int main() {
// options
unsigned int n=32; // number of training symbols
unsigned int p=10; // equalizer order
float mu=0.500f; // LMS learning rate
// allocate memory for arrays
float complex x[n]; // received samples
float complex d_hat[n]; // output symbols
float complex d[n]; // traning symbols
// ...initialize x, d_hat, d...
// create LMS equalizer and set learning rate
eqlms_cccf q = eqlms_cccf_create(NULL,p);
eqlms_cccf_set_bw(q, mu);
// iterate through equalizer learning
unsigned int i;
{
// push input sample
eqlms_cccf_push(q, x[i]);
// compute output sample
eqlms_cccf_execute(q, &d_hat[i]);
// update internal weights
eqlms_cccf_step(q, d[i], d_hat[i]);
}
// clean up allocated memory
eqlms_cccf_destroy(q);
}
// Helper function to keep code base small
void eqlms_cccf_train_bench(struct rusage *_start,
struct rusage *_finish,
unsigned long int *_num_iterations,
unsigned int _h_len)
{
// scale number of iterations appropriately
// log(cycles/trial) ~ 5.63 + 0.767*log(_h_len)
*_num_iterations *= 3200;
*_num_iterations /= (unsigned int) expf(5.63f + 0.767f*logf(_h_len));
*_num_iterations = (*_num_iterations < 4) ? 4 : *_num_iterations;
eqlms_cccf eq = eqlms_cccf_create(NULL,_h_len);
unsigned long int i;
// set up initial arrays to 'randomize' inputs/outputs
float complex y[11];
for (i=0; i<11; i++)
y[i] = randnf() + _Complex_I*randnf();
float complex d[13];
for (i=0; i<13; i++)
d[i] = randnf() + _Complex_I*randnf();
unsigned int iy=0;
unsigned int id=0;
float complex z;
// start trials
getrusage(RUSAGE_SELF, _start);
for (i=0; i<(*_num_iterations); i++) {
eqlms_cccf_push(eq, y[iy]); // push input into equalizer
eqlms_cccf_execute(eq, &z); // compute equalizer output
eqlms_cccf_step(eq, d[id], z); // step equalizer internals
// update counters
iy = (iy+1)%11;
id = (id+1)%13;
}
getrusage(RUSAGE_SELF, _finish);
eqlms_cccf_destroy(eq);
}
// step receiver mixer, matched filter, decimator
// _q : frame synchronizer
// _x : input sample
// _y : output symbol
int flexframesync_step(flexframesync _q,
float complex _x,
float complex * _y)
{
// mix sample down
float complex v;
nco_crcf_mix_down(_q->mixer, _x, &v);
nco_crcf_step (_q->mixer);
// push sample into filterbank
firpfb_crcf_push (_q->mf, v);
firpfb_crcf_execute(_q->mf, _q->pfb_index, &v);
#if FLEXFRAMESYNC_ENABLE_EQ
// push sample through equalizer
eqlms_cccf_push(_q->equalizer, v);
#endif
// increment counter to determine if sample is available
_q->mf_counter++;
int sample_available = (_q->mf_counter >= 1) ? 1 : 0;
// set output sample if available
if (sample_available) {
#if FLEXFRAMESYNC_ENABLE_EQ
// compute equalizer output
eqlms_cccf_execute(_q->equalizer, &v);
#endif
// set output
*_y = v;
// decrement counter by k=2 samples/symbol
_q->mf_counter -= 2;
}
// return flag
return sample_available;
}
//
// AUTOTEST: static channel filter, blind equalization on QPSK symbols
//
void autotest_eqlms_cccf_blind()
{
// parameters
float tol = 2e-2f; // error tolerance
unsigned int k = 2; // samples/symbol
unsigned int m = 7; // filter delay
float beta = 0.3f; // excess bandwidth factor
unsigned int p = 7; // equalizer order
