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//
// eqrls_cccf_example.c
//
// Tests recursive least-squares (RLS) equalizer (EQ) on a QPSK
// signal at the symbol level.
//
#include <stdio.h>
#include <stdlib.h>
#include <complex.h>
#include "liquid.h"
#define OUTPUT_FILENAME "eqrls_cccf_example.m"
int main() {
// options
unsigned int n=512; // number of symbols to observe
unsigned int ntrain=256;// number of training symbols
unsigned int h_len=6; // channel filter length
unsigned int p=12; // equalizer order
// bookkeeping variables
float complex d[n]; // data sequence
float complex y[n]; // received data sequence (filtered by channel)
float complex d_hat[n]; // recovered data sequence
float complex h[h_len]; // channel filter coefficients
float complex w[p]; // equalizer filter coefficients
unsigned int i;
// create equalizer (default initial coefficients)
eqrls_cccf eq = eqrls_cccf_create(NULL,p);
// create channel filter (random delay taps)
h[0] = 1.0f;
for (i=1; i<h_len; i++)
h[i] = (randnf() + randnf()*_Complex_I) * 0.1f;
firfilt_cccf f = firfilt_cccf_create(h,h_len);
// generate random data signal
for (i=0; i<n; i++)
d[i] = (rand() % 2 ? 1.0f : -1.0f) +
(rand() % 2 ? 1.0f : -1.0f)*_Complex_I;
// filter data signal through channel
for (i=0; i<n; i++) {
firfilt_cccf_push(f,d[i]);
firfilt_cccf_execute(f,&y[i]);
}
// run equalizer
for (i=0; i<p; i++)
w[i] = 0;
eqrls_cccf_train(eq, w, y, d, ntrain);
// create filter from equalizer output
firfilt_cccf feq = firfilt_cccf_create(w,p);
// run equalizer filter
for (i=0; i<n; i++) {
firfilt_cccf_push(feq,y[i]);
firfilt_cccf_execute(feq,&d_hat[i]);
}
//
// print results
//
printf("channel:\n");
for (i=0; i<h_len; i++)
printf(" h(%3u) = %12.8f + j*%12.8f\n", i, crealf(h[i]), cimagf(h[i]));
printf("equalizer:\n");
for (i=0; i<p; i++)
printf(" w(%3u) = %12.8f + j*%12.8f\n", i, crealf(w[i]), cimagf(w[i]));
// compute MSE
float complex e;
float mse=0.0f;
for (i=0; i<n; i++) {
// compute mse
e = d[i] - d_hat[i];
mse += crealf(e*conj(e));
}
mse /= n;
printf("mse: %12.8f\n", mse);
// clean up objects
firfilt_cccf_destroy(f);
eqrls_cccf_destroy(eq);
firfilt_cccf_destroy(feq);
//
// 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,"n=%u;\n",n);
fprintf(fid,"ntrain=%u;\n",ntrain);
fprintf(fid,"p=%u;\n",p);
fprintf(fid,"h_len=%u;\n",h_len);
for (i=0; i<h_len; i++)
fprintf(fid," h(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(h[i]), cimagf(h[i]));
for (i=0; i<p; i++)
fprintf(fid," w(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(w[i]), cimagf(w[i]));
for (i=0; i<n; i++) {
fprintf(fid," d(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(d[i]), cimagf(d[i]));
fprintf(fid," y(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(y[i]), cimagf(y[i]));
fprintf(fid," d_hat(%3u) = %12.4e + j*%12.4e;\n", i+1, crealf(d_hat[i]), cimagf(d_hat[i]));
}
// plot results
fprintf(fid,"\n\n");
fprintf(fid,"nfft=512;\n");
fprintf(fid,"f=[0:(nfft-1)]/nfft - 0.5;\n");
fprintf(fid,"H=20*log10(abs(fftshift(fft(h,nfft))));\n");
fprintf(fid,"W=20*log10(abs(fftshift(fft(w,nfft))));\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(f,H,'-r',f,W,'-b', f,H+W,'-k','LineWidth',2);\n");
fprintf(fid,"xlabel('Normalied Frequency');\n");
fprintf(fid,"ylabel('Power Spectral Density [dB]');\n");
fprintf(fid,"axis([-0.5 0.5 -10 10]);\n");
fprintf(fid,"legend('channel','equalizer','composite',0);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"subplot(2,1,1);\n");
fprintf(fid,"hold on;\n");
fprintf(fid,"stem(0:(h_len-1),real(h),'-r');\n");
fprintf(fid,"stem(0:(p-1), real(w),'-b');\n");
fprintf(fid,"hold off;\n");
fprintf(fid,"ylabel('Real Coefficients');\n");
fprintf(fid,"legend('channel','equalizer',0);\n");
fprintf(fid,"axis([-0.25 max(h_len,p)-0.75 -0.5 1.5]);\n");
fprintf(fid,"subplot(2,1,2);\n");
fprintf(fid,"hold on;\n");
fprintf(fid,"stem(0:(h_len-1),imag(h),'-r');\n");
fprintf(fid,"stem(0:(p-1), imag(w),'-b');\n");
fprintf(fid,"hold off;\n");
fprintf(fid,"ylabel('Imag Coefficients');\n");
fprintf(fid,"legend('channel','equalizer',0);\n");
fprintf(fid,"axis([-0.25 max(h_len,p)-0.75 -0.5 1.5]);\n");
fprintf(fid,"figure;\n");
fprintf(fid,"plot(y,'xr',d_hat,'xb');\n");
fprintf(fid,"axis('square');\n");
fprintf(fid,"xlabel('in-phase');\n");
fprintf(fid,"ylabel('quadrature');\n");
fprintf(fid,"legend('received','equalized',1');\n");
fclose(fid);
printf("results written to %s.\n",OUTPUT_FILENAME);
return 0;
}
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