DSP/QAM/qam.c

#include <math.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <complex.h>
#include <string.h>

#define A 10

struct qam_system_s {
    int M; // Nombre de symboles M-QAM
    int k; // Nombre de bits/symboles
    int sm; // sqrt M
    double Fs; // Fréquence d'échantillionage
    double Ts; // Temps d'échantillionage
    int N; // Nombre d'échantillions
    double Fc; // Fréquence de la porteuse
    double complex* constellation; // Tableau de symboles I + j Q 1D
};
typedef struct qam_system_s qam_system;

// Initialisation de la constellation (double tableau de taille sqrt(M)), 
void init_constellation (qam_system* qam) {
    qam->constellation = (double complex*)malloc(sizeof(double complex) * qam->M);

    double norm_factor = sqrt((double)(qam->M - 1) / 3.0); // Pour puissance unitaire

    for (int i = 0; i < qam->sm; i++) {
        double ip = -(qam->sm - 1) + 2 * i;
        for (int j = 0; j < qam->sm; j++) {
            double qp = -(qam->sm - 1) + 2 * j;
            int idx = i * qam->sm + j;
            qam->constellation[idx] = (ip + I * qp) / norm_factor;
        }
    }
}

int bin_to_gray (int x) {
    return x ^ (x >> 1);
}

// Iteration de XOR
int gray_to_bin(int g) {
    int b = g;
    while (g >>= 1)
        b ^= g;
    return b;
}

// Modulation QAM 
void modulate (qam_system* qam, double complex* symbols, int nb_symbols, double complex* s) {
    for (int k = 0; k < nb_symbols; k++) {
        double complex iq = symbols[k];
        for (int n = 0; n < qam->N; n++) {
            int idx = k * qam->N + n;
            s[idx] = A * iq * cexp(2 * I * M_PI * qam->Fc * ((double)idx / qam->Fs));
        }
    }
}

// Demodulation QAM 
void demodulate(qam_system* qam, double complex* s, int nb_symbols, uint8_t* bits_hat, FILE *fp_constel) {
    for (int k = 0; k < nb_symbols; k++) {
        double complex r = 0;
        for (int n = 0; n < qam->N; n++) {
            r += s[k * qam->N + n] * cexp(-2 * I * M_PI * qam->Fc * ((double)(k * qam->N + n) / qam->Fs)) / A;
        }
        r /= qam->N;

        if (fp_constel) {
            fprintf(fp_constel, "% .8f % .8f\n", creal(r), cimag(r));
            fflush(fp_constel); 
        }

        // Distance euclidien de Ir et Qr pour avoir le point le plus proche de la constellation (lent)
        double min_d = INFINITY;
        int i_cl = 0;
        int j_cl = 0;
        for (int idx = 0; idx < qam->M; idx++) {
        double d = cabs(r - qam->constellation[idx]);
            if (d < min_d) {
                min_d = d;
                i_cl = idx / qam->sm;
                j_cl = idx % qam->sm;
            }
        }

        // Gray mapping 
        if (qam->k % 2 != 0) {
            printf("demodulate : k pair (k = %d)\n", qam->k);
            exit(1);
        }
        int bits_per_axis = qam->k / 2;

        int i_bin = gray_to_bin(i_cl);
        int j_bin = gray_to_bin(j_cl);

        for (int b = 0; b < bits_per_axis; b++) {
            bits_hat[k * qam->k + b] = (i_bin >> (bits_per_axis - 1 - b)) & 1;
            bits_hat[k * qam->k + bits_per_axis + b] = (j_bin >> (bits_per_axis - 1 - b)) & 1;
        }
    }
}

// Calcul du bruit gaussien pour un sigma donné
// Formule de Box-Muller
double gaussian_noise (double sigma) {
    double u1 = (rand() + 1) / ((double)RAND_MAX + 2);
    double u2 = (rand() + 1) / ((double)RAND_MAX + 2);
    return sigma * sqrt(-2 * log(u1)) * cos(2 * M_PI * u2);
}

// Ajout du bruit
void add_noise (double complex* s, int len, double sigma) {
    //double signal_power = (2.0/3.0)*(qam.M-1);
    //double snr_dB = 5; // SNR en dB
    //double snr_lin = pow(10.0, snr_dB / 10.0);
    //double sigma = sqrt(signal_power / snr_lin);
    for (int i = 0; i < len; i++) {
        double nr = gaussian_noise(sigma);
        double ni = gaussian_noise(sigma);
        s[i] += nr + I * ni;
    }
}