float mu = 0.7f; // equalizer bandwidth
unsigned int num_symbols = 400; // number of symbols to observe
// create sequence generator for repeatability
msequence ms = msequence_create_default(12);
// create interpolating filter
firinterp_crcf interp = firinterp_crcf_create_prototype(LIQUID_FIRFILT_ARKAISER,k,m,beta,0);
// create equalizer
eqlms_cccf eq = eqlms_cccf_create_rnyquist(LIQUID_FIRFILT_ARKAISER,k,p,beta,0);
eqlms_cccf_set_bw(eq, mu);
// create channel filter
float complex h[5] = {
{ 1.00f, 0.00f},
{ 0.00f, -0.01f},
{-0.11f, 0.02f},
{ 0.02f, 0.01f},
{-0.09f, -0.04f} };
firfilt_cccf fchannel = firfilt_cccf_create(h,5);
// arrays
float complex buf[k]; // filter buffer
float complex sym_in [num_symbols]; // input symbols
float complex sym_out[num_symbols]; // equalized symbols
// run equalization
unsigned int i;
unsigned int j;
for (i=0; i<num_symbols; i++) {
// generate input symbol
sym_in[i] = ( msequence_advance(ms) ? M_SQRT1_2 : -M_SQRT1_2 ) +
( msequence_advance(ms) ? M_SQRT1_2 : -M_SQRT1_2 ) * _Complex_I;
// interpolate
firinterp_crcf_execute(interp, sym_in[i], buf);
// apply channel filter (in place)
firfilt_cccf_execute_block(fchannel, buf, k, buf);
// apply equalizer as filter
for (j=0; j<k; j++) {
eqlms_cccf_push(eq, buf[j]);
// decimate by k
if ( (j%k) != 0 ) continue;
eqlms_cccf_execute(eq, &sym_out[i]);
// update equalization (blind operation)
if (i > m + p)
eqlms_cccf_step(eq, sym_out[i]/cabsf(sym_out[i]), sym_out[i]);
}
}
// compare input, output
unsigned int settling_delay = 285;
for (i=m+p; i<num_symbols; i++) {
// compensate for delay
j = i-m-p;
// absolute error
float error = cabsf(sym_in[j]-sym_out[i]);
if (liquid_autotest_verbose) {
printf("x[%3u] = {%12.8f,%12.8f}, y[%3u] = {%12.8f,%12.8f}, error=%12.8f %s\n",
j, crealf(sym_in [j]), cimagf(sym_in [j]),
i, crealf(sym_out[i]), cimagf(sym_out[i]),
error, error > tol ? "*" : "");
if (i == settling_delay + m + p)
printf("--- start of test ---\n");
}
// check error
if (i > settling_delay + m + p)
CONTEND_DELTA(error, 0.0f, tol);
}
// clean up objects
firfilt_cccf_destroy(fchannel);
eqlms_cccf_destroy(eq);
msequence_destroy(ms);
}
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;
}
int main(int argc, char*argv[])
{
// options
unsigned int num_symbols=500; // number of symbols to observe
float SNRdB = 30.0f; // signal-to-noise ratio [dB]
unsigned int hc_len=5; // channel filter length
unsigned int k=2; // matched filter samples/symbol
unsigned int m=3; // matched filter delay (symbols)
float beta=0.3f; // matched filter excess bandwidth factor
unsigned int p=3; // equalizer length (symbols, gr_len = 2*k*p+1)
float mu = 0.09f; // LMS learning rate
// modulation type/depth
modulation_scheme ms = LIQUID_MODEM_QPSK;
// plotting options
unsigned int nfft = 512; // fft size
float gnuplot_version = 4.2;
char filename_base[256] = "figures.gen/eqlms_cccf_blind";
int dopt;
while ((dopt = getopt(argc,argv,"hf:g:n:s:c:k:m:b:p:u:M:")) != EOF) {
switch (dopt) {
case 'h': usage(); return 0;
case 'f': strncpy(filename_base,optarg,256); break;
case 'g': gnuplot_version = atoi(optarg); break;
case 'n': num_symbols = atoi(optarg); break;
