// demodulate array of samples (coherent)
void cpfskdem_demodulate_coherent(cpfskdem _q,
float complex _y,
unsigned int * _s,
unsigned int * _nw)
{
// clear output counter
*_nw = 0;
// push input sample through filter
firfilt_crcf_push(_q->data.coherent.mf, _y);
#if DEBUG_CPFSKDEM
// compute output sample
float complex zp;
firfilt_crcf_execute(_q->data.coherent.mf, &zp);
printf("y(end+1) = %12.8f + 1i*%12.8f;\n", crealf(_y), cimagf(_y));
printf("z(end+1) = %12.8f + 1i*%12.8f;\n", crealf(zp), cimagf(zp));
#endif
// decimate output
_q->counter++;
if ( (_q->counter % _q->k)==0 ) {
// reset sample counter
_q->counter = 0;
// compute output sample
float complex z;
firfilt_crcf_execute(_q->data.coherent.mf, &z);
// compute instantaneous frequency scaled by modulation index
// TODO: pre-compute scaling factor
float phi_hat = cargf(conjf(_q->z_prime) * z) / (_q->h * M_PI);
// estimate transmitted symbol
float v = (phi_hat + (_q->M-1.0))*0.5f;
unsigned int sym_out = ((int) roundf(v)) % _q->M;
// save current point
_q->z_prime = z;
#if 1
// print result to screen
printf(" %3u : %12.8f + j%12.8f, <f=%8.4f : %8.4f> (%1u)\n",
_q->index++, crealf(z), cimagf(z), phi_hat, v, sym_out);
#endif
// save output
*_s = sym_out;
*_nw = 1;
}
}
// demodulate array of samples (coherent)
unsigned int cpfskdem_demodulate_coherent(cpfskdem _q,
float complex * _y)
{
unsigned int i;
unsigned int sym_out = 0;
for (i=0; i<_q->k; i++) {
// push input sample through filter
firfilt_crcf_push(_q->data.coherent.mf, _y[i]);
#if DEBUG_CPFSKDEM
// compute output sample
float complex zp;
firfilt_crcf_execute(_q->data.coherent.mf, &zp);
printf("y(end+1) = %12.8f + 1i*%12.8f;\n", crealf(_y), cimagf(_y));
printf("z(end+1) = %12.8f + 1i*%12.8f;\n", crealf(zp), cimagf(zp));
#endif
// decimate output
if ( i == 0 ) {
// compute output sample
float complex z;
firfilt_crcf_execute(_q->data.coherent.mf, &z);
// compute instantaneous frequency scaled by modulation index
// TODO: pre-compute scaling factor
float phi_hat = cargf(conjf(_q->z_prime) * z) / (_q->h * M_PI);
// estimate transmitted symbol
float v = (phi_hat + (_q->M-1.0))*0.5f;
sym_out = ((int) roundf(v)) % _q->M;
// save current point
_q->z_prime = z;
#if DEBUG_CPFSKDEM
// print result to screen
printf(" %3u : %12.8f + j%12.8f, <f=%8.4f : %8.4f> (%1u)\n",
_q->index++, crealf(z), cimagf(z), phi_hat, v, sym_out);
#endif
}
}
return sym_out;
}
// Helper function to keep code base small
void firfilt_crcf_bench(struct rusage *_start,
struct rusage *_finish,
unsigned long int *_num_iterations,
unsigned int _n)
{
// adjust number of iterations:
// cycles/trial ~ 107 + 4.3*_n
*_num_iterations *= 1000;
*_num_iterations /= (unsigned int)(107+4.3*_n);
// generate coefficients
float h[_n];
unsigned long int i;
for (i=0; i<_n; i++)
h[i] = randnf();
// create filter object
firfilt_crcf f = firfilt_crcf_create(h,_n);
// generate input vector
float complex x[4];
for (i=0; i<4; i++)
x[i] = randnf() + _Complex_I*randnf();
// output vector
float complex y[4];
// start trials
getrusage(RUSAGE_SELF, _start);
for (i=0; i<(*_num_iterations); i++) {
firfilt_crcf_push(f, x[0]); firfilt_crcf_execute(f, &y[0]);
firfilt_crcf_push(f, x[1]); firfilt_crcf_execute(f, &y[1]);
firfilt_crcf_push(f, x[2]); firfilt_crcf_execute(f, &y[2]);
firfilt_crcf_push(f, x[3]); firfilt_crcf_execute(f, &y[3]);
}
getrusage(RUSAGE_SELF, _finish);
*_num_iterations *= 4;
firfilt_crcf_destroy(f);
}
int main(int argc, char*argv[])
{
// options
unsigned int bps = 1; // number of bits/symbol
float h = 0.5f; // modulation index (h=1/2 for MSK)
unsigned int k = 4; // filter samples/symbol
unsigned int m = 3; // filter delay (symbols)
float beta = 0.35f; // GMSK bandwidth-time factor
unsigned int num_symbols = 20; // number of data symbols
float SNRdB = 40.0f; // signal-to-noise ratio [dB]
float cfo = 0.0f; // carrier frequency offset
float cpo = 0.0f; // carrier phase offset
float tau = 0.0f; // fractional symbol timing offset
int filter_type = LIQUID_CPFSK_SQUARE;
int dopt;
while ((dopt = getopt(argc,argv,"ht:p:H:k:m:b:n:s:F:P:T:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
case 't':
if (strcmp(optarg,"square")==0) {
filter_type = LIQUID_CPFSK_SQUARE;
} else if (strcmp(optarg,"rcos-full")==0) {
filter_type = LIQUID_CPFSK_RCOS_FULL;
} else if (strcmp(optarg,"rcos-half")==0) {
filter_type = LIQUID_CPFSK_RCOS_PARTIAL;
} else if (strcmp(optarg,"gmsk")==0) {
filter_type = LIQUID_CPFSK_GMSK;
} else {
fprintf(stderr,"error: %s, unknown filter type '%s'\n", argv[0], optarg);
exit(1);
}
break;
case 'p': bps = atoi(optarg); break;
case 'H': h = atof(optarg); break;
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;
case 's': SNRdB = atof(optarg); break;
case 'F': cfo = atof(optarg); break;
case 'P': cpo = atof(optarg); break;
case 'T': tau = atof(optarg); break;
default:
exit(1);
}
}
unsigned int i;
// derived values
unsigned int num_samples = k*num_symbols;
unsigned int M = 1 << bps; // constellation size
float nstd = powf(10.0f, -SNRdB/20.0f);
// arrays
unsigned int sym_in[num_symbols]; // input symbols
float complex x[num_samples]; // transmitted signal
float complex y[num_samples]; // received signal
unsigned int sym_out[num_symbols]; // output symbols
// create modem objects
cpfskmod mod = cpfskmod_create(bps, h, k, m, beta, filter_type);
cpfskdem dem = cpfskdem_create(bps, h, k, m, beta, filter_type);
// print modulator
cpfskmod_print(mod);
// generate message signal
for (i=0; i<num_symbols; i++)
sym_in[i] = rand() % M;
// modulate signal
for (i=0; i<num_symbols; i++)
cpfskmod_modulate(mod, sym_in[i], &x[k*i]);
// push through channel
float sample_offset = -tau * k;
int sample_delay = (int)roundf(sample_offset);
float dt = sample_offset - (float)sample_delay;
printf("symbol delay : %f\n", tau);
printf("sample delay : %f = %d + %f\n", sample_offset, sample_delay, dt);
firfilt_crcf fchannel = firfilt_crcf_create_kaiser(8*k+2*sample_delay+1, 0.45f, 40.0f, dt);
for (i=0; i<num_samples; i++) {
// push through channel delay
firfilt_crcf_push(fchannel, x[i]);
firfilt_crcf_execute(fchannel, &y[i]);
// add carrier frequency/phase offset
y[i] *= cexpf(_Complex_I*(cfo*i + cpo));
// add noise
y[i] += nstd*(randnf() + _Complex_I*randnf())*M_SQRT1_2;
}
firfilt_crcf_destroy(fchannel);
// demodulate signal
unsigned int nw=0;
cpfskdem_demodulate(dem, y, num_samples, sym_out, &nw);
printf("demodulator wrote %u symbols\n", nw);
// destroy modem objects
cpfskmod_destroy(mod);
cpfskdem_destroy(dem);
// compute power spectral density of transmitted signal
unsigned int nfft = 1024;
float psd[nfft];
spgramcf periodogram = spgramcf_create_kaiser(nfft, nfft/2, 8.0f);
spgramcf_estimate_psd(periodogram, x, num_samples, psd);
spgramcf_destroy(periodogram);
//
// 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,"k = %u;\n", k);
fprintf(fid,"h = %f;\n", h);
fprintf(fid,"num_symbols = %u;\n", num_symbols);
fprintf(fid,"num_samples = %u;\n", num_samples);
