int main(int argc, char*argv[]) {
// options
unsigned int k=4; // samples/symbol
unsigned int m=3; // filter delay [symbols]
float BT = 0.3f; // bandwidth-time product
// read properties from command line
int dopt;
while ((dopt = getopt(argc,argv,"uhk:m:b:")) != EOF) {
switch (dopt) {
case 'u':
case 'h': usage(); return 0;
case 'k': k = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': BT = atof(optarg); break;
default:
exit(1);
}
}
// validate input
if (k < 2) {
fprintf(stderr,"error: %s, k must be at least 2\n", argv[0]);
exit(1);
} else if (m < 1) {
fprintf(stderr,"error: %s, m must be at least 1\n", argv[0]);
exit(1);
} else if (BT <= 0.0f || BT >= 1.0f) {
fprintf(stderr,"error: %s, BT must be in (0,1)\n", argv[0]);
exit(1);
}
unsigned int i;
// derived values
unsigned int h_len = 2*k*m+1; // filter length
// arrays
float ht[h_len]; // transmit filter coefficients
float hr[h_len]; // recieve filter coefficients
// design transmit filter
liquid_firdes_gmsktx(k,m,BT,0.0f,ht);
// print results to screen
printf("gmsk transmit filter:\n");
for (i=0; i<h_len; i++)
printf(" ht(%3u) = %12.8f;\n", i+1, ht[i]);
//
// start of filter design procedure
//
float beta = BT; // prototype filter cut-off
float delta = 1e-2f; // filter design correction factor
// temporary arrays
float h_primef[h_len]; // temporary buffer for real coefficients
float g_primef[h_len]; //
float complex h_tx[h_len]; // impulse response of transmit filter
float complex h_prime[h_len]; // impulse response of 'prototype' filter
float complex g_prime[h_len]; // impulse response of 'gain' filter
float complex h_hat[h_len]; // impulse response of receive filter
float complex H_tx[h_len]; // frequency response of transmit filter
float complex H_prime[h_len]; // frequency response of 'prototype' filter
float complex G_prime[h_len]; // frequency response of 'gain' filter
float complex H_hat[h_len]; // frequency response of receive filter
// create 'prototype' matched filter
// for now use raised-cosine
liquid_firdes_nyquist(LIQUID_NYQUIST_RCOS,k,m,beta,0.0f,h_primef);
// create 'gain' filter to improve stop-band rejection
float fc = (0.7f + 0.1*beta) / (float)k;
float As = 60.0f;
liquid_firdes_kaiser(h_len, fc, As, 0.0f, g_primef);
// copy to fft input buffer, shifting appropriately
for (i=0; i<h_len; i++) {
h_prime[i] = h_primef[ (i+k*m)%h_len ];
g_prime[i] = g_primef[ (i+k*m)%h_len ];
h_tx[i] = ht[ (i+k*m)%h_len ];
}
// run ffts
fft_run(h_len, h_prime, H_prime, FFT_FORWARD, 0);
fft_run(h_len, g_prime, G_prime, FFT_FORWARD, 0);
fft_run(h_len, h_tx, H_tx, FFT_FORWARD, 0);
#if 0
// print results
for (i=0; i<h_len; i++)
printf("Ht(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(H_tx[i]), cimagf(H_tx[i]));
for (i=0; i<h_len; i++)
printf("H_prime(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(H_prime[i]), cimagf(H_prime[i]));
for (i=0; i<h_len; i++)
printf("G_prime(%3u) = %12.8f + j*%12.8f;\n", i+1, crealf(G_prime[i]), cimagf(G_prime[i]));
#endif
// find minimum of reponses
float H_tx_min = 0.0f;
float H_prime_min = 0.0f;
float G_prime_min = 0.0f;
for (i=0; i<h_len; i++) {
if (i==0 || crealf(H_tx[i]) < H_tx_min) H_tx_min = crealf(H_tx[i]);
if (i==0 || crealf(H_prime[i]) < H_prime_min) H_prime_min = crealf(H_prime[i]);
if (i==0 || crealf(G_prime[i]) < G_prime_min) G_prime_min = crealf(G_prime[i]);
}