case 's': SNRdB = atof(optarg); break;
case 'c': hc_len = atoi(optarg); break;
case 'k': k = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': beta = atof(optarg); break;
case 'p': p = atoi(optarg); break;
case 'u': mu = atof(optarg); break;
case 'M':
ms = liquid_getopt_str2mod(optarg);
if (ms == LIQUID_MODEM_UNKNOWN) {
fprintf(stderr,"error: %s, unknown/unsupported modulation scheme '%s'\n", argv[0], optarg);
return 1;
}
break;
default:
exit(1);
}
}
// validate input
if (num_symbols == 0) {
fprintf(stderr,"error: %s, number of symbols must be greater than zero\n", argv[0]);
exit(1);
} else if (hc_len == 0) {
fprintf(stderr,"error: %s, channel must have at least 1 tap\n", argv[0]);
exit(1);
} else if (k < 2) {
fprintf(stderr,"error: %s, samples/symbol must be at least 2\n", argv[0]);
exit(1);
} else if (m == 0) {
fprintf(stderr,"error: %s, filter semi-length must be at least 1 symbol\n", argv[0]);
exit(1);
} else if (beta < 0.0f || beta > 1.0f) {
fprintf(stderr,"error: %s, filter excess bandwidth must be in [0,1]\n", argv[0]);
exit(1);
} else if (p == 0) {
fprintf(stderr,"error: %s, equalizer semi-length must be at least 1 symbol\n", argv[0]);
exit(1);
} else if (mu < 0.0f || mu > 1.0f) {
fprintf(stderr,"error: %s, equalizer learning rate must be in [0,1]\n", argv[0]);
exit(1);
}
// set 'random' seed on options
srand( hc_len + p + nfft );
// derived values
unsigned int gt_len = 2*k*m+1; // matched filter length
unsigned int gr_len = 2*k*p+1; // equalizer filter length
unsigned int num_samples = k*num_symbols;
// bookkeeping variables
float complex sym_tx[num_symbols]; // transmitted data sequence
float complex x[num_samples]; // interpolated time series
float complex y[num_samples]; // channel output
float complex z[num_samples]; // equalized output
// least mean-squares (LMS) equalizer
float mse[num_symbols]; // equalizer mean-squared error
float complex gr[gr_len]; // equalizer filter coefficients
unsigned int i;
// generate matched filter response
float gtf[gt_len]; // matched filter response
liquid_firdes_rnyquist(LIQUID_RNYQUIST_RRC, k, m, beta, 0.0f, gtf);
// convert to complex coefficients
float complex gt[gt_len];
for (i=0; i<gt_len; i++)
gt[i] = gtf[i]; //+ 0.1f*(randnf() + _Complex_I*randnf());
// create interpolator
interp_cccf interp = interp_cccf_create(k, gt, gt_len);
// create the modem objects
modem mod = modem_create(ms);
modem demod = modem_create(ms);
unsigned int bps = modem_get_bps(mod);
unsigned int M = 1 << bps;
// generate channel impulse response, filter
#if 0
float complex hc[hc_len]; // channel filter coefficients
hc[0] = 1.0f;
for (i=1; i<hc_len; i++)
hc[i] = 0.09f*(randnf() + randnf()*_Complex_I);
#else
// use fixed channel
hc_len = 8;
float complex hc[hc_len]; // channel filter coefficients
hc[0] = 1.00000000+ 0.00000000*_Complex_I;
hc[1] = 0.08077553+ -0.00247592*_Complex_I;
hc[2] = 0.03625883+ -0.09219734*_Complex_I;
hc[3] = 0.05764082+ 0.03277601*_Complex_I;
hc[4] = -0.04773349+ -0.18766306*_Complex_I;
hc[5] = -0.00101735+ -0.00270737*_Complex_I;
hc[6] = -0.05796884+ -0.12665297*_Complex_I;
hc[7] = 0.03805391+ -0.07609370*_Complex_I;
#endif