// Changer le tableau de bits en boolen ou alors la represenation binaire et shifter pour extraire les bits (pas bien si M plus grand)
void bits_to_symbols (qam_system* qam, uint8_t* bits, int nb_bits, double complex* symbols) {
    int nb_symbols = nb_bits / qam->k;

    // k pair 
    if (qam->k % 2 != 0) {
        printf("bits_to_symbols : k doit être pair (k = %d) \n", qam->k);
        exit(1);
    }
    int bits_per_axis = qam->k / 2;

    for (int sym = 0; sym < nb_symbols; sym++) {
        // Construire les indices binaires i_bin (MSB...) et j_bin (LSB...)
        int i_bin = 0;
        int j_bin = 0;
        for (int b = 0; b < bits_per_axis; b++) {
            i_bin = (i_bin << 1) | bits[sym * qam->k + b];
            j_bin = (j_bin << 1) | bits[sym * qam->k + bits_per_axis + b];
        }

        int i_gray = bin_to_gray(i_bin);
        int j_gray = bin_to_gray(j_bin);

        if (i_gray < 0 || i_gray >= qam->sm || j_gray < 0 || j_gray >= qam->sm) {
            printf("bits_to_symbols : IOOR i_gray = %d j_gray = %d sm = %d \n", i_gray, j_gray, qam->sm);
            exit(1);
        }
        symbols[sym] = qam->constellation[i_gray * qam->sm + j_gray];
    }
}

double compare_bits(uint8_t* bits1, uint8_t* bits2, int nb_bits) {
    int errors = 0;
    for (int i = 0; i < nb_bits; i++) {
        if (bits1[i] != bits2[i]) errors++;
    }
    return (double)errors / nb_bits;
}

void add_dephasage(double complex* s, double phi_offset, int total_samples) {
    for (int i = 0; i < total_samples; i++) {
        s[i] *= cexp(I * phi_offset);
    }
}

void add_freq(qam_system* qam, double complex* s, double freq_offset, int total_samples) {
    for (int i = 0; i < total_samples; i++) {
        double t = (double)i / qam->Fs;
        s[i] *= cexp(I * 2 * M_PI * freq_offset * t);
    }
}

void fill_constellation_data(qam_system* qam, FILE *fp_ref) {
    for (int i = 0; i < qam->sm; i++) {
        for (int j = 0; j < qam->sm; j++) {
            int idx = i * qam->sm + j;
            fprintf(fp_ref, "% .8f % .8f\n", creal(qam->constellation[idx]), cimag(qam->constellation[idx]));
        }
    }
}

void reconstruction_text(int nb_chars, uint8_t* output_bits, char* texte_recup) {
    for(int i = 0; i < nb_chars; i++){
        char c = 0;
        for(int b = 0; b < 8; b++){
            c |= output_bits[i*8 + b] << (7-b);
        }
        texte_recup[i] = c;
    }
    texte_recup[nb_chars] = '\0';
}

void text_to_bits(int nb_chars, int nb_bits, char* texte, uint8_t* input_bits) {
    for(int i = 0; i < nb_chars; i++){
        for(int b = 0; b < 8; b++){
            input_bits[i*8 + b] = (texte[i] >> (7-b)) & 1;
        }
    }
}

// Libération de la mémoire
void free_constellation(qam_system* qam) {
    free(qam->constellation);
}

// Préambule QAM
void generate_preamble(qam_system* qam, double complex* preamble, int L) {
    // L 1er symboles de la constellation
    for (int i = 0; i < L; i++) {
        preamble[i] = qam->constellation[i % qam->M];
    }
}

// Concatène le préambule avec le signal modulé
double complex* concat_preamble_signal(double complex* preamble_mod, int preamble_len, double complex* s_mod, int nb_symbols, int N) {
    int total_samples = (preamble_len + nb_symbols) * N;
    double complex* s_concat = malloc(sizeof(double complex) * total_samples);

    // Copier le préambule modulé
    for (int i = 0; i < preamble_len * N; i++) {
        s_concat[i] = preamble_mod[i];
    }