// compute 'prototype' response, removing minima, and add correction factor
for (i=0; i<h_len; i++) {
// compute response necessary to yeild prototype response (not exact, but close)
H_hat[i] = crealf(H_prime[i] - H_prime_min + delta) / crealf(H_tx[i] - H_tx_min + delta);
// include additional term to add stop-band suppression
H_hat[i] *= crealf(G_prime[i] - G_prime_min) / crealf(G_prime[0]);
}
// compute ifft and copy response
fft_run(h_len, H_hat, h_hat, FFT_REVERSE, 0);
for (i=0; i<h_len; i++)
hr[i] = crealf( h_hat[(i+k*m+1)%h_len] ) / (float)(k*h_len);
//
// end of filter design procedure
//
// print results to screen
printf("gmsk receive filter:\n");
for (i=0; i<h_len; i++)
printf(" hr(%3u) = %12.8f;\n", i+1, hr[i]);
// compute isi
float rxy0 = liquid_filter_crosscorr(ht,h_len, hr,h_len, 0);
float isi_rms = 0.0f;
for (i=1; i<2*m; i++) {
float e = liquid_filter_crosscorr(ht,h_len, hr,h_len, i*k) / rxy0;
isi_rms += e*e;
}
isi_rms = sqrtf(isi_rms / (float)(2*m-1));
printf("\n");
printf("ISI (RMS) = %12.8f dB\n", 20*log10f(isi_rms));
//
// export output file
//
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,"\n\n");
fprintf(fid,"k = %u;\n", k);
fprintf(fid,"m = %u;\n", m);
fprintf(fid,"beta = %f;\n", BT);
fprintf(fid,"h_len = 2*k*m+1;\n");
fprintf(fid,"nfft = 1024;\n");
fprintf(fid,"ht = zeros(1,h_len);\n");
fprintf(fid,"hp = zeros(1,h_len);\n");
fprintf(fid,"hr = zeros(1,h_len);\n");
// print results
for (i=0; i<h_len; i++) fprintf(fid,"ht(%3u) = %12.4e;\n", i+1, ht[i] / k);
for (i=0; i<h_len; i++) fprintf(fid,"hr(%3u) = %12.4e;\n", i+1, hr[i] * k);
for (i=0; i<h_len; i++) fprintf(fid,"hp(%3u) = %12.4e;\n", i+1, h_primef[i]);
fprintf(fid,"hc = k*conv(ht,hr);\n");
// plot results
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"Ht = 20*log10(abs(fftshift(fft(ht, nfft))));\n");
fprintf(fid,"Hp = 20*log10(abs(fftshift(fft(hp/k,nfft))));\n");
fprintf(fid,"Hr = 20*log10(abs(fftshift(fft(hr, nfft))));\n");
fprintf(fid,"Hc = 20*log10(abs(fftshift(fft(hc/k,nfft))));\n");
fprintf(fid,"\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(f,Ht,'LineWidth',1,'Color',[0.00 0.25 0.50],...\n");
fprintf(fid," f,Hp,'LineWidth',1,'Color',[0.80 0.80 0.80],...\n");
fprintf(fid," f,Hr,'LineWidth',1,'Color',[0.00 0.50 0.25],...\n");
fprintf(fid," f,Hc,'LineWidth',2,'Color',[0.50 0.00 0.00],...\n");
fprintf(fid," [-0.5/k 0.5/k], [1 1]*20*log10(0.5),'or');\n");
fprintf(fid,"legend('transmit','prototype','receive','composite','alias points',1);\n");
fprintf(fid,"xlabel('Normalized Frequency');\n");
fprintf(fid,"ylabel('PSD');\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"axis([-0.5 0.5 -100 20]);\n");
fprintf(fid,"\n");
fprintf(fid,"figure;\n");
fprintf(fid,"tr = [ -k*m:k*m]/k;\n");
fprintf(fid,"tc = [-2*k*m:2*k*m]/k;\n");
fprintf(fid,"ic = [0:k:(4*k*m)]+1;\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid," plot(tr,ht,'-x', tr,hr,'-x');\n");
fprintf(fid," legend('transmit','receive',1);\n");
fprintf(fid," xlabel('Time');\n");
fprintf(fid," ylabel('GMSK Tx/Rx Filters');\n");
fprintf(fid," grid on;\n");
fprintf(fid," axis([-2*m 2*m floor(5*min([hr ht]))/5 ceil(5*max([hr ht]))/5]);\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid," plot(tc,hc,'-x', tc(ic),hc(ic),'or');\n");
fprintf(fid," xlabel('Time');\n");
fprintf(fid," ylabel('GMSK Composite Response');\n");
fprintf(fid," grid on;\n");