firfilt_cccf fchannel = firfilt_cccf_create(hc, hc_len);
firfilt_cccf_print(fchannel);
// generate random symbols
for (i=0; i<num_symbols; i++)
modem_modulate(mod, rand()%M, &sym_tx[i]);
// interpolate
for (i=0; i<num_symbols; i++)
interp_cccf_execute(interp, sym_tx[i], &x[i*k]);
// push through channel
float nstd = powf(10.0f, -SNRdB/20.0f);
for (i=0; i<num_samples; i++) {
firfilt_cccf_push(fchannel, x[i]);
firfilt_cccf_execute(fchannel, &y[i]);
// add noise
y[i] += nstd*(randnf() + randnf()*_Complex_I)*M_SQRT1_2;
}
// push through equalizers
float grf[gr_len];
liquid_firdes_rnyquist(LIQUID_RNYQUIST_RRC, k, p, beta, 0.0f, grf);
for (i=0; i<gr_len; i++) {
gr[i] = grf[i] / (float)k;
}
// create LMS equalizer
eqlms_cccf eq = eqlms_cccf_create(gr, gr_len);
eqlms_cccf_set_bw(eq, mu);
// filtered error vector magnitude (emperical MSE)
//float zeta=0.05f; // smoothing factor (small zeta -> smooth MSE)
float complex d_hat = 0.0f;
unsigned int num_symbols_rx=0;
for (i=0; i<num_samples; i++) {
// push samples into equalizers
eqlms_cccf_push(eq, y[i]);
// compute outputs
eqlms_cccf_execute(eq, &d_hat);
// store outputs
z[i] = d_hat;
// check to see if buffer is full
if ( i < gr_len) continue;
// decimate by k
if ( (i%k) != 0 ) continue;
// estimate transmitted signal
unsigned int sym_out; // output symbol
float complex d_prime; // estimated input sample
// LMS
modem_demodulate(demod, d_hat, &sym_out);
modem_get_demodulator_sample(demod, &d_prime);
// update equalizers
eqlms_cccf_step(eq, d_prime, d_hat);
#if 0
// update filtered evm estimate
float evm = crealf( (d_prime-d_hat)*conjf(d_prime-d_hat) );
if (num_symbols_rx == 0) {
mse[num_symbols_rx] = evm;
} else {
mse[num_symbols_rx] = mse[num_symbols_rx-1]*(1-zeta) + evm*zeta;
}
#else
// compute ISI for entire system
eqlms_cccf_get_weights(eq, gr);
mse[num_symbols_rx] = eqlms_cccf_isi(k, gt, gt_len, hc, hc_len, gr, gr_len);
#endif
// print filtered evm (emperical rms error)
if ( ((num_symbols_rx+1)%100) == 0 )
printf("%4u : mse = %12.8f dB\n",
num_symbols_rx+1,
20*log10f(mse[num_symbols_rx]));
// increment output symbol counter
num_symbols_rx++;
}
// get equalizer weights
eqlms_cccf_get_weights(eq, gr);
// destroy objects
eqlms_cccf_destroy(eq);
interp_cccf_destroy(interp);
firfilt_cccf_destroy(fchannel);
modem_destroy(mod);
modem_destroy(demod);
//
// export output
//
FILE * fid = NULL;
char filename[300];
//
// const: constellation
//
strncpy(filename, filename_base, 256);
strcat(filename, "_const.gnu");
fid = fopen(filename,"w");
if (!fid) {
fprintf(stderr,"error: %s, could not open file '%s' for writing\n", argv[0], filename);
return 1;
}
fprintf(fid,"# %s: auto-generated file\n\n", filename);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set size ratio 1\n");
fprintf(fid,"set xrange [-1.5:1.5];\n");
fprintf(fid,"set yrange [-1.5:1.5];\n");
fprintf(fid,"set xlabel 'In-phase'\n");
fprintf(fid,"set ylabel 'Quadrature phase'\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' linewidth 1\n",LIQUID_DOC_COLOR_GRID);
fprintf(fid,"plot '-' using 1:2 with points pointtype 7 pointsize 0.5 linecolor rgb '%s' title 'first 50%%',\\\n", LIQUID_DOC_COLOR_GRAY);
