_I,
-0.5148340361931273 - 0.9280592566729803*_Complex_I,
0.2161568611325566 + 0.6733975332035558*_Complex_I,
0.0839518201284991 + 0.1322999766902112*_Complex_I,
-0.6315273751217851 - 1.9349833522993918*_Complex_I,
-0.1802738843582426 - 1.0140990020385570*_Complex_I,
-0.6633477953463869 + 1.2345872139588425*_Complex_I,
0.2389286180406733 - 0.0208875205761288*_Complex_I,
-2.4194326982205623 + 0.0115301585066081*_Complex_I,
-0.9963057787840456 - 0.0682465221110653*_Complex_I };
float tol = 1e-6;
unsigned int i;
for (i=0; i<4; i++)
firinterp_crcf_execute(q, x[i], &y[i*M]);
for (i=0; i<16; i++) {
CONTEND_DELTA( crealf(y[i]), crealf(test[i]), tol);
CONTEND_DELTA( cimagf(y[i]), cimagf(test[i]), tol);
if (liquid_autotest_verbose)
printf(" y(%u) = %8.4f + j%8.4f;\n", i+1, crealf(y[i]), cimagf(y[i]));
}
if (liquid_autotest_verbose)
firinterp_crcf_print(q);
// destroy interpolator object
firinterp_crcf_destroy(q);
}
int main(int argc, char*argv[]) {
srand(time(NULL));
// options
unsigned int k=2; // samples/symbol (input)
unsigned int m=3; // filter delay (symbols)
float beta=0.5f; // filter excess bandwidth factor
unsigned int npfb=32; // number of filters in the bank
unsigned int p=3; // equalizer length (symbols, hp_len = 2*k*p+1)
float mu = 0.05f; // equalizer learning rate
unsigned int num_symbols=500; // number of data symbols
unsigned int hc_len=5; // channel filter length
float SNRdB = 30.0f; // signal-to-noise ratio
liquid_firfilt_type ftype = LIQUID_FIRFILT_ARKAISER;
float bt=0.05f; // symbol synchronizer loop filter bandwidth
float tau=-0.1f; // fractional symbol offset
int dopt;
while ((dopt = getopt(argc,argv,"uhk:m:b:n:B:w:p:W:s:c:t:")) != EOF) {
switch (dopt) {
case 'u':
case 'h': usage(); return 0;
// transmit filter properties
case 'k': k = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': beta = atof(optarg); break;
case 'n': num_symbols = atoi(optarg); break;
// symsync properties
case 'B': npfb = atoi(optarg); break;
case 'w': bt = atof(optarg); break;
// equalizer properties
case 'p': p = atoi(optarg); break;
case 'W': mu = atof(optarg); break;
// equalizer properties
case 's': SNRdB = atof(optarg); break;
case 'c': hc_len = atoi(optarg); break;
case 't': tau = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (k < 2) {
fprintf(stderr,"error: %s,k (samples/symbol) must be at least 2\n", argv[0]);
exit(1);
} else if (m < 1) {
fprintf(stderr,"error: %s,m (filter delay) must be greater than 0\n", argv[0]);
exit(1);
} else if (beta <= 0.0f || beta > 1.0f) {
fprintf(stderr,"error: %s,beta (excess bandwidth factor) must be in (0,1]\n", argv[0]);
exit(1);
} else if (num_symbols == 0) {
fprintf(stderr,"error: %s,number of symbols must be greater than 0\n", argv[0]);
exit(1);
} else if (npfb == 0) {
fprintf(stderr,"error: %s,number of polyphase filters must be greater than 0\n", argv[0]);
exit(1);
} else if (bt < 0.0f) {
fprintf(stderr,"error: %s,timing PLL bandwidth cannot be negative\n", argv[0]);
exit(1);
} else if (p == 0) {
fprintf(stderr,"error: %s, equalizer order must be at least 1\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);
} else if (hc_len < 1) {
fprintf(stderr,"error: %s, channel response must have at least 1 tap\n", argv[0]);
exit(1);
} else if (tau < -1.0f || tau > 1.0f) {
fprintf(stderr,"error: %s,timing phase offset must be in [-1,1]\n", argv[0]);
exit(1);
}
// derived values
unsigned int ht_len = 2*k*m+1; // transmit filter order
unsigned int hp_len = 2*k*p+1; // equalizer order
float nstd = powf(10.0f, -SNRdB/20.0f);
float dt = tau; // fractional sample offset
unsigned int ds = 0; // full sample delay
unsigned int i;
unsigned int num_samples = k*num_symbols;
float complex s[num_symbols]; // data symbols
float complex x[num_samples]; // interpolated samples
float complex y[num_samples]; // channel output
float complex z[k*num_symbols + 64]; // synchronized samples
float complex sym_out[num_symbols + 64]; // synchronized symbols
for (i=0; i<num_symbols; i++) {
s[i] = (rand() % 2 ? M_SQRT1_2 : -M_SQRT1_2) +
(rand() % 2 ? M_SQRT1_2 : -M_SQRT1_2) * _Complex_I;
}
//
// create and run interpolator
//
// design interpolating filter
float ht[ht_len];
liquid_firdes_prototype(ftype,k,m,beta,dt,ht);
firinterp_crcf q = firinterp_crcf_create(k, ht, ht_len);
for (i=0; i<num_symbols; i++)
firinterp_crcf_execute(q, s[i], &x[i*k]);
firinterp_crcf_destroy(q);
//
// channel
//
// generate channel impulse response, filter
float complex hc[hc_len];
hc[0] = 1.0f;
