예제 #1
0
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);
}
예제 #2
0
// 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);
}
예제 #3
0
// 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;
}
예제 #4
0
// 
// 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;
}
예제 #6
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;
}
예제 #7
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;
}