fprintf(fid," '-' using 1:2 with points pointtype 7 pointsize 0.7 linecolor rgb '%s' title 'last 50%%'\n", LIQUID_DOC_COLOR_RED);
// first half of symbols
for (i=2*p; i<num_symbols/2; i+=k)
fprintf(fid," %12.4e %12.4e\n", crealf(y[i]), cimagf(y[i]));
fprintf(fid,"e\n");
// second half of symbols
for ( ; i<num_symbols; i+=k)
fprintf(fid," %12.4e %12.4e\n", crealf(z[i]), cimagf(z[i]));
fprintf(fid,"e\n");
fclose(fid);
printf("results written to '%s'\n", filename);
//
// mse : mean-squared error
//
strncpy(filename, filename_base, 256);
strcat(filename, "_mse.gnu");
fid = fopen(filename,"w");
if (!fid) {
fprintf(stderr,"error: %s, could not open file '%s' for writing\n", argv[0], filename);
return 1;
}
fprintf(fid,"# %s: auto-generated file\n\n", filename);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set size ratio 0.3\n");
fprintf(fid,"set xrange [0:%u];\n", num_symbols);
fprintf(fid,"set yrange [1e-3:1e-1];\n");
fprintf(fid,"set format y '10^{%%L}'\n");
fprintf(fid,"set log y\n");
fprintf(fid,"set xlabel 'symbol index'\n");
fprintf(fid,"set ylabel 'mean-squared error'\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' linewidth 1\n",LIQUID_DOC_COLOR_GRID);
fprintf(fid,"plot '-' using 1:2 with lines linewidth 4 linetype 1 linecolor rgb '%s' title 'LMS MSE'\n", LIQUID_DOC_COLOR_RED);
// LMS
for (i=0; i<num_symbols_rx; i++)
fprintf(fid," %4u %16.8e\n", i, mse[i]);
fprintf(fid,"e\n");
fclose(fid);
printf("results written to '%s'\n", filename);
//
// psd : power spectral density
//
// scale transmit filter appropriately
for (i=0; i<gt_len; i++) gt[i] /= (float)k;
float complex Gt[nfft]; // transmit matched filter
float complex Hc[nfft]; // channel response
float complex Gr[nfft]; // equalizer response
liquid_doc_compute_psdcf(gt, gt_len, Gt, nfft, LIQUID_DOC_PSDWINDOW_NONE, 0);
liquid_doc_compute_psdcf(hc, hc_len, Hc, nfft, LIQUID_DOC_PSDWINDOW_NONE, 0);
liquid_doc_compute_psdcf(gr, gr_len, Gr, nfft, LIQUID_DOC_PSDWINDOW_NONE, 0);
fft_shift(Gt, nfft);
fft_shift(Hc, nfft);
fft_shift(Gr, nfft);
float freq[nfft];
for (i=0; i<nfft; i++)
freq[i] = (float)(i) / (float)nfft - 0.5f;
strncpy(filename, filename_base, 256);
strcat(filename, "_freq.gnu");
fid = fopen(filename,"w");
if (!fid) {
fprintf(stderr,"error: %s, could not open file '%s' for writing\n", argv[0], filename);
return 1;
}
fprintf(fid,"# %s: auto-generated file\n\n", filename);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set size ratio 0.6\n");
fprintf(fid,"set xrange [-0.5:0.5];\n");
fprintf(fid,"set yrange [-10:6]\n");
fprintf(fid,"set xlabel 'Normalized Frequency'\n");
fprintf(fid,"set ylabel 'Power Spectral Density [dB]'\n");
fprintf(fid,"set key top right nobox\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' lw 1\n",LIQUID_DOC_COLOR_GRID);
fprintf(fid,"plot '-' using 1:2 with lines linetype 1 linewidth 1.5 linecolor rgb '%s' title 'transmit',\\\n", LIQUID_DOC_COLOR_GRAY);
fprintf(fid," '-' using 1:2 with lines linetype 1 linewidth 1.5 linecolor rgb '%s' title 'channel',\\\n", LIQUID_DOC_COLOR_RED);
fprintf(fid," '-' using 1:2 with lines linetype 1 linewidth 1.5 linecolor rgb '%s' title 'equalizer',\\\n", LIQUID_DOC_COLOR_GREEN);