fprintf(fid,"nfft = %u;\n", nfft);
fprintf(fid,"delay = %u; %% receive filter delay\n", m);
fprintf(fid,"x = zeros(1,num_samples);\n");
fprintf(fid,"y = zeros(1,num_samples);\n");
for (i=0; i<num_samples; i++) {
fprintf(fid,"x(%4u) = %12.8f + j*%12.8f;\n", i+1, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"y(%4u) = %12.8f + j*%12.8f;\n", i+1, crealf(y[i]), cimagf(y[i]));
}
// save power spectral density
fprintf(fid,"psd = zeros(1,nfft);\n");
for (i=0; i<nfft; i++)
fprintf(fid,"psd(%4u) = %12.8f;\n", i+1, psd[i]);
fprintf(fid,"t=[0:(num_samples-1)]/k;\n");
fprintf(fid,"i = 1:k:num_samples;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(3,4,1:3);\n");
fprintf(fid," plot(t,real(x),'-', t(i),real(x(i)),'ob',...\n");
fprintf(fid," t,imag(x),'-', t(i),imag(x(i)),'og');\n");
fprintf(fid," axis([0 num_symbols -1.2 1.2]);\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('x(t)');\n");
fprintf(fid," grid on;\n");
fprintf(fid,"subplot(3,4,5:7);\n");
fprintf(fid," plot(t,real(y),'-', t(i),real(y(i)),'ob',...\n");
fprintf(fid," t,imag(y),'-', t(i),imag(y(i)),'og');\n");
fprintf(fid," axis([0 num_symbols -1.2 1.2]);\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('y(t)');\n");
fprintf(fid," grid on;\n");
// plot I/Q constellations
fprintf(fid,"subplot(3,4,4);\n");
fprintf(fid," plot(real(x),imag(x),'-',real(x(i)),imag(x(i)),'rs','MarkerSize',4);\n");
fprintf(fid," xlabel('I');\n");
fprintf(fid," ylabel('Q');\n");
fprintf(fid," axis([-1 1 -1 1]*1.2);\n");
fprintf(fid," axis square;\n");
fprintf(fid," grid on;\n");
fprintf(fid,"subplot(3,4,8);\n");
fprintf(fid," plot(real(y),imag(y),'-',real(y(i)),imag(y(i)),'rs','MarkerSize',4);\n");
fprintf(fid," xlabel('I');\n");
fprintf(fid," ylabel('Q');\n");
fprintf(fid," axis([-1 1 -1 1]*1.2);\n");
fprintf(fid," axis square;\n");
fprintf(fid," grid on;\n");
// plot PSD
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"subplot(3,4,9:12);\n");
fprintf(fid," plot(f,psd,'LineWidth',1.5);\n");
fprintf(fid," axis([-0.5 0.5 -60 20]);\n");
fprintf(fid," xlabel('Normalized Frequency [f/F_s]');\n");
fprintf(fid," ylabel('PSD [dB]');\n");
fprintf(fid," grid on;\n");
fclose(fid);
printf("results written to '%s'\n", OUTPUT_FILENAME);
return 0;
}
int main() {
// options
unsigned int num_channels=4; // number of channels
unsigned int p=3; // filter length (symbols)
unsigned int num_symbols=6; // number of symbols
// derived values
unsigned int num_samples = num_channels * num_symbols;
unsigned int i;
unsigned int j;
// generate synthesis filter
// NOTE : these coefficients can be random; the purpose of this
// exercise is to demonstrate mathematical equivalence
unsigned int h_len = p*num_channels;
float h[h_len];
for (i=0; i<h_len; i++) h[i] = randnf();
// generate analysis filter
unsigned int g_len = p*num_channels;
float g[g_len];
for (i=0; i<g_len; i++)
g[i] = h[g_len-i-1];
// create synthesis/analysis filter objects
firfilt_crcf fs = firfilt_crcf_create(h, h_len);
firfilt_crcf fa = firfilt_crcf_create(g, g_len);
// create synthesis/analysis filterbank channelizer objects
firpfbch_crcf qs = firpfbch_crcf_create(LIQUID_SYNTHESIZER, num_channels, p, h);
firpfbch_crcf qa = firpfbch_crcf_create(LIQUID_ANALYZER, num_channels, p, g);
float complex x[num_samples]; // random input (noise)
float complex Y0[num_symbols][num_channels]; // channelized output (filterbank)
float complex Y1[num_symbols][num_channels]; // channelized output
float complex z0[num_samples]; // time-domain output (filterbank)
float complex z1[num_samples]; // time-domain output
// generate input sequence (complex noise)
for (i=0; i<num_samples; i++)
x[i] = randnf() * cexpf(_Complex_I*randf()*2*M_PI);
//
// ANALYZERS
//
//
// run analysis filter bank
//
for (i=0; i<num_symbols; i++)
firpfbch_crcf_analyzer_execute(qa, &x[i*num_channels], &Y0[i][0]);
//
// run traditional down-converter (inefficient)
//
float dphi; // carrier frequency
unsigned int n=0;
for (i=0; i<num_channels; i++) {
// reset filter
firfilt_crcf_clear(fa);
// set center frequency
dphi = 2.0f * M_PI * (float)i / (float)num_channels;
// reset symbol counter
n=0;
for (j=0; j<num_samples; j++) {
// push down-converted sample into filter
firfilt_crcf_push(fa, x[j]*cexpf(-_Complex_I*j*dphi));
// compute output at the appropriate sample time
assert(n<num_symbols);
if ( ((j+1)%num_channels)==0 ) {
firfilt_crcf_execute(fa, &Y1[n][i]);
n++;
}
}
assert(n==num_symbols);
}
//
// SYNTHESIZERS
//
//
// run synthesis filter bank
//
for (i=0; i<num_symbols; i++)
firpfbch_crcf_synthesizer_execute(qs, &Y0[i][0], &z0[i*num_channels]);
//
// run traditional up-converter (inefficient)
//
// clear output array
for (i=0; i<num_samples; i++)
z1[i] = 0.0f;
float complex y_hat;
for (i=0; i<num_channels; i++) {
// reset filter
firfilt_crcf_clear(fs);
// set center frequency
dphi = 2.0f * M_PI * (float)i / (float)num_channels;
// reset input symbol counter
n=0;
for (j=0; j<num_samples; j++) {
// interpolate sequence
if ( (j%num_channels)==0 ) {
assert(n<num_symbols);
firfilt_crcf_push(fs, Y1[n][i]);
n++;
} else {
firfilt_crcf_push(fs, 0);
}
firfilt_crcf_execute(fs, &y_hat);
// accumulate up-converted sample
z1[j] += y_hat * cexpf(_Complex_I*j*dphi);
}
assert(n==num_symbols);
}
// destroy objects
firfilt_crcf_destroy(fs);
firfilt_crcf_destroy(fa);
firpfbch_crcf_destroy(qs);
firpfbch_crcf_destroy(qa);
//
// RESULTS
//
//
// analyzers
//
// print filterbank channelizer
printf("\n");
printf("filterbank channelizer:\n");
for (i=0; i<num_symbols; i++) {
printf("%3u: ", i);
for (j=0; j<num_channels; j++) {
printf(" %8.5f+j%8.5f, ", crealf(Y0[i][j]), cimagf(Y0[i][j]));
}
printf("\n");
}
// print traditional channelizer
printf("\n");
printf("traditional channelizer:\n");
for (i=0; i<num_symbols; i++) {
printf("%3u: ", i);
for (j=0; j<num_channels; j++) {
printf(" %8.5f+j%8.5f, ", crealf(Y1[i][j]), cimagf(Y1[i][j]));
}
printf("\n");
}
float mse_analyzer[num_channels];
float complex d;
for (i=0; i<num_channels; i++) {
mse_analyzer[i] = 0.0f;
for (j=0; j<num_symbols; j++) {
d = Y0[j][i] - Y1[j][i];
mse_analyzer[i] += crealf(d*conjf(d));
}
mse_analyzer[i] /= num_symbols;
}
printf("\n");
printf("rmse: ");
for (i=0; i<num_channels; i++)
printf("%12.4e ", sqrt(mse_analyzer[i]));
printf("\n");
//
// synthesizers
//
printf("\n");
printf("output: filterbank: traditional:\n");
for (i=0; i<num_samples; i++) {
printf("%3u: %10.5f+%10.5fj %10.5f+%10.5fj\n",
i,
crealf(z0[i]), cimagf(z0[i]),
crealf(z1[i]), cimagf(z1[i]));
}
float mse_synthesizer = 0.0f;
for (i=0; i<num_samples; i++) {
d = z0[i] - z1[i];
mse_synthesizer += crealf(d*conjf(d));
}
mse_synthesizer /= num_samples;
printf("\n");
printf("rmse: %12.4e\n", sqrtf(mse_synthesizer));
//
// EXPORT DATA TO 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,"num_channels=%u;\n", num_channels);
fprintf(fid,"num_symbols=%u;\n", num_symbols);
fprintf(fid,"num_samples = num_channels*num_symbols;\n");
fprintf(fid,"x = zeros(1,num_samples);\n");