fprintf(fid," axis([-2*m 2*m -0.2 1.2]);\n");
fprintf(fid," axis([-2*m 2*m floor(5*min(hc))/5 ceil(5*max(hc))/5]);\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
return 0;
}
// Design GMSK receive filter
// _k : samples/symbol
// _m : symbol delay
// _beta : rolloff factor (0 < beta <= 1)
// _dt : fractional sample delay
// _h : output coefficient buffer (length: 2*k*m+1)
void liquid_firdes_gmskrx(unsigned int _k,
unsigned int _m,
float _beta,
float _dt,
float * _h)
{
// validate input
if ( _k < 1 ) {
fprintf(stderr,"error: liquid_firdes_gmskrx(): k must be greater than 0\n");
exit(1);
} else if ( _m < 1 ) {
fprintf(stderr,"error: liquid_firdes_gmskrx(): m must be greater than 0\n");
exit(1);
} else if ( (_beta < 0.0f) || (_beta > 1.0f) ) {
fprintf(stderr,"error: liquid_firdes_gmskrx(): beta must be in [0,1]\n");
exit(1);
} else;
unsigned int k = _k;
unsigned int m = _m;
float BT = _beta;
// internal options
float beta = BT; // prototype filter cut-off
float delta = 1e-3f; // filter design correction factor
liquid_firfilt_type prototype = LIQUID_FIRFILT_KAISER; // Nyquist prototype
unsigned int i;
// derived values
unsigned int h_len = 2*k*m+1; // filter length
// arrays
float ht[h_len]; // transmit filter coefficients
float hr[h_len]; // recieve filter coefficients
// design transmit filter
liquid_firdes_gmsktx(k,m,BT,0.0f,ht);
//
// start of filter design procedure
//
// 'internal' arrays
float h_primef[h_len]; // temporary buffer for real 'prototype' coefficients
float g_primef[h_len]; // temporary buffer for real 'gain' coefficient
float complex h_tx[h_len]; // impulse response of transmit filter
float complex h_prime[h_len]; // impulse response of 'prototype' filter
float complex g_prime[h_len]; // impulse response of 'gain' filter
float complex h_hat[h_len]; // impulse response of receive filter
float complex H_tx[h_len]; // frequency response of transmit filter
float complex H_prime[h_len]; // frequency response of 'prototype' filter
float complex G_prime[h_len]; // frequency response of 'gain' filter
float complex H_hat[h_len]; // frequency response of receive filter
// create 'prototype' matched filter
liquid_firdes_nyquist(prototype,k,m,beta,0.0f,h_primef);
// create 'gain' filter to improve stop-band rejection
float fc = (0.7f + 0.1*beta) / (float)k;
float As = 60.0f;
liquid_firdes_kaiser(h_len, fc, As, 0.0f, g_primef);
// copy to fft input buffer, shifting appropriately
for (i=0; i<h_len; i++) {
h_prime[i] = h_primef[ (i+k*m)%h_len ];
g_prime[i] = g_primef[ (i+k*m)%h_len ];
h_tx[i] = ht[ (i+k*m)%h_len ];
}
// run ffts
fft_run(h_len, h_prime, H_prime, LIQUID_FFT_FORWARD, 0);
fft_run(h_len, g_prime, G_prime, LIQUID_FFT_FORWARD, 0);
fft_run(h_len, h_tx, H_tx, LIQUID_FFT_FORWARD, 0);
// find minimum of reponses
float H_tx_min = 0.0f;
float H_prime_min = 0.0f;
float G_prime_min = 0.0f;
for (i=0; i<h_len; i++) {
if (i==0 || crealf(H_tx[i]) < H_tx_min) H_tx_min = crealf(H_tx[i]);
if (i==0 || crealf(H_prime[i]) < H_prime_min) H_prime_min = crealf(H_prime[i]);
if (i==0 || crealf(G_prime[i]) < G_prime_min) G_prime_min = crealf(G_prime[i]);
}
// compute 'prototype' response, removing minima, and add correction factor
for (i=0; i<h_len; i++) {
// compute response necessary to yeild prototype response (not exact, but close)
H_hat[i] = crealf(H_prime[i] - H_prime_min + delta) / crealf(H_tx[i] - H_tx_min + delta);