fprintf(fid," '-' using 1:2 with lines linetype 1 linewidth 4.0 linecolor rgb '%s' title 'composite',\\\n", LIQUID_DOC_COLOR_BLUE);
fprintf(fid," '-' using 1:2 with points pointtype 7 pointsize 0.6 linecolor rgb '%s' notitle\n", LIQUID_DOC_COLOR_BLUE);
// received signal
for (i=0; i<nfft; i++)
fprintf(fid,"%12.8f %12.4e\n", freq[i], 20*log10f(cabsf(Gt[i])) );
fprintf(fid,"e\n");
// channel
for (i=0; i<nfft; i++)
fprintf(fid,"%12.8f %12.4e\n", freq[i], 20*log10f(cabsf(Hc[i])) );
fprintf(fid,"e\n");
// equalizer
for (i=0; i<nfft; i++)
fprintf(fid,"%12.8f %12.4e\n", freq[i], 20*log10f(cabsf(Gr[i])) );
fprintf(fid,"e\n");
// composite
for (i=0; i<nfft; i++)
fprintf(fid,"%12.8f %12.4e\n", freq[i], 20*log10f( cabsf(Gt[i])*cabsf(Hc[i])*cabsf(Gr[i])) );
fprintf(fid,"e\n");
// composite
fprintf(fid,"%12.8f %12.4e\n", -0.5f/(float)k, 20*log10f(0.5f));
fprintf(fid,"%12.8f %12.4e\n", 0.5f/(float)k, 20*log10f(0.5f));
fprintf(fid,"e\n");
fclose(fid);
printf("results written to '%s'\n", filename);
//
// time...
//
strncpy(filename, filename_base, 256);
strcat(filename, "_time.gnu");
fid = fopen(filename,"w");
if (!fid) {
fprintf(stderr,"error: %s, could not open file '%s' for writing\n", argv[0], filename);
return 1;
}
fprintf(fid,"# %s: auto-generated file\n\n", filename);
fprintf(fid,"reset\n");
fprintf(fid,"set terminal postscript eps enhanced color solid rounded\n");
fprintf(fid,"set xrange [0:%u];\n",num_symbols);
fprintf(fid,"set yrange [-1.5:1.5]\n");
fprintf(fid,"set size ratio 0.3\n");
fprintf(fid,"set xlabel 'Symbol Index'\n");
fprintf(fid,"set key top right nobox\n");
//fprintf(fid,"set ytics -5,1,5\n");
fprintf(fid,"set grid xtics ytics\n");
fprintf(fid,"set pointsize 0.6\n");
fprintf(fid,"set grid linetype 1 linecolor rgb '%s' lw 1\n", LIQUID_DOC_COLOR_GRID);
fprintf(fid,"set multiplot layout 2,1 scale 1.0,1.0\n");
// real
fprintf(fid,"# real\n");
fprintf(fid,"set ylabel 'Real'\n");
fprintf(fid,"plot '-' using 1:2 with lines linetype 1 linewidth 1 linecolor rgb '#999999' notitle,\\\n");
fprintf(fid," '-' using 1:2 with points pointtype 7 linecolor rgb '%s' notitle'\n", LIQUID_DOC_COLOR_BLUE);
//
for (i=0; i<num_samples; i++)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k, crealf(z[i]));
fprintf(fid,"e\n");
//
for (i=0; i<num_samples; i+=k)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k, crealf(z[i]));
fprintf(fid,"e\n");
// imag
fprintf(fid,"# imag\n");
fprintf(fid,"set ylabel 'Imag'\n");
fprintf(fid,"plot '-' using 1:2 with lines linetype 1 linewidth 1 linecolor rgb '#999999' notitle,\\\n");
fprintf(fid," '-' using 1:2 with points pointtype 7 linecolor rgb '%s' notitle'\n", LIQUID_DOC_COLOR_GREEN);
//
for (i=0; i<num_samples; i++)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k, cimagf(z[i]));
fprintf(fid,"e\n");
//
for (i=0; i<num_samples; i+=k)
fprintf(fid,"%12.8f %12.4e\n", (float)i/(float)k, cimagf(z[i]));
fprintf(fid,"e\n");
fprintf(fid,"unset multiplot\n");
// close output file
fclose(fid);
printf("results written to '%s'\n", filename);
return 0;
}
int main(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;
}