fprintf(fid,"y0 = zeros(num_symbols,num_channels);\n");
fprintf(fid,"y1 = zeros(num_symbols,num_channels);\n");
fprintf(fid,"z0 = zeros(1,num_samples);\n");
fprintf(fid,"z1 = zeros(1,num_samples);\n");
// input
for (i=0; i<num_samples; i++)
fprintf(fid,"x(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(x[i]), cimag(x[i]));
// analysis
for (i=0; i<num_symbols; i++) {
for (j=0; j<num_channels; j++) {
fprintf(fid,"y0(%4u,%4u) = %12.4e + j*%12.4e;\n", i+1, j+1, crealf(Y0[i][j]), cimag(Y0[i][j]));
fprintf(fid,"y1(%4u,%4u) = %12.4e + j*%12.4e;\n", i+1, j+1, crealf(Y1[i][j]), cimag(Y1[i][j]));
}
}
// synthesis
for (i=0; i<num_samples; i++) {
fprintf(fid,"z0(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(z0[i]), cimag(z0[i]));
fprintf(fid,"z1(%4u) = %12.4e + j*%12.4e;\n", i+1, crealf(z1[i]), cimag(z1[i]));
}
fprintf(fid,"z0 = z0 / num_channels;\n");
fprintf(fid,"z1 = z1 / num_channels;\n");
// plot results
fprintf(fid,"\n\n");
fprintf(fid,"ts = 0:(num_symbols-1);\n");
fprintf(fid,"for i=1:num_channels,\n");
fprintf(fid,"figure;\n");
fprintf(fid,"title(['channel ' num2str(i)]);\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid," plot(ts,real(y0(:,i)),'-x', ts,real(y1(:,i)),'s');\n");
//fprintf(fid," axis([0 (num_symbols-1) -2 2]);\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid," plot(ts,imag(y0(:,i)),'-x', ts,imag(y1(:,i)),'s');\n");
//fprintf(fid," axis([0 (num_symbols-1) -2 2]);\n");
fprintf(fid,"end;\n");
fprintf(fid,"t = 0:(num_samples-1);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"title('composite');\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid," plot(t,real(z0),'-x', t,real(z1),'s');\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid," plot(t,imag(z0),'-x', t,imag(z1),'s');\n");
fclose(fid);
printf("results written to '%s'\n", OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
int main() {
// options
unsigned int num_channels=4; // number of channels
unsigned int m=5; // filter delay
unsigned int num_symbols=12; // number of symbols
// derived values
unsigned int num_samples = num_channels * num_symbols;
unsigned int i;
unsigned int j;
// generate filter
// NOTE : these coefficients can be random; the purpose of this
// exercise is to demonstrate mathematical equivalence
unsigned int h_len = 2*m*num_channels;
float h[h_len];
for (i=0; i<h_len; i++) h[i] = randnf();
//for (i=0; i<h_len; i++) h[i] = 0.1f*i;
//for (i=0; i<h_len; i++) h[i] = (i<=m) ? 1.0f : 0.0f;
//for (i=0; i<h_len; i++) h[i] = 1.0f;
// create filterbank manually
dotprod_crcf dp[num_channels]; // vector dot products
windowcf w[num_channels]; // window buffers
#if DEBUG
// print coefficients
printf("h_prototype:\n");
for (i=0; i<h_len; i++)
printf(" h[%3u] = %12.8f\n", i, h[i]);
#endif
// create objects
unsigned int h_sub_len = 2*m;
float h_sub[h_sub_len];
for (i=0; i<num_channels; i++) {
// sub-sample prototype filter, loading coefficients in
// reverse order
#if 0
for (j=0; j<h_sub_len; j++)
h_sub[j] = h[j*num_channels+i];
#else
for (j=0; j<h_sub_len; j++)
h_sub[h_sub_len-j-1] = h[j*num_channels+i];
#endif
// create window buffer and dotprod objects
dp[i] = dotprod_crcf_create(h_sub, h_sub_len);
w[i] = windowcf_create(h_sub_len);
#if DEBUG
printf("h_sub[%u] : \n", i);
for (j=0; j<h_sub_len; j++)
printf(" h[%3u] = %12.8f\n", j, h_sub[j]);
#endif
}
// generate DFT object
float complex x[num_channels]; // time-domain buffer
float complex X[num_channels]; // freq-domain buffer
#if 0
fftplan fft = fft_create_plan(num_channels, X, x, LIQUID_FFT_BACKWARD, 0);
#else
fftplan fft = fft_create_plan(num_channels, X, x, LIQUID_FFT_FORWARD, 0);
#endif
// generate filter object
firfilt_crcf f = firfilt_crcf_create(h, h_len);
float complex y[num_samples]; // time-domain input
float complex Y0[num_symbols][num_channels]; // channelized output
float complex Y1[num_symbols][num_channels]; // channelized output
// generate input sequence (complex noise)
for (i=0; i<num_samples; i++)
y[i] = randnf() * cexpf(_Complex_I*randf()*2*M_PI);
//
// run analysis filter bank
//
#if 0
unsigned int filter_index = 0;
#else
unsigned int filter_index = num_channels-1;
#endif
float complex y_hat; // input sample
float complex * r; // read pointer
for (i=0; i<num_symbols; i++) {
// load buffers
for (j=0; j<num_channels; j++) {
// grab sample
y_hat = y[i*num_channels + j];
// push sample into buffer at filter index
windowcf_push(w[filter_index], y_hat);
// decrement filter index
filter_index = (filter_index + num_channels - 1) % num_channels;
//filter_index = (filter_index + 1) % num_channels;
}
// execute filter outputs, reversing order of output (not
// sure why this is necessary)
for (j=0; j<num_channels; j++) {
windowcf_read(w[j], &r);
dotprod_crcf_execute(dp[j], r, &X[num_channels-j-1]);
}
// execute DFT, store result in buffer 'x'
fft_execute(fft);
// move to output array
for (j=0; j<num_channels; j++)
Y0[i][j] = x[j];
}
//
// run traditional down-converter (inefficient)
//
float dphi; // carrier frequency
unsigned int n=0;
for (i=0; i<num_channels; i++) {
// reset filter
firfilt_crcf_reset(f);
// set center frequency
dphi = 2.0f * M_PI * (float)i / (float)num_channels;
// reset symbol counter
n=0;
for (j=0; j<num_samples; j++) {
// push down-converted sample into filter
firfilt_crcf_push(f, y[j]*cexpf(-_Complex_I*j*dphi));
// compute output at the appropriate sample time
assert(n<num_symbols);
if ( ((j+1)%num_channels)==0 ) {
firfilt_crcf_execute(f, &Y1[n][i]);
n++;
}
}
assert(n==num_symbols);
}
// destroy objects
for (i=0; i<num_channels; i++) {
dotprod_crcf_destroy(dp[i]);
windowcf_destroy(w[i]);
}
fft_destroy_plan(fft);
firfilt_crcf_destroy(f);
// print filterbank channelizer
printf("\n");
printf("filterbank channelizer:\n");
for (i=0; i<num_symbols; i++) {
printf("%3u: ", i);
for (j=0; j<num_channels; j++) {
printf(" %8.5f+j%8.5f, ", crealf(Y0[i][j]), cimagf(Y0[i][j]));
}
printf("\n");
}
// print traditional channelizer
printf("\n");
printf("traditional channelizer:\n");
for (i=0; i<num_symbols; i++) {
printf("%3u: ", i);
for (j=0; j<num_channels; j++) {
printf(" %8.5f+j%8.5f, ", crealf(Y1[i][j]), cimagf(Y1[i][j]));
}
printf("\n");
}
//
// compare results
//
float mse[num_channels];
float complex d;
for (i=0; i<num_channels; i++) {
mse[i] = 0.0f;
for (j=0; j<num_symbols; j++) {
d = Y0[j][i] - Y1[j][i];
mse[i] += crealf(d*conjf(d));
}
mse[i] /= num_symbols;
}
printf("\n");
printf("rmse: ");
for (i=0; i<num_channels; i++)
printf("%12.4e ", sqrt(mse[i]));
printf("\n");
printf("done.\n");
return 0;
}
int main(int argc, char*argv[])
{
// options
unsigned int sequence_len = 80; // number of sync symbols
unsigned int k = 2; // samples/symbol
unsigned int m = 7; // filter delay [symbols]
float beta = 0.3f; // excess bandwidth factor
int ftype = LIQUID_FIRFILT_ARKAISER;
float gamma = 10.0f; // channel gain
float tau = -0.3f; // fractional sample timing offset
float dphi = -0.01f; // carrier frequency offset