for (i=1; i<hc_len; i++)
hc[i] = 0.07f*(randnf() + randnf()*_Complex_I);
firfilt_cccf fchannel = firfilt_cccf_create(hc, hc_len);
// push through channel
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;
}
firfilt_cccf_destroy(fchannel);
//
// symbol timing recovery
//
// create symbol synchronizer
symsync_crcf d = symsync_crcf_create_rnyquist(ftype, k, m, beta, npfb);
symsync_crcf_set_lf_bw(d,bt);
symsync_crcf_set_output_rate(d,k);
unsigned int num_samples_sync=0;
unsigned int nw;
for (i=ds; i<num_samples; i++) {
// push through symbol synchronizer
symsync_crcf_execute(d, &y[i], 1, &z[num_samples_sync], &nw);
num_samples_sync += nw;
}
printf("num samples : %6u (%6u synchronized)\n", num_samples, num_samples_sync);
symsync_crcf_destroy(d);
//
// equalizer/decimator
//
// create equalizer as low-pass filter
float complex hp[hp_len];
eqlms_cccf eq = eqlms_cccf_create_lowpass(hp_len, 0.4f);
eqlms_cccf_set_bw(eq, mu);
// push through equalizer and decimate
unsigned int num_symbols_sync = 0;
float complex d_hat = 0.0f;
for (i=0; i<num_samples_sync; i++) {
// push sample into equalizer
eqlms_cccf_push(eq, z[i]);
// decimate by k
if ( (i%k) != 0) continue;
// compute output
eqlms_cccf_execute(eq, &d_hat);
sym_out[num_symbols_sync++] = d_hat;
// check if buffer is full
if ( i < hp_len ) continue;
// estimate transmitted signal
float complex d_prime = (crealf(d_hat) > 0.0f ? M_SQRT1_2 : -M_SQRT1_2) +
(cimagf(d_hat) > 0.0f ? M_SQRT1_2 : -M_SQRT1_2) * _Complex_I;
// update equalizer
eqlms_cccf_step(eq, d_prime, d_hat);
}
// get equalizer weights
eqlms_cccf_get_weights(eq, hp);
// destroy equalizer object
eqlms_cccf_destroy(eq);
// print last several symbols to screen
printf("output symbols:\n");
for (i=num_symbols_sync-10; i<num_symbols_sync; i++)
printf(" sym_out(%2u) = %8.4f + j*%8.4f;\n", i+1, crealf(sym_out[i]), cimagf(sym_out[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,"npfb=%u;\n",npfb);
fprintf(fid,"num_symbols=%u;\n",num_symbols);
for (i=0; i<ht_len; i++)
fprintf(fid,"ht(%3u) = %12.5f;\n", i+1, ht[i]);
for (i=0; i<hc_len; i++)
fprintf(fid,"hc(%3u) = %12.5f + j*%12.8f;\n", i+1, crealf(hc[i]), cimagf(hc[i]));
for (i=0; i<hp_len; i++)
fprintf(fid,"hp(%3u) = %12.5f + j*%12.8f;\n", i+1, crealf(hp[i]), cimagf(hp[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; i++)
fprintf(fid,"y(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(y[i]), cimagf(y[i]));
for (i=0; i<num_samples_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,"sym_out(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(sym_out[i]), cimagf(sym_out[i]));
#if 0
fprintf(fid,"\n\n");
fprintf(fid,"%% scale QPSK in-phase by sqrt(2)\n");
fprintf(fid,"z = z*sqrt(2);\n");
fprintf(fid,"\n\n");
fprintf(fid,"tz = [0:length(z)-1]/k;\n");
fprintf(fid,"iz = 1:k:length(z);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(tz, real(z), '-',...\n");
fprintf(fid," tz(iz), real(z(iz)),'or');\n");
fprintf(fid,"xlabel('Time');\n");
fprintf(fid,"ylabel('Output Signal (real)');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"legend('output time series','optimim timing',1);\n");
#endif
// compute composite response
fprintf(fid,"hd = real(conv(ht/k,conv(hc,hp)));\n");
// plot frequency response
fprintf(fid,"nfft = 1024;\n");
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"Ht = 20*log10(abs(fftshift(fft(ht/k,nfft))));\n");
fprintf(fid,"Hc = 20*log10(abs(fftshift(fft(hc, nfft))));\n");
fprintf(fid,"Hp = 20*log10(abs(fftshift(fft(hp, nfft))));\n");
fprintf(fid,"Hd = 20*log10(abs(fftshift(fft(hd, nfft))));\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(f,Ht, f,Hc, f,Hp, f,Hd,'-k','LineWidth',2);\n");
fprintf(fid,"axis([-0.5 0.5 -20 10]);\n");
fprintf(fid,"axis([-0.5 0.5 -6 6 ]);\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"legend('transmit','channel','equalizer','composite','location','northeast');\n");
fprintf(fid,"i0 = [1:round(length(sym_out)/2)];\n");
fprintf(fid,"i1 = [round(length(sym_out)/2):length(sym_out)];\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(real(sym_out(i0)),imag(sym_out(i0)),'x','MarkerSize',4,'Color',[0.60 0.60 0.60],...\n");
fprintf(fid," real(sym_out(i1)),imag(sym_out(i1)),'x','MarkerSize',4,'Color',[0.00 0.25 0.50]);\n");
fprintf(fid,"axis square;\n");
fprintf(fid,"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 50%%'],['last 50%%'],'location','northeast');\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
// clean it up
printf("done.\n");
return 0;
}