    // Copier le signal modulé après le préambule
    for (int i = 0; i < nb_symbols * N; i++) {
        s_concat[preamble_len * N + i] = s_mod[i];
    }

    return s_concat;
}

// Coarse Frequency Offset avec préambule avec N = 1 (lag 1)
void cfo(double complex* s_with_preamble, int N, int L, double Fs, int total_samples, double Fc) {
    double complex sum = 0;
    int lag = 5;
    for (int n = lag; n < L * N; n++) {
        sum += s_with_preamble[n] * conj(s_with_preamble[n - lag]);
    }
    double phi = carg(sum);
    double f_est = (phi / (2.0 * M_PI * lag)) * Fs;
    double f_offset = f_est - Fc;
    printf("CFO estimé : %f Hz \n", f_offset);
    for (int n = 0; n < total_samples; n++) {
        s_with_preamble[n] *= cexp(-I * 2.0 * M_PI * f_offset * n / Fs);
    }
}

// Fine Frequency Offset (FFO) Correction
void ffo(qam_system* qam, double complex* s_with_preamble, double complex* preamble_ref, int L, int total_samples) {
    
    double complex r_preamble[L];
    for (int k = 0; k < L; k++) {
        double complex r = 0;
        for (int n = 0; n < qam->N; n++) {
            int idx = k * qam->N + n;
            r += s_with_preamble[idx] * cexp(-2 * I * M_PI * qam->Fc * ((double)idx / qam->Fs)) / A;
        }
        r /= qam->N;
        r_preamble[k] = r;
    }

    double complex diff_phase_sum = 0;
    double Ts_symbole = qam->N / qam->Fs;
    
    for (int k = 1; k < L; k++) {
        double complex error_k = r_preamble[k] * conj(preamble_ref[k]);
        double complex error_k_minus_1 = r_preamble[k - 1] * conj(preamble_ref[k - 1]);
        
        diff_phase_sum += error_k * conj(error_k_minus_1);
    }
    
    double phi_sym = carg(diff_phase_sum);
    double delta_f_fine_est = phi_sym / (2.0 * M_PI * Ts_symbole);

    printf("FFO estimé (Delta f fine) : %f Hz\n", delta_f_fine_est);
    
    for (int n = 0; n < total_samples; n++) {
        s_with_preamble[n] *= cexp(-I * 2.0 * M_PI * delta_f_fine_est * n / qam->Fs);
    }
}

// Phase Offset (PO) Correction
void po(qam_system* qam, double complex* s_with_preamble, double complex* preamble_ref, int L, int total_samples) {
    double complex r_preamble[L];
    
    for (int k = 0; k < L; k++) {
        double complex r = 0;
        for (int n = 0; n < qam->N; n++) {
            int idx = k * qam->N + n;
            r += s_with_preamble[idx] * cexp(-2 * I * M_PI * qam->Fc * ((double)idx / qam->Fs)) / A;
        }
        r /= qam->N;
        r_preamble[k] = r;
    }

    double complex phase_error_sum = 0;
    for (int k = 0; k < L; k++) {
        phase_error_sum += r_preamble[k] * conj(preamble_ref[k]);
    }

    double phi_est = carg(phase_error_sum);

    printf("Phase Offset (PO) estimée : %f radians (soit %f degrés)\n", phi_est, phi_est * 180.0 / M_PI);

    double complex phase_corr = cexp(-I * phi_est);

    for (int n = 0; n < total_samples; n++) {
        s_with_preamble[n] *= phase_corr; 
    }
}

// Costas loop
void pll(qam_system* qam, double complex* s_with_preamble, double complex* r_corr, int L, int total_samples, int nb_symbols, double Kp, double Ki, double alpha, FILE* fp_error) {
    double phase_est = 0.0;
    double integrator = 0.0;
    double filtered_error = 0.0;

    int start_data_idx = L * qam->N;
    int N = qam->N;

    for (int k = 0; k < nb_symbols; k++) {
        double complex r_k = 0;
        for (int n = 0; n < N; n++) {
            int idx = start_data_idx + k * N + n;
            double t = (double)idx / qam->Fs;
            r_k += s_with_preamble[idx] * cexp(-2.0 * I * M_PI * qam->Fc * t) / A;
        }
        double complex r_symbol = r_k / N;

        r_symbol *= cexp(-I * phase_est);

        double min_dist = INFINITY;
        double complex closest = 0;
        for (int idx = 0; idx < qam->M; idx++) {
            double dist = cabs(r_symbol - qam->constellation[idx]);
            if (dist < min_dist) {
                min_dist = dist;
                closest = qam->constellation[idx];
            }
        }

        double error = carg(r_symbol * conj(closest));

        filtered_error = (1.0 - alpha) * filtered_error + alpha * error;

        integrator += Ki * filtered_error;
        phase_est += Kp * filtered_error + integrator;