float phi = 0.5f; // carrier phase offset
float SNRdB = 20.0f; // signal-to-noise ratio [dB]
float threshold = 0.5f; // detection threshold
int dopt;
while ((dopt = getopt(argc,argv,"hn:k:m:b:F:T:S:t:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
case 'n': sequence_len = atoi(optarg); break;
case 'k': k = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': beta = atof(optarg); break;
case 'F': dphi = atof(optarg); break;
case 'T': tau = atof(optarg); break;
case 'S': SNRdB = atof(optarg); break;
case 't': threshold = atof(optarg); break;
default:
exit(1);
}
}
unsigned int i;
// validate input
if (tau < -0.5f || tau > 0.5f) {
fprintf(stderr,"error: %s, fractional sample offset must be in [-0.5,0.5]\n", argv[0]);
exit(1);
}
// generate synchronization sequence (QPSK symbols)
float complex sequence[sequence_len];
for (i=0; i<sequence_len; i++) {
sequence[i] = (rand() % 2 ? 1.0f : -1.0f) * M_SQRT1_2 +
(rand() % 2 ? 1.0f : -1.0f) * M_SQRT1_2 * _Complex_I;
}
//
float tau_hat = 0.0f;
float gamma_hat = 0.0f;
float dphi_hat = 0.0f;
float phi_hat = 0.0f;
int frame_detected = 0;
// create detector
qdetector_cccf q = qdetector_cccf_create_linear(sequence, sequence_len, ftype, k, m, beta);
qdetector_cccf_set_threshold(q, threshold);
qdetector_cccf_print(q);
//
unsigned int seq_len = qdetector_cccf_get_seq_len(q);
unsigned int buf_len = qdetector_cccf_get_buf_len(q);
unsigned int num_samples = 2*buf_len; // double buffer length to ensure detection
unsigned int num_symbols = buf_len;
// arrays
float complex y[num_samples]; // received signal
float complex syms_rx[num_symbols]; // recovered symbols
// get pointer to sequence and generate full sequence
float complex * v = (float complex*) qdetector_cccf_get_sequence(q);
unsigned int filter_delay = 15;
firfilt_crcf filter = firfilt_crcf_create_kaiser(2*filter_delay+1, 0.4f, 60.0f, -tau);
float nstd = 0.1f;
for (i=0; i<num_samples; i++) {
// add delay
firfilt_crcf_push(filter, i < seq_len ? v[i] : 0);
firfilt_crcf_execute(filter, &y[i]);
// channel gain
y[i] *= gamma;
// carrier offset
y[i] *= cexpf(_Complex_I*(dphi*i + phi));
// noise
y[i] += nstd*(randnf() + _Complex_I*randnf())*M_SQRT1_2;
}
firfilt_crcf_destroy(filter);
// run detection on sequence
for (i=0; i<num_samples; i++) {
v = qdetector_cccf_execute(q,y[i]);
if (v != NULL) {
printf("\nframe detected!\n");
frame_detected = 1;
// get statistics
tau_hat = qdetector_cccf_get_tau(q);
gamma_hat = qdetector_cccf_get_gamma(q);
dphi_hat = qdetector_cccf_get_dphi(q);
phi_hat = qdetector_cccf_get_phi(q);
break;
}
}
unsigned int num_syms_rx = 0; // output symbol counter
unsigned int counter = 0; // decimation counter
if (frame_detected) {
// recover symbols
firfilt_crcf mf = firfilt_crcf_create_rnyquist(ftype, k, m, beta, tau_hat);
firfilt_crcf_set_scale(mf, 1.0f / (float)(k*gamma_hat));
nco_crcf nco = nco_crcf_create(LIQUID_VCO);
nco_crcf_set_frequency(nco, dphi_hat);
nco_crcf_set_phase (nco, phi_hat);
for (i=0; i<buf_len; i++) {
//
float complex sample;
nco_crcf_mix_down(nco, v[i], &sample);
nco_crcf_step(nco);
// apply decimator
firfilt_crcf_push(mf, sample);
counter++;
if (counter == k-1)
firfilt_crcf_execute(mf, &syms_rx[num_syms_rx++]);
counter %= k;
}
nco_crcf_destroy(nco);
firfilt_crcf_destroy(mf);
}
// destroy objects
qdetector_cccf_destroy(q);
// print results
printf("\n");
printf("frame detected : %s\n", frame_detected ? "yes" : "no");
printf(" gamma hat : %8.3f, actual=%8.3f (error=%8.3f)\n", gamma_hat, gamma, gamma_hat - gamma);
printf(" tau hat : %8.3f, actual=%8.3f (error=%8.3f) samples\n", tau_hat, tau, tau_hat - tau );
printf(" dphi hat : %8.5f, actual=%8.5f (error=%8.5f) rad/sample\n", dphi_hat, dphi, dphi_hat - dphi );
printf(" phi hat : %8.5f, actual=%8.5f (error=%8.5f) radians\n", phi_hat, phi, phi_hat - phi );
printf(" symbols rx : %u\n", num_syms_rx);
printf("\n");
//
// 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,"sequence_len= %u;\n", sequence_len);
fprintf(fid,"num_samples = %u;\n", num_samples);
fprintf(fid,"y = zeros(1,num_samples);\n");
for (i=0; i<num_samples; i++)
fprintf(fid,"y(%4u) = %12.8f + j*%12.8f;\n", i+1, crealf(y[i]), cimagf(y[i]));
fprintf(fid,"num_syms_rx = %u;\n", num_syms_rx);
fprintf(fid,"syms_rx = zeros(1,num_syms_rx);\n");
for (i=0; i<num_syms_rx; i++)
fprintf(fid,"syms_rx(%4u) = %12.8f + j*%12.8f;\n", i+1, crealf(syms_rx[i]), cimagf(syms_rx[i]));
fprintf(fid,"t=[0:(num_samples-1)];\n");
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(4,1,1);\n");
fprintf(fid," plot(t,real(y), t,imag(y));\n");
fprintf(fid," grid on;\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('received signal');\n");
fprintf(fid,"subplot(4,1,2:4);\n");
fprintf(fid," plot(real(syms_rx), imag(syms_rx), 'x');\n");
fprintf(fid," axis([-1 1 -1 1]*1.5);\n");
fprintf(fid," axis square;\n");
fprintf(fid," grid on;\n");
fprintf(fid," xlabel('real');\n");
fprintf(fid," ylabel('imag');\n");
fclose(fid);
printf("results written to '%s'\n", OUTPUT_FILENAME);
return 0;
}
int main(int argc, char*argv[]) {
// options
unsigned int k = 8; // filter samples/symbol
unsigned int bps= 1; // number of bits/symbol
float h = 0.5f; // modulation index (h=1/2 for MSK)
unsigned int num_data_symbols = 20; // number of data symbols
float SNRdB = 80.0f; // signal-to-noise ratio [dB]
float cfo = 0.0f; // carrier frequency offset
float cpo = 0.0f; // carrier phase offset
float tau = 0.0f; // fractional symbol offset
enum {
TXFILT_SQUARE=0,
TXFILT_RCOS_FULL,
TXFILT_RCOS_HALF,
TXFILT_GMSK,
} tx_filter_type = TXFILT_SQUARE;
float gmsk_bt = 0.35f; // GMSK bandwidth-time factor
int dopt;
while ((dopt = getopt(argc,argv,"ht:k:b:H:B:n:s:F:P:T:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
case 't':
if (strcmp(optarg,"square")==0) {
tx_filter_type = TXFILT_SQUARE;
} else if (strcmp(optarg,"rcos-full")==0) {
tx_filter_type = TXFILT_RCOS_FULL;
} else if (strcmp(optarg,"rcos-half")==0) {
tx_filter_type = TXFILT_RCOS_HALF;
} else if (strcmp(optarg,"gmsk")==0) {
tx_filter_type = TXFILT_GMSK;
} else {
fprintf(stderr,"error: %s, unknown filter type '%s'\n", argv[0], optarg);
exit(1);
}
break;
case 'k': k = atoi(optarg); break;
case 'b': bps = atoi(optarg); break;
case 'H': h = atof(optarg); break;
case 'B': gmsk_bt = atof(optarg); break;
case 'n': num_data_symbols = atoi(optarg); break;
case 's': SNRdB = atof(optarg); break;
case 'F': cfo = atof(optarg); break;
case 'P': cpo = atof(optarg); break;
case 'T': tau = atof(optarg); break;
default:
exit(1);
}
}
unsigned int i;
// derived values
unsigned int num_symbols = num_data_symbols;
unsigned int num_samples = k*num_symbols;
unsigned int M = 1 << bps; // constellation size
float nstd = powf(10.0f, -SNRdB/20.0f);
// arrays
unsigned char sym_in[num_symbols]; // input symbols
float phi[num_samples]; // transmitted phase
float complex x[num_samples]; // transmitted signal
float complex y[num_samples]; // received signal
float complex z[num_samples]; // output...
