DSP/QAM/qamold/qamclean.c

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

#define A 1 

struct qam_system_s {
    int M; // Nombre de symboles M-QAM
    int k; // Nombre de bits/symboles
    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
};
typedef struct qam_system_s qam_system;

// Initialisation de la constellation (double tableau de taille sqrt(M)), 
// ToDo : changer à un tableau à 1 dimension pour éviter de calculer sqrt(M)
void init_constellation (qam_system* qam) {
    int sm = (int)sqrt(qam->M);
    qam->constellation = (double complex**)malloc(sizeof(double complex*) * sm);
    
    for (int i = 0; i < sm; i++) {
       qam->constellation[i] = (double complex*)malloc(sizeof(double complex) * sm);
    }

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

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

// 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) {
    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;
    int sm = sqrt(qam->M);
    for (int k = 0; k < nb_symbols; k++) {
        int id = 0;
        for (int b = 0 ; b < qam->k; b++) {
            id = id * 2 + bits[k * qam->k + b];
        }
        int i = id / sm; 
        int j = id % sm;
        symbols[k] = qam->constellation[i][j];
    }
}

// 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++) {
            s[k * qam->N + n] = iq * cexp(2 * I * M_PI * qam->Fc * ((double)n / qam->Fs)); 
        }
    }
}

// Demodulation QAM 
void demodulate(qam_system* qam, double complex* s, int nb_symbols, uint8_t* bits_hat) {
    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)n / qam->Fs));
        }
        r /= qam->N;

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

                // index du symbole (id) : même mappage que dans bits_to_symbols()
        int id = i_cl * sm + j_cl;

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

// Libération de la mémoire
void free_constellation(qam_system* qam) {
    int sm = (int)sqrt(qam->M);
    for (int i = 0; i < sm; i++)
        free(qam->constellation[i]);
    free(qam->constellation);
}

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;
}

int main () {
    qam_system qam;
    qam.M = 16;
    qam.k = (int)log2((double)(qam.M));
    qam.Fs = 44100;
    qam.Ts = 0.0003;
    qam.N = (int)qam.Fs * qam.Ts;
    qam.Fc = 2000;
    init_constellation(&qam);

    int nb_bits = 1000;
    int nb_symbols = nb_bits / qam.k;

    uint8_t* input_bits = malloc(nb_bits * sizeof(uint8_t));
    for (int i = 0; i < nb_bits; i++) {
        input_bits[i] = rand() % 2;
    }
    
    // Conversion en symboles
    double complex* symbols = malloc(sizeof(double complex) * nb_symbols);
    bits_to_symbols(&qam, input_bits, nb_bits, symbols);

    // Modulation
    int total_samples = qam.N * nb_symbols;
    double complex* s = malloc(sizeof(double complex) * total_samples);
    modulate(&qam, symbols, nb_symbols, s);

    // Ajout du bruit
    double signal_power = (2.0/3.0)*(qam.M-1); // puissance moyenne
    double snr_dB = 10; // SNR en dB
    double snr_lin = pow(10.0, snr_dB / 10.0);
    double sigma = sqrt(signal_power / snr_lin);
    add_noise(s, total_samples, sigma);

    // Démodulation
    uint8_t* output_bits = malloc(nb_bits * sizeof(uint8_t));
    demodulate(&qam, s, nb_symbols, output_bits);

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

    // Libération mémoire
    free(input_bits);
    free(output_bits);
    free(symbols);
    free(s);
    free_constellation(&qam);

    return 0;
}