// include additional term to add stop-band suppression
H_hat[i] *= crealf(G_prime[i] - G_prime_min) / crealf(G_prime[0]);
}
// compute ifft and copy response
fft_run(h_len, H_hat, h_hat, LIQUID_FFT_BACKWARD, 0);
for (i=0; i<h_len; i++)
hr[i] = crealf( h_hat[(i+k*m+1)%h_len] ) / (float)(k*h_len);
// copy result, scaling by (samples/symbol)^2
for (i=0; i<h_len; i++)
_h[i] = hr[i]*_k*_k;
}
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;
}
// Design (root-)Nyquist filter from prototype
// _type : filter type (e.g. LIQUID_FIRFILT_RRRC)
// _k : samples/symbol
// _m : symbol delay
// _beta : excess bandwidth factor, _beta in [0,1]
// _dt : fractional sample delay
// _h : output coefficient buffer (length: 2*k*m+1)
void liquid_firdes_prototype(liquid_firfilt_type _type,
unsigned int _k,
unsigned int _m,
float _beta,
float _dt,
float * _h)
{
// compute filter parameters
unsigned int h_len = 2*_k*_m + 1; // length
float fc = 0.5f / (float)_k; // cut-off frequency
float df = _beta / (float)_k; // transition bandwidth
float As = estimate_req_filter_As(df,h_len); // stop-band attenuation
// Parks-McClellan algorithm parameters
float bands[6] = { 0.0f, fc-0.5f*df,
fc, fc,
fc+0.5f*df, 0.5f};
float des[3] = { (float)_k, 0.5f*_k, 0.0f };
float weights[3] = {1.0f, 1.0f, 1.0f};
liquid_firdespm_wtype wtype[3] = { LIQUID_FIRDESPM_FLATWEIGHT,
LIQUID_FIRDESPM_FLATWEIGHT,
LIQUID_FIRDESPM_FLATWEIGHT};
switch (_type) {
// Nyquist filter prototypes
case LIQUID_FIRFILT_KAISER:
liquid_firdes_kaiser(h_len, fc, As, _dt, _h);
break;
case LIQUID_FIRFILT_PM:
// WARNING: input timing offset is ignored here
firdespm_run(h_len, 3, bands, des, weights, wtype, LIQUID_FIRDESPM_BANDPASS, _h);
break;
case LIQUID_FIRFILT_RCOS:
liquid_firdes_rcos(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_FEXP:
liquid_firdes_fexp(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_FSECH:
liquid_firdes_fsech(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_FARCSECH:
liquid_firdes_farcsech(_k, _m, _beta, _dt, _h);
break;
// root-Nyquist filter prototypes
case LIQUID_FIRFILT_ARKAISER:
liquid_firdes_arkaiser(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RKAISER:
liquid_firdes_rkaiser(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RRC:
liquid_firdes_rrcos(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_hM3:
liquid_firdes_hM3(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_GMSKTX:
liquid_firdes_gmsktx(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_GMSKRX:
liquid_firdes_gmskrx(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RFEXP:
liquid_firdes_rfexp(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RFSECH:
liquid_firdes_rfsech(_k, _m, _beta, _dt, _h);
break;
case LIQUID_FIRFILT_RFARCSECH:
liquid_firdes_rfarcsech(_k, _m, _beta, _dt, _h);
break;
default:
fprintf(stderr,"error: liquid_firdes_prototype(), invalid root-Nyquist filter type '%d'\n", _type);
exit(1);
}
}
//
// output debugging file
//
void gmskdem_debug_print(gmskdem _q,
const char * _filename)
{
// open output filen for writing
FILE * fid = fopen(_filename,"w");
if (!fid) {
fprintf(stderr,"error: gmskdem_debug_print(), could not open '%s' for writing\n", _filename);
exit(1);
}
fprintf(fid,"%% %s : auto-generated file\n", _filename);
fprintf(fid,"clear all\n");
fprintf(fid,"close all\n");