        if (fp_error) {
            fprintf(fp_error, "%d % .8f\n", k, 100 * filtered_error);
            fflush(fp_error);
        }

        for (int n = 0; n < N; n++) {
            int idx = start_data_idx + k * N + n;
            r_corr[idx] = s_with_preamble[idx] * cexp(-I * phase_est);
        }
    }
}


int main () {
    // Initialisation du system qam
    qam_system qam;
    qam.M = 16;
    qam.k = (int)log2((double)(qam.M));
    qam.sm = (int)sqrt(qam.M);
    qam.Fs = 44100;
    qam.Ts = 0.01;
    qam.N = (int)(qam.Fs * qam.Ts);
    qam.Fc = 2000;
    init_constellation(&qam);

    // Conversion du texte en bits
    char* texte = "Vif juge, trempez ce blond whisky aqueux, Vif juge, trempez ce blond whisky aqueux, Vif juge, trempez ce blond whisky aqueux, Vif juge, trempez ce blond whisky aqueux, Vif juge, trempez ce blond whisky aqueux";  
    int nb_chars = strlen(texte);
    int nb_bits = nb_chars * 8;
    int nb_symbols = (nb_bits + qam.k - 1) / qam.k;
    uint8_t* input_bits = malloc(nb_bits * sizeof(uint8_t));
    text_to_bits(nb_chars, nb_bits, texte, input_bits);
    
    // Conversion en symboles
    double complex* symbols = malloc(sizeof(double complex) * nb_symbols);
    bits_to_symbols(&qam, input_bits, nb_bits, symbols);

    // Initialisation du préambule
    int L = 16;
    int total_samples = qam.N * (nb_symbols + L);

    double complex* preamble = malloc(sizeof(double complex) * L);
    generate_preamble(&qam, preamble, L);
    double complex* preamble_mod = malloc(sizeof(double complex) * L * qam.N);
    modulate(&qam, preamble, L, preamble_mod);

    double complex* s_mod = malloc(sizeof(double complex) * nb_symbols * qam.N);
    modulate(&qam, symbols, nb_symbols, s_mod);

    double complex* s = malloc(sizeof(double complex) * total_samples);
    double complex* s_with_preamble = concat_preamble_signal(preamble_mod, L, s_mod, nb_symbols, qam.N);

    // Ajout du bruit
    add_noise(s_with_preamble, total_samples, 24);

    FILE *fp_ref = fopen("constellation_ref.dat", "w");
    fill_constellation_data(&qam, fp_ref);
    fclose(fp_ref);

    // Ajout de dephasage
    add_dephasage(s_with_preamble, M_PI / 6.0 , total_samples);
    
    // AJout de decalage de fréquence
    add_freq(&qam, s_with_preamble, 50, total_samples); 

    // Estimation / correction du CFO
    cfo(s_with_preamble, qam.N, L, qam.Fs, total_samples, qam.Fc);
    ffo(&qam, s_with_preamble, preamble, L, total_samples);

    // Correction phase
    po(&qam, s_with_preamble, preamble, L, total_samples);

    // PLL
    double complex* s_corrected = malloc(sizeof(double complex) * total_samples);
    double Kp = 0.5;
    double Ki = 0.01;
    double alpha = 0.1;
    FILE *fp_pll_error = fopen("pll_error.dat", "w");
    pll(&qam, s_with_preamble, s_corrected, L, total_samples, nb_symbols, Kp, Ki, alpha, fp_pll_error);
    fclose(fp_pll_error);



    // Démodulation
    FILE *fp_constel = fopen("constellation.dat", "w");
    uint8_t* output_bits = (uint8_t*)malloc(nb_bits * sizeof(uint8_t));
    demodulate(&qam, s_corrected + L * qam.N, nb_symbols, output_bits, fp_constel);
    fclose(fp_constel);

    // Reconstruction du texte
    char* texte_recup = malloc(nb_chars + 1);
    reconstruction_text(nb_chars, output_bits, texte_recup);

    printf("Texte original : %s\n\n", texte);
    printf("Texte demodulé : %s\n", texte_recup);

    // Calcul du BER
    double ber = compare_bits(input_bits, output_bits, nb_bits);
    printf("Taux d'erreur blind QAM: %.4f\n", ber * 100);

    // Libération mémoire
    free(input_bits);
    free(output_bits);
    free(symbols);
    free(preamble);
    free(preamble_mod);
    free(s_with_preamble);
    free(texte_recup);
    free_constellation(&qam);

    return 0;
}