//unsigned char sym_out[num_symbols]; // output symbols
unsigned int ht_len = 0;
unsigned int tx_delay = 0;
float * ht = NULL;
switch (tx_filter_type) {
case TXFILT_SQUARE:
// regular MSK
ht_len = k;
tx_delay = 1;
ht = (float*) malloc(ht_len *sizeof(float));
for (i=0; i<ht_len; i++)
ht[i] = h * M_PI / (float)k;
break;
case TXFILT_RCOS_FULL:
// full-response raised-cosine pulse
ht_len = k;
tx_delay = 1;
ht = (float*) malloc(ht_len *sizeof(float));
for (i=0; i<ht_len; i++)
ht[i] = h * M_PI / (float)k * (1.0f - cosf(2.0f*M_PI*i/(float)ht_len));
break;
case TXFILT_RCOS_HALF:
// partial-response raised-cosine pulse
ht_len = 3*k;
tx_delay = 2;
ht = (float*) malloc(ht_len *sizeof(float));
for (i=0; i<ht_len; i++)
ht[i] = 0.0f;
for (i=0; i<2*k; i++)
ht[i+k/2] = h * 0.5f * M_PI / (float)k * (1.0f - cosf(2.0f*M_PI*i/(float)(2*k)));
break;
case TXFILT_GMSK:
ht_len = 2*k*3+1+k;
tx_delay = 4;
ht = (float*) malloc(ht_len *sizeof(float));
for (i=0; i<ht_len; i++)
ht[i] = 0.0f;
liquid_firdes_gmsktx(k,3,gmsk_bt,0.0f,&ht[k/2]);
for (i=0; i<ht_len; i++)
ht[i] *= h * 2.0f / (float)k;
break;
default:
fprintf(stderr,"error: %s, invalid tx filter type\n", argv[0]);
exit(1);
}
for (i=0; i<ht_len; i++)
printf("ht(%3u) = %12.8f;\n", i+1, ht[i]);
firinterp_rrrf interp_tx = firinterp_rrrf_create(k, ht, ht_len);
// generate symbols and interpolate
// phase-accumulating filter (trapezoidal integrator)
float b[2] = {0.5f, 0.5f};
if (tx_filter_type == TXFILT_SQUARE) {
// square filter: rectangular integration with one sample of delay
b[0] = 0.0f;
b[1] = 1.0f;
}
float a[2] = {1.0f, -1.0f};
iirfilt_rrrf integrator = iirfilt_rrrf_create(b,2,a,2);
float theta = 0.0f;
for (i=0; i<num_symbols; i++) {
sym_in[i] = rand() % M;
float v = 2.0f*sym_in[i] - (float)(M-1); // +/-1, +/-3, ... +/-(M-1)
firinterp_rrrf_execute(interp_tx, v, &phi[k*i]);
// accumulate phase
unsigned int j;
for (j=0; j<k; j++) {
iirfilt_rrrf_execute(integrator, phi[i*k+j], &theta);
x[i*k+j] = cexpf(_Complex_I*theta);
}
}
iirfilt_rrrf_destroy(integrator);
// push through channel
for (i=0; i<num_samples; i++) {
// add carrier frequency/phase offset
y[i] = x[i]*cexpf(_Complex_I*(cfo*i + cpo));
// add noise
y[i] += nstd*(randnf() + _Complex_I*randnf())*M_SQRT1_2;
}
// create decimator
unsigned int m = 3;
float bw = 0.0f;
float beta = 0.0f;
firfilt_crcf decim_rx = NULL;
switch (tx_filter_type) {
case TXFILT_SQUARE:
//bw = 0.9f / (float)k;
bw = 0.4f;
decim_rx = firfilt_crcf_create_kaiser(2*k*m+1, bw, 60.0f, 0.0f);
firfilt_crcf_set_scale(decim_rx, 2.0f * bw);
break;
case TXFILT_RCOS_FULL:
if (M==2) {
decim_rx = firfilt_crcf_create_rnyquist(LIQUID_FIRFILT_GMSKRX,k,m,0.5f,0);
firfilt_crcf_set_scale(decim_rx, 1.33f / (float)k);
} else {
decim_rx = firfilt_crcf_create_rnyquist(LIQUID_FIRFILT_GMSKRX,k/2,2*m,0.9f,0);
firfilt_crcf_set_scale(decim_rx, 3.25f / (float)k);
}
break;
case TXFILT_RCOS_HALF:
if (M==2) {
decim_rx = firfilt_crcf_create_rnyquist(LIQUID_FIRFILT_GMSKRX,k,m,0.3f,0);
firfilt_crcf_set_scale(decim_rx, 1.10f / (float)k);
} else {
decim_rx = firfilt_crcf_create_rnyquist(LIQUID_FIRFILT_GMSKRX,k/2,2*m,0.27f,0);
firfilt_crcf_set_scale(decim_rx, 2.90f / (float)k);
}
break;
case TXFILT_GMSK:
bw = 0.5f / (float)k;
// TODO: figure out beta value here
beta = (M == 2) ? 0.8*gmsk_bt : 1.0*gmsk_bt;
decim_rx = firfilt_crcf_create_rnyquist(LIQUID_FIRFILT_GMSKRX,k,m,beta,0);
firfilt_crcf_set_scale(decim_rx, 2.0f * bw);
break;
default:
fprintf(stderr,"error: %s, invalid tx filter type\n", argv[0]);
exit(1);
}
printf("bw = %f\n", bw);
// run receiver
unsigned int n=0;
unsigned int num_errors = 0;
unsigned int num_symbols_checked = 0;
float complex z_prime = 0.0f;
for (i=0; i<num_samples; i++) {
// push through filter
firfilt_crcf_push(decim_rx, y[i]);
firfilt_crcf_execute(decim_rx, &z[i]);
// decimate output
if ( (i%k)==0 ) {
// compute instantaneous frequency scaled by modulation index
float phi_hat = cargf(conjf(z_prime) * z[i]) / (h * M_PI);
// estimate transmitted symbol
float v = (phi_hat + (M-1.0))*0.5f;
unsigned int sym_out = ((int) roundf(v)) % M;
// save current point
z_prime = z[i];
// print result to screen
printf("%3u : %12.8f + j%12.8f, <f=%8.4f : %8.4f> (%1u)",
n, crealf(z[i]), cimagf(z[i]), phi_hat, v, sym_out);
if (n >= m+tx_delay) {
num_errors += (sym_out == sym_in[n-m-tx_delay]) ? 0 : 1;
num_symbols_checked++;
printf(" (%1u)\n", sym_in[n-m-tx_delay]);
} else {
printf("\n");
}
n++;
}
}
// print number of errors
printf("errors : %3u / %3u\n", num_errors, num_symbols_checked);
// destroy objects
firinterp_rrrf_destroy(interp_tx);
firfilt_crcf_destroy(decim_rx);
// compute power spectral density of transmitted signal
unsigned int nfft = 1024;
float psd[nfft];
spgramcf periodogram = spgramcf_create_kaiser(nfft, nfft/2, 8.0f);
spgramcf_estimate_psd(periodogram, y, num_samples, psd);
spgramcf_destroy(periodogram);
//
// 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,"k = %u;\n", k);
fprintf(fid,"h = %f;\n", h);
fprintf(fid,"num_symbols = %u;\n", num_symbols);
fprintf(fid,"num_samples = %u;\n", num_samples);
fprintf(fid,"nfft = %u;\n", nfft);
fprintf(fid,"delay = %u; %% receive filter delay\n", tx_delay);
fprintf(fid,"x = zeros(1,num_samples);\n");
fprintf(fid,"y = zeros(1,num_samples);\n");
fprintf(fid,"z = zeros(1,num_samples);\n");
fprintf(fid,"phi = zeros(1,num_samples);\n");
for (i=0; i<num_samples; i++) {
fprintf(fid,"x(%4u) = %12.8f + j*%12.8f;\n", i+1, crealf(x[i]), cimagf(x[i]));
fprintf(fid,"y(%4u) = %12.8f + j*%12.8f;\n", i+1, crealf(y[i]), cimagf(y[i]));
fprintf(fid,"z(%4u) = %12.8f + j*%12.8f;\n", i+1, crealf(z[i]), cimagf(z[i]));
fprintf(fid,"phi(%4u) = %12.8f;\n", i+1, phi[i]);
}
// save PSD
fprintf(fid,"psd = zeros(1,nfft);\n");
for (i=0; i<nfft; i++)
fprintf(fid,"psd(%4u) = %12.8f;\n", i+1, psd[i]);
fprintf(fid,"t=[0:(num_samples-1)]/k;\n");
fprintf(fid,"i = 1:k:num_samples;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(3,4,1:3);\n");
fprintf(fid," plot(t,real(x),'-', t(i),real(x(i)),'bs','MarkerSize',4,...\n");
fprintf(fid," t,imag(x),'-', t(i),imag(x(i)),'gs','MarkerSize',4);\n");
fprintf(fid," axis([0 num_symbols -1.2 1.2]);\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('x(t)');\n");
fprintf(fid," grid on;\n");
fprintf(fid,"subplot(3,4,5:7);\n");
fprintf(fid," plot(t-delay,real(z),'-', t(i)-delay,real(z(i)),'bs','MarkerSize',4,...\n");
fprintf(fid," t-delay,imag(z),'-', t(i)-delay,imag(z(i)),'gs','MarkerSize',4);\n");
fprintf(fid," axis([0 num_symbols -1.2 1.2]);\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('\"matched\" filter output');\n");