#if DEBUG_GMSKDEM
//
unsigned int i;
float * r;
fprintf(fid,"n = %u;\n", DEBUG_BUFFER_LEN);
fprintf(fid,"k = %u;\n", _q->k);
fprintf(fid,"m = %u;\n", _q->m);
fprintf(fid,"t = [0:(n-1)]/k;\n");
// plot receive filter response
fprintf(fid,"ht = zeros(1,2*k*m+1);\n");
float ht[_q->h_len];
liquid_firdes_gmsktx(_q->k, _q->m, _q->BT, 0.0f, ht);
for (i=0; i<_q->h_len; i++)
fprintf(fid,"ht(%4u) = %12.4e;\n", i+1, ht[i]);
#if GMSKDEM_USE_EQUALIZER
float hr[_q->h_len];
eqlms_rrrf_get_weights(_q->eq, hr);
for (i=0; i<_q->h_len; i++)
fprintf(fid,"hr(%4u) = %12.4e * %u;\n", i+1, hr[i], _q->k);
#else
for (i=0; i<_q->h_len; i++)
fprintf(fid,"hr(%4u) = %12.4e;\n", i+1, _q->h[i]);
#endif
fprintf(fid,"hc = conv(ht,hr)/k;\n");
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,"Hr = 20*log10(abs(fftshift(fft(hr/k, nfft))));\n");
fprintf(fid,"Hc = 20*log10(abs(fftshift(fft(hc/k, nfft))));\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(f,Ht, f,Hr, f,Hc,'-k','LineWidth',2);\n");
fprintf(fid,"axis([-0.5 0.5 -50 10]);\n");
fprintf(fid,"xlabel('Normalized Frequency');\n");
fprintf(fid,"ylabel('Power Spectral Density [dB]');\n");
fprintf(fid,"legend('transmit','receive','composite',1);\n");
fprintf(fid,"grid on;\n");
fprintf(fid,"mfout = zeros(1,n);\n");
windowf_read(_q->debug_mfout, &r);
for (i=0; i<DEBUG_BUFFER_LEN; i++)
fprintf(fid,"mfout(%5u) = %12.4e;\n", i+1, r[i]);
fprintf(fid,"i0 = 1; %%mod(k+n,k)+k;\n");
fprintf(fid,"isym = i0:k:n;\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(t,mfout,'-', t(isym),mfout(isym),'o','MarkerSize',4);\n");
fprintf(fid,"grid on;\n");
#endif
fclose(fid);
printf("gmskdem: internal debugging written to '%s'\n", _filename);
}
// design transmit filter
void cpfskmod_firdes(unsigned int _k,
unsigned int _m,
float _beta,
int _type,
float * _ht,
unsigned int _ht_len)
{
unsigned int i;
// create filter based on specified type
switch(_type) {
case LIQUID_CPFSK_SQUARE:
// square pulse
if (_ht_len != _k) {
fprintf(stderr,"error: cpfskmodem_firdes(), invalid filter length (square)\n");
exit(1);
}
for (i=0; i<_ht_len; i++)
_ht[i] = 1.0f;
break;
case LIQUID_CPFSK_RCOS_FULL:
// full-response raised-cosine pulse
if (_ht_len != _k) {
fprintf(stderr,"error: cpfskmodem_firdes(), invalid filter length (rcos)\n");
exit(1);
}
for (i=0; i<_ht_len; i++)
_ht[i] = 1.0f - cosf(2.0f*M_PI*i/(float)_ht_len);
break;
case LIQUID_CPFSK_RCOS_PARTIAL:
// full-response raised-cosine pulse
if (_ht_len != 3*_k) {
fprintf(stderr,"error: cpfskmodem_firdes(), invalid filter length (rcos)\n");
exit(1);
}
// initialize with zeros
for (i=0; i<_ht_len; i++)
_ht[i] = 0.0f;
// adding raised-cosine pulse with half-symbol delay
for (i=0; i<2*_k; i++)
_ht[i+_k/2] = 1.0f - cosf(2.0f*M_PI*i/(float)(2*_k));
break;
case LIQUID_CPFSK_GMSK:
// Gauss minimum-shift keying pulse
if (_ht_len != 2*_k*_m + _k + 1) {
fprintf(stderr,"error: cpfskmodem_firdes(), invalid filter length (gmsk)\n");
exit(1);
}
// initialize with zeros
for (i=0; i<_ht_len; i++)
_ht[i] = 0.0f;
// adding Gauss pulse with half-symbol delay
liquid_firdes_gmsktx(_k,_m,_beta,0.0f,&_ht[_k/2]);
break;
default:
fprintf(stderr,"error: cpfskmodem_firdes(), invalid filter type '%d'\n", _type);
exit(1);
}
// normalize pulse area to unity
float ht_sum = 0.0f;
for (i=0; i<_ht_len; i++)
ht_sum += _ht[i];
for (i=0; i<_ht_len; i++)
_ht[i] *= 1.0f / ht_sum;
}