// 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=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;
}
int main(int argc, char*argv[]) {
// options
unsigned int k=2; // samples/symbol
unsigned int m=4; // symbol delay
float beta=0.33f; // excess bandwidth factor
int ftype = LIQUID_NYQUIST_RCOS;
int dopt;
while ((dopt = getopt(argc,argv,"uht:k:m:b:")) != EOF) {
switch (dopt) {
case 'u':
case 'h':
usage();
return 0;
case 't':
if (strcmp(optarg,"kaiser")==0) {
ftype = LIQUID_NYQUIST_KAISER;
} else if (strcmp(optarg,"pm")==0) {
ftype = LIQUID_NYQUIST_PM;
} else if (strcmp(optarg,"rcos")==0) {
ftype = LIQUID_NYQUIST_RCOS;
} else if (strcmp(optarg,"fexp")==0) {
ftype = LIQUID_NYQUIST_FEXP;
} else if (strcmp(optarg,"fsech")==0) {
ftype = LIQUID_NYQUIST_FSECH;
} else if (strcmp(optarg,"farcsech")==0) {
ftype = LIQUID_NYQUIST_FARCSECH;
} else {
fprintf(stderr,"error: %s, unknown filter type '%s'\n", argv[0], optarg);
exit(1);
}
break;
case 'k': k = atoi(optarg); break;
case 'm': m = atoi(optarg); break;
case 'b': beta = atof(optarg); break;
default:
exit(1);
}
}
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 (beta <= 0.0f || beta >= 1.0f) {
fprintf(stderr,"error: %s, beta must be in (0,1)\n", argv[0]);
exit(1);
}
// initialize objects
unsigned int h_len = 2*k*m+1;
float h[h_len];
// design the filter
liquid_firdes_nyquist(ftype,k,m,beta,0,h);
// print the coefficients to the screen
unsigned int i;
for (i=0; i<h_len; i++)
printf("h(%3u) = %12.8f\n", i+1, h[i]);
//
// export output file
//
FILE * fid = fopen(OUTPUT_FILENAME,"w");
fprintf(fid,"%% %s : auto-generated file\n\n", OUTPUT_FILENAME);
fprintf(fid,"clear all;\n");
fprintf(fid,"close all;\n");
fprintf(fid,"k = %u;\n", k);
fprintf(fid,"m = %u;\n", m);
fprintf(fid,"beta = %12.8f;\n", beta);
fprintf(fid,"h_len = 2*k*m+1;\n");
fprintf(fid,"h = zeros(1,h_len);\n");
for (i=0; i<h_len; i++)
fprintf(fid,"h(%3u) = %20.8e;\n", i+1, h[i]);
fprintf(fid,"nfft=1024;\n");
fprintf(fid,"f = [0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"H = 20*log10(abs(fftshift(fft(h/k,nfft))));\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(f,H,'-','LineWidth',2,...\n");
fprintf(fid," [0.5/k],[-20*log10(2)],'or',...\n");
fprintf(fid," [0.5/k*(1-beta) 0.5/k*(1-beta)],[-100 10],'-r',...\n");
fprintf(fid," [0.5/k*(1+beta) 0.5/k*(1+beta)],[-100 10],'-r');\n");
fprintf(fid,"xlabel('normalized frequency');\n");
fprintf(fid,"ylabel('PSD');\n");
fprintf(fid,"axis([-0.5 0.5 -100 10]);\n");
fprintf(fid,"grid on;\n");
fclose(fid);
printf("results written to %s.\n", OUTPUT_FILENAME);
printf("done.\n");
return 0;
}