fprintf(fid," grid on;\n");
// plot I/Q constellations
fprintf(fid,"subplot(3,4,4);\n");
fprintf(fid," plot(real(y),imag(y),'-',real(y(i)),imag(y(i)),'rs','MarkerSize',3);\n");
fprintf(fid," xlabel('I');\n");
fprintf(fid," ylabel('Q');\n");
fprintf(fid," axis([-1 1 -1 1]*1.2);\n");
fprintf(fid," axis square;\n");
fprintf(fid," grid on;\n");
fprintf(fid,"subplot(3,4,8);\n");
fprintf(fid," plot(real(z),imag(z),'-',real(z(i)),imag(z(i)),'rs','MarkerSize',3);\n");
fprintf(fid," xlabel('I');\n");
fprintf(fid," ylabel('Q');\n");
fprintf(fid," axis([-1 1 -1 1]*1.2);\n");
fprintf(fid," axis square;\n");
fprintf(fid," grid on;\n");
// plot PSD
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"subplot(3,4,9:12);\n");
fprintf(fid," plot(f,psd,'LineWidth',1.5);\n");
fprintf(fid," axis([-0.5 0.5 -40 20]);\n");
fprintf(fid," xlabel('Normalized Frequency [f/F_s]');\n");
fprintf(fid," ylabel('PSD [dB]');\n");
fprintf(fid," grid on;\n");
#if 0
fprintf(fid,"figure;\n");
fprintf(fid," %% compute instantaneous received frequency\n");
fprintf(fid," freq_rx = arg( conj(z(:)) .* circshift(z(:),-1) )';\n");
fprintf(fid," freq_rx(1:(k*delay)) = 0;\n");
fprintf(fid," freq_rx(end) = 0;\n");
fprintf(fid," %% compute instantaneous tx/rx phase\n");
if (tx_filter_type == TXFILT_SQUARE) {
fprintf(fid," theta_tx = filter([0 1],[1 -1],phi)/(h*pi);\n");
fprintf(fid," theta_rx = filter([0 1],[1 -1],freq_rx)/(h*pi);\n");
} else {
fprintf(fid," theta_tx = filter([0.5 0.5],[1 -1],phi)/(h*pi);\n");
fprintf(fid," theta_rx = filter([0.5 0.5],[1 -1],freq_rx)/(h*pi);\n");
}
fprintf(fid," %% plot instantaneous tx/rx phase\n");
fprintf(fid," plot(t, theta_tx,'-b', t(i), theta_tx(i),'sb',...\n");
fprintf(fid," t-delay,theta_rx,'-r', t(i)-delay,theta_rx(i),'sr');\n");
fprintf(fid," xlabel('time');\n");
fprintf(fid," ylabel('instantaneous phase/(h \\pi)');\n");
fprintf(fid," legend('transmitted','syms','received/filtered','syms','location','northwest');\n");
fprintf(fid," grid on;\n");
#else
// plot filter response
fprintf(fid,"ht_len = %u;\n", ht_len);
fprintf(fid,"ht = zeros(1,ht_len);\n");
for (i=0; i<ht_len; i++)
fprintf(fid,"ht(%4u) = %12.8f;\n", i+1, ht[i]);
fprintf(fid,"gt1 = filter([0.5 0.5],[1 -1],ht) / (pi*h);\n");
fprintf(fid,"gt2 = filter([0.0 1.0],[1 -1],ht) / (pi*h);\n");
fprintf(fid,"tfilt = [0:(ht_len-1)]/k - delay + 0.5;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(tfilt,ht, '-x','MarkerSize',4,...\n");
fprintf(fid," tfilt,gt1,'-x','MarkerSize',4,...\n");
fprintf(fid," tfilt,gt2,'-x','MarkerSize',4);\n");
fprintf(fid,"axis([tfilt(1) tfilt(end) -0.1 1.1]);\n");
fprintf(fid,"legend('pulse','trap. int.','rect. int.','location','northwest');\n");
fprintf(fid,"grid on;\n");
#endif
fclose(fid);
printf("results written to '%s'\n", OUTPUT_FILENAME);
// free allocated filter memory
free(ht);
return 0;
}
//
// AUTOTEST: validate analysis correctness
//
void autotest_firpfbch_crcf_analysis()
{
float tol = 1e-4f; // error tolerance
unsigned int num_channels=4; // number of channels
unsigned int p=5; // filter length (symbols)
unsigned int num_symbols=12; // number of symbols
// derived values
unsigned int num_samples = num_channels * num_symbols;
unsigned int i;
unsigned int j;
// generate filter
// NOTE : these coefficients can be random; the purpose of this
// exercise is to demonstrate mathematical equivalence
unsigned int h_len = p*num_channels;
float h[h_len];
for (i=0; i<h_len; i++) h[i] = randnf();
// create filterbank object
firpfbch_crcf q = firpfbch_crcf_create(LIQUID_ANALYZER, num_channels, p, h);
// generate filter object
firfilt_crcf f = firfilt_crcf_create(h, h_len);
// allocate memory for arrays
float complex y[num_samples]; // time-domain input
float complex Y0[num_symbols][num_channels]; // channelized output
float complex Y1[num_symbols][num_channels]; // channelized output
// generate input sequence (complex noise)
for (i=0; i<num_samples; i++)
y[i] = randnf() * cexpf(_Complex_I*randf()*2*M_PI);
//
// run analysis filter bank
//
for (i=0; i<num_symbols; i++)
firpfbch_crcf_analyzer_execute(q, &y[i*num_channels], &Y0[i][0]);
//
// run traditional down-converter (inefficient)
//
float dphi; // carrier frequency
unsigned int n=0;
for (i=0; i<num_channels; i++) {
// reset filter
firfilt_crcf_clear(f);
// set center frequency
dphi = 2.0f * M_PI * (float)i / (float)num_channels;
// reset symbol counter
n=0;
for (j=0; j<num_samples; j++) {
// push down-converted sample into filter
firfilt_crcf_push(f, y[j]*cexpf(-_Complex_I*j*dphi));
// compute output at the appropriate sample time
assert(n<num_symbols);
if ( ((j+1)%num_channels)==0 ) {
firfilt_crcf_execute(f, &Y1[n][i]);
n++;
}
}
assert(n==num_symbols);
}
// destroy objects
firfilt_crcf_destroy(f);
firpfbch_crcf_destroy(q);
if (liquid_autotest_verbose) {
// print filterbank channelizer
printf("\n");
printf("filterbank channelizer:\n");
for (i=0; i<num_symbols; i++) {
printf("%3u: ", i);
for (j=0; j<num_channels; j++) {
printf(" %8.5f+j%8.5f, ", crealf(Y0[i][j]), cimagf(Y0[i][j]));
}
printf("\n");
}
// print traditional channelizer
printf("\n");
printf("traditional channelizer:\n");
for (i=0; i<num_symbols; i++) {
printf("%3u: ", i);
for (j=0; j<num_channels; j++) {
printf(" %8.5f+j%8.5f, ", crealf(Y1[i][j]), cimagf(Y1[i][j]));
}
printf("\n");
}
}
// compare results
for (i=0; i<num_symbols; i++) {
for (j=0; j<num_channels; j++) {
CONTEND_DELTA( crealf(Y0[i][j]), crealf(Y1[i][j]), tol );
CONTEND_DELTA( cimagf(Y0[i][j]), cimagf(Y1[i][j]), tol );
}
}
}
int main(int argc, char*argv[])
{
// options
unsigned int h_len = 51; // doppler filter length
float fd = 0.1f; // maximum doppler frequency
float K = 2.0f; // Rice fading factor
float omega = 1.0f; // mean power
float theta = 0.0f; // angle of arrival
unsigned int num_samples=1200; // number of samples
int dopt;
while ((dopt = getopt(argc,argv,"hn:f:K:O:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
case 'n': num_samples = atoi(optarg); break;
case 'f': fd = atof(optarg); break;
case 'K': K = atof(optarg); break;
case 'O': omega = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (K < 0.0f) {
fprintf(stderr,"error: %s, fading factor K must be greater than zero\n", argv[0]);
exit(1);
} else if (omega < 0.0f) {
fprintf(stderr,"error: %s, signal power Omega must be greater than zero\n", argv[0]);
exit(1);
} else if (fd <= 0.0f || fd >= 0.5f) {
fprintf(stderr,"error: %s, Doppler frequency must be in (0,0.5)\n", argv[0]);
exit(1);
} else if (h_len < 4) {
fprintf(stderr,"error: %s, Doppler filter length too small\n", argv[0]);
exit(1);
} else if (num_samples == 0) {
fprintf(stderr,"error: %s, number of samples must be greater than zero\n", argv[0]);
exit(1);
}
unsigned int i;
// allocate array for output samples
float complex * y = (float complex*) malloc(num_samples*sizeof(float complex));
// generate Doppler filter coefficients
float h[h_len];
liquid_firdes_doppler(h_len, fd, K, theta, h);
// normalize filter coefficients such that output Gauss random
// variables have unity variance
float std = 0.0f;
for (i=0; i<h_len; i++)
std += h[i]*h[i];
std = sqrtf(std);
for (i=0; i<h_len; i++)
h[i] /= std;
// create Doppler filter from coefficients
firfilt_crcf fdoppler = firfilt_crcf_create(h,h_len);
// generate complex circular Gauss random variables
float complex v; // circular Gauss random variable (uncorrelated)
float complex x; // circular Gauss random variable (correlated w/ Doppler filter)
float s = sqrtf((omega*K)/(K+1.0));
float sig = sqrtf(0.5f*omega/(K+1.0));
for (i=0; i<num_samples; i++) {
// generate complex Gauss random variable
crandnf(&v);
// push through Doppler filter
firfilt_crcf_push(fdoppler, v);
firfilt_crcf_execute(fdoppler, &x);
// convert result to random variable with Rice-K distribution
y[i] = _Complex_I*( crealf(x)*sig + s ) +
( cimagf(x)*sig );
}
// destroy filter object
firfilt_crcf_destroy(fdoppler);
// export results to 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,"\n");
fprintf(fid,"h_len = %u;\n", h_len);
fprintf(fid,"num_samples = %u;\n", num_samples);
// save filter coefficients
for (i=0; i<h_len; i++)
fprintf(fid,"h(%6u) = %12.4e;\n", i+1, h[i]);
// save samples
for (i=0; i<num_samples; i++)
fprintf(fid,"y(%6u) = %12.4e + 1i*%12.4e;\n", i+1, crealf(y[i]), cimagf(y[i]));
// plot power spectral density of filter
fprintf(fid,"nfft = min(1024, 2^(ceil(log2(h_len))+4));\n");
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"H = 20*log10(abs(fftshift(fft(h,nfft))));\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(f,H);\n");
fprintf(fid,"axis([-0.5 0.5 -80 20]);\n");
fprintf(fid,"xlabel('Normalized Frequency [f/F_s]');\n");
fprintf(fid,"ylabel('Filter Power Spectral Density [dB]');\n");
fprintf(fid,"grid on;\n");
// plot fading profile
fprintf(fid,"figure;\n");
fprintf(fid,"t = 0:(num_samples-1);\n");
fprintf(fid,"plot(t,20*log10(abs(y)));\n");
fprintf(fid,"xlabel('Normalized Time [t F_s]');\n");
fprintf(fid,"ylabel('Fading Power Envelope [dB]');\n");
fprintf(fid,"axis([0 num_samples -40 10]);\n");
fprintf(fid,"grid on;\n");
// plot distribution
fprintf(fid,"[nn xx] = hist(abs(y),15);\n");
fprintf(fid,"bin_width = xx(2) - xx(1);\n");
fprintf(fid,"ymax = max(abs(y));\n");
fprintf(fid,"s = %12.4e;\n", s);
fprintf(fid,"sig = %12.4e;\n", sig);
fprintf(fid,"yp = 1.1*ymax*[1:500]/500;\n");
fprintf(fid,"pdf = (yp/sig^2) .* exp(-(yp.^2+s^2)/(2*sig^2)) .* besseli(0,yp*s/sig^2);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(yp,pdf,'-', xx,nn/(num_samples*bin_width),'x');\n");
fprintf(fid,"xlabel('Fading Magnitude');\n");
fprintf(fid,"ylabel('Probability Density');\n");
fprintf(fid,"legend('theory','data','location','northeast');\n");
// close output file
fclose(fid);
printf("results written to %s\n", OUTPUT_FILENAME);
// clean up allocated arrays
free(y);
printf("done.\n");
return 0;
}
// autotest helper function
// _n : sequence length
// _dt : fractional sample offset
// _dphi : carrier frequency offset
void detector_cccf_runtest(unsigned int _n,
float _dt,
float _dphi)
{
// TODO: validate input
unsigned int i;
// fixed values
float noise_floor = -80.0f; // noise floor [dB]
float SNRdB = 30.0f; // signal-to-noise ratio [dB]
unsigned int m = 11; // resampling filter semi-length
float threshold = 0.3f; // detection threshold
// derived values
unsigned int num_samples = _n + 2*m + 1;
float nstd = powf(10.0f, noise_floor/20.0f);
float gamma = powf(10.0f, (SNRdB + noise_floor)/20.0f);
float delay = (float)(_n + m) + _dt; // expected delay
// arrays
float complex s[_n]; // synchronization pattern (samples)
float complex x[num_samples]; // resampled signal with noise and offsets
// generate synchronization pattern (two samples per symbol)
unsigned int n2 = (_n - (_n%2)) / 2; // n2 = floor(n/2)
unsigned int mm = liquid_nextpow2(n2); // mm = ceil( log2(n2) )
msequence ms = msequence_create_default(mm);
float complex v = 0.0f;
for (i=0; i<_n; i++) {
if ( (i%2)==0 )
v = msequence_advance(ms) ? 1.0f : -1.0f;
s[i] = v;
}
msequence_destroy(ms);
// create fractional sample interpolator
firfilt_crcf finterp = firfilt_crcf_create_kaiser(2*m+1, 0.45f, 40.0f, _dt);
// generate sequence
for (i=0; i<num_samples; i++) {
// add fractional sample timing offset
if (i < _n) firfilt_crcf_push(finterp, s[i]);
else firfilt_crcf_push(finterp, 0.0f);
// compute output
firfilt_crcf_execute(finterp, &x[i]);
// add channel gain
x[i] *= gamma;
// add carrier offset
x[i] *= cexpf(_Complex_I*_dphi*i);
// add noise
x[i] += nstd * ( randnf() + _Complex_I*randnf() ) * M_SQRT1_2;
}
// destroy fractional sample interpolator
firfilt_crcf_destroy(finterp);
// create detector
detector_cccf sync = detector_cccf_create(s, _n, threshold, 2*_dphi);
// push signal through detector
float tau_hat = 0.0f; // fractional sample offset estimate
float dphi_hat = 0.0f; // carrier offset estimate
float gamma_hat = 1.0f; // signal level estimate (linear)
float delay_hat = 0.0f; // total delay offset estimate
int signal_detected = 0; // signal detected flag
for (i=0; i<num_samples; i++) {
// correlate
int detected = detector_cccf_correlate(sync, x[i], &tau_hat, &dphi_hat, &gamma_hat);
if (detected) {
signal_detected = 1;
delay_hat = (float)i + (float)tau_hat;
if (liquid_autotest_verbose) {
printf("****** preamble found, tau_hat=%8.6f, dphi_hat=%8.6f, gamma_hat=%8.6f\n",
tau_hat, dphi_hat, gamma_hat);
}
}
}
// destroy objects
detector_cccf_destroy(sync);
//
// run tests
//
// convert to dB
gamma = 20*log10f(gamma);
gamma_hat = 20*log10f(gamma_hat);
if (liquid_autotest_verbose) {
printf("detector autotest [%3u]: signal detected? %s\n", _n, signal_detected ? "yes" : "no");
printf(" dphi : estimate = %12.6f (expected %12.6f)\n", dphi_hat, _dphi);
printf(" delay : estimate = %12.6f (expected %12.6f)\n", delay_hat, delay);
printf(" gamma : estimate = %12.6f (expected %12.6f)\n", gamma_hat, gamma);
}
// ensure signal was detected
CONTEND_EXPRESSION( signal_detected );
// check carrier offset estimate
CONTEND_DELTA( dphi_hat, _dphi, 0.01f );
// check delay estimate
CONTEND_DELTA( delay_hat, delay, 0.2f );
// check signal level estimate
CONTEND_DELTA( gamma_hat, gamma, 2.0f );
}
int main(int argc, char*argv[])
{
// options
unsigned int num_channels=6; // number of channels (must be even)
unsigned int m=4; // filter delay
unsigned int num_symbols=4*m; // number of symbols
// validate input
if (num_channels%2) {
fprintf(stderr,"error: %s, number of channels must be even\n", argv[0]);
exit(1);
}
// derived values
unsigned int num_samples = num_channels * num_symbols;
unsigned int i;
unsigned int j;
// generate filter
// NOTE : these coefficients can be random; the purpose of this
// exercise is to demonstrate mathematical equivalence
#if 0
unsigned int h_len = 2*m*num_channels;
float h[h_len];
for (i=0; i<h_len; i++) h[i] = randnf();
#else
unsigned int h_len = 2*m*num_channels+1;
float h[h_len];
// NOTE: 81.29528 dB > beta = 8.00000 (6 channels, m=4)
liquid_firdes_kaiser(h_len, 1.0f/(float)num_channels, 81.29528f, 0.0f, h);
#endif
// normalize
float hsum = 0.0f;
for (i=0; i<h_len; i++) hsum += h[i];
for (i=0; i<h_len; i++) h[i] = h[i] * num_channels / hsum;
// sub-sampled filters for M=6 channels, m=4, beta=8.0
// -3.2069e-19 -6.7542e-04 -1.3201e-03 2.2878e-18 3.7613e-03 5.8033e-03
// -7.2899e-18 -1.2305e-02 -1.7147e-02 1.6510e-17 3.1187e-02 4.0974e-02
// -3.0032e-17 -6.8026e-02 -8.6399e-02 4.6273e-17 1.3732e-01 1.7307e-01
// -6.2097e-17 -2.8265e-01 -3.7403e-01 7.3699e-17 8.0663e-01 1.6438e+00
// 2.0001e+00 1.6438e+00 8.0663e-01 7.3699e-17 -3.7403e-01 -2.8265e-01
// -6.2097e-17 1.7307e-01 1.3732e-01 4.6273e-17 -8.6399e-02 -6.8026e-02
// -3.0032e-17 4.0974e-02 3.1187e-02 1.6510e-17 -1.7147e-02 -1.2305e-02
// -7.2899e-18 5.8033e-03 3.7613e-03 2.2878e-18 -1.3201e-03 -6.7542e-04
// create filterbank manually
dotprod_crcf dp[num_channels]; // vector dot products
windowcf w[num_channels]; // window buffers
#if DEBUG
// print coefficients
printf("h_prototype:\n");
for (i=0; i<h_len; i++)
printf(" h[%3u] = %12.8f\n", i, h[i]);
#endif
// create objects
unsigned int h_sub_len = 2*m;
float h_sub[h_sub_len];
for (i=0; i<num_channels; i++) {
// sub-sample prototype filter
#if 0
for (j=0; j<h_sub_len; j++)
h_sub[j] = h[j*num_channels+i];
#else
// load coefficients in reverse order
for (j=0; j<h_sub_len; j++)
h_sub[h_sub_len-j-1] = h[j*num_channels+i];
#endif
// create window buffer and dotprod objects
dp[i] = dotprod_crcf_create(h_sub, h_sub_len);
w[i] = windowcf_create(h_sub_len);
#if DEBUG
printf("h_sub[%u] : \n", i);
for (j=0; j<h_sub_len; j++)
printf(" h[%3u] = %12.8f\n", j, h_sub[j]);
#endif
}
// generate DFT object
float complex x[num_channels]; // time-domain buffer
float complex X[num_channels]; // freq-domain buffer
#if 1
fftplan fft = fft_create_plan(num_channels, X, x, LIQUID_FFT_BACKWARD, 0);
#else
fftplan fft = fft_create_plan(num_channels, X, x, LIQUID_FFT_FORWARD, 0);
#endif
float complex y[num_samples]; // time-domain input
float complex Y0[2*num_symbols][num_channels]; // channelizer output
float complex Y1[2*num_symbols][num_channels]; // conventional output
// generate input sequence
for (i=0; i<num_samples; i++) {
//y[i] = randnf() * cexpf(_Complex_I*randf()*2*M_PI);
y[i] = (i==0) ? 1.0f : 0.0f;
y[i] = cexpf(_Complex_I*sqrtf(2.0f)*i*i);
printf("y[%3u] = %12.8f + %12.8fj\n", i, crealf(y[i]), cimagf(y[i]));
}
//
// run analysis filter bank
//
#if 0
unsigned int filter_index = 0;
#else
unsigned int filter_index = num_channels/2-1;
#endif
float complex y_hat; // input sample
float complex * r; // buffer read pointer
int toggle = 0; // flag indicating buffer/filter alignment
//
for (i=0; i<2*num_symbols; i++) {
// load buffers in blocks of num_channels/2
for (j=0; j<num_channels/2; j++) {
// grab sample
y_hat = y[i*num_channels/2 + j];
// push sample into buffer at filter index
windowcf_push(w[filter_index], y_hat);
// decrement filter index
filter_index = (filter_index + num_channels - 1) % num_channels;
//filter_index = (filter_index + 1) % num_channels;
}
// execute filter outputs
// reversing order of output (not sure why this is necessary)
unsigned int offset = toggle ? num_channels/2 : 0;
toggle = 1-toggle;
for (j=0; j<num_channels; j++) {
unsigned int buffer_index = (offset+j)%num_channels;
unsigned int dotprod_index = j;
windowcf_read(w[buffer_index], &r);
//dotprod_crcf_execute(dp[dotprod_index], r, &X[num_channels-j-1]);
dotprod_crcf_execute(dp[dotprod_index], r, &X[buffer_index]);
}
printf("***** i = %u\n", i);
for (j=0; j<num_channels; j++)
printf(" v2[%4u] = %12.8f + %12.8fj\n", j, crealf(X[j]), cimagf(X[j]));
// execute DFT, store result in buffer 'x'
fft_execute(fft);
// scale fft output
for (j=0; j<num_channels; j++)
x[j] *= 1.0f / (num_channels);
// move to output array
for (j=0; j<num_channels; j++)
Y0[i][j] = x[j];
}
// destroy objects
for (i=0; i<num_channels; i++) {
dotprod_crcf_destroy(dp[i]);
windowcf_destroy(w[i]);
}
fft_destroy_plan(fft);
//
// run traditional down-converter (inefficient)
//
// generate filter object
firfilt_crcf f = firfilt_crcf_create(h, h_len);
float dphi; // carrier frequency
unsigned int n=0;
for (i=0; i<num_channels; i++) {
// reset filter
firfilt_crcf_clear(f);
// set center frequency
dphi = 2.0f * M_PI * (float)i / (float)num_channels;
// reset symbol counter
n=0;
for (j=0; j<num_samples; j++) {
// push down-converted sample into filter
firfilt_crcf_push(f, y[j]*cexpf(-_Complex_I*j*dphi));
// compute output at the appropriate sample time
assert(n<2*num_symbols);
if ( ((j+1)%(num_channels/2))==0 ) {
firfilt_crcf_execute(f, &Y1[n][i]);
n++;
}
}
assert(n==2*num_symbols);
}
firfilt_crcf_destroy(f);
// print filterbank channelizer
printf("\n");
printf("filterbank channelizer:\n");
for (i=0; i<2*num_symbols; i++) {
printf("%2u:", i);
for (j=0; j<num_channels; j++) {
printf("%6.3f+%6.3fj, ", crealf(Y0[i][j]), cimagf(Y0[i][j]));
}
printf("\n");
}
#if 0
// print traditional channelizer
printf("\n");
printf("traditional channelizer:\n");
for (i=0; i<2*num_symbols; i++) {
printf("%2u:", i);
for (j=0; j<num_channels; j++) {
printf("%6.3f+%6.3fj, ", crealf(Y1[i][j]), cimagf(Y1[i][j]));
}
printf("\n");
}
//
// compare results
//
float mse[num_channels];
float complex d;
for (i=0; i<num_channels; i++) {
mse[i] = 0.0f;
for (j=0; j<2*num_symbols; j++) {
d = Y0[j][i] - Y1[j][i];
mse[i] += crealf(d*conjf(d));
}
mse[i] /= num_symbols;
}
printf("\n");
printf(" e:");
for (i=0; i<num_channels; i++)
printf("%12.4e ", sqrt(mse[i]));
printf("\n");
#endif
printf("done.\n");
return 0;
}