發現了一個重大的錯誤，在 Beamforming 演算法中 ww 要放在分母，之前的實驗都誤植程在分子，這也難怪噪音會超大聲。

原來程式：

gsl_blas_zgemm(CblasNoTrans, CblasNoTrans, double2complex(1.,0.), AA, invR, double2complex(0.,0.), tempww);
gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, double2complex(1.,0.), tempww, AA, double2complex(0.,0.), ww);
gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, gsl_matrix_complex_get(ww,0,0), invR, AA, double2complex(0.,0.), w);

$$ w= ({AR^{-1}A^H}){R^{-1}A} \textbf{ (wrong!)} $$

應該要改為：

gsl_blas_zgemm(CblasNoTrans, CblasNoTrans, double2complex(1.,0.), AA, invR, double2complex(0.,0.), tempww);
gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, double2complex(1.,0.), tempww, AA, double2complex(0.,0.), ww);
gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, gsl_complex_div(double2complex(1.,0.),gsl_matrix_complex_get(ww,0,0)), invR, AA, double2complex(0.,0.), w);

$$ w= \frac{R^{-1}A}{AR^{-1}A^H} $$

修正之後也安靜了許多，此外，在進行 invR 之後也為了避免記憶體溢位當機，讓 invR 內的元素若高於一個閥值便令其為1：

if (gsl_matrix_complex_get(matrix, i, j).dat[0]<=Ka){
     // do nothing
}
else{
    gsl_matrix_complex_set(matrix, i, j, double2complex(1., 0.));
}

經過多次測試之後，這是目前最穩定的版本，架構如下：

圖：系統方塊圖

#include <stdio.h>
#include <math.h>
#include <unistd.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_fft_complex.h>
#include <gsl/gsl_complex.h>
#include <gsl/gsl_complex_math.h>
#include <gsl/gsl_sf.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_blas.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_statistics_double.h>
#include <gsl/gsl_linalg.h>
#include <fftw3.h>
#include <complex.h>

#include "portaudio.h"

#define REAL(z,i) ((z)[2*(i)])
#define IMAG(z,i) ((z)[2*(i)+1])
#define DEG2RAD(x) (x*M_PI/180)

#define FRAME_BLOCK_LEN 512
#define SAMPLING_RATE 44100
#define INPUT_CHANNEL 8
#define USED_CH 6
#define OUTPUT_CHANNEL 1

#define TEMPERATURE 334.
#define LDA TEMPERATURE/600.
#define Radii 0.0463

#define Ka 10000.           //Adjust compressor strength
#define Kb 1.          //Adjust compressor strength (Bypass: Ka=1, Kb=0)
#define Kmvdr 1.        //Adjust snr strength
#define snr_gate 0          //treshold of snr
#define GAIN 0.8
#define Kp 0.05
#define Ki 0.0
#define Kd 0.0

#define wKp 0.5
#define wKi 0.0
#define wKd 0.

float snr=1.;
float snr0=0.;
float snr_Intergral_val=0.;
float snr_Previous_error=0.;
gsl_matrix_complex *w0;
gsl_matrix_complex *w_Intergral_val;
gsl_matrix_complex *w_Previous_error;

PaStream *audioStream;
    
gsl_complex double2complex(float re, float im){
    gsl_complex b;
    b.dat[0]=re;
    b.dat[1]=im;
    return b;
}

gsl_matrix_complex PID_matrix(gsl_matrix_complex *a, gsl_matrix_complex *a0){
    gsl_matrix_complex *Derivative_val=gsl_matrix_complex_alloc(a->size1, a->size2);
    gsl_matrix_complex *error=gsl_matrix_complex_alloc(a->size1, a->size2);
    gsl_matrix_complex *new_val=gsl_matrix_complex_alloc(a->size1, a->size2);
    for(int i=0;i<a->size1;i++){
        for(int j=0;j<a->size2;j++){
            gsl_matrix_complex_set(error,i,j,gsl_complex_sub(
                gsl_matrix_complex_get(a,i,j),
                gsl_matrix_complex_get(a0,i,j)));
            gsl_matrix_complex_set(w_Intergral_val,i,j,gsl_complex_add(
                gsl_matrix_complex_get(w_Intergral_val,i,j),
                gsl_matrix_complex_get(error,i,j)));
            gsl_matrix_complex_set(Derivative_val,i,j,gsl_complex_sub(
                gsl_matrix_complex_get(error,i,j),
                gsl_matrix_complex_get(w_Previous_error,i,j)));
            gsl_matrix_complex_set(w_Previous_error,i,j,gsl_matrix_complex_get(error,i,j));
            
            gsl_matrix_complex_set(new_val,i,j,
                gsl_complex_add(gsl_complex_add(gsl_complex_add(
                    gsl_matrix_complex_get(a0,i,j),
                    gsl_complex_mul(double2complex(wKp,0.), gsl_matrix_complex_get(error,i,j))),
                    gsl_complex_mul(double2complex(wKi,0.), gsl_matrix_complex_get(w_Intergral_val,i,j))),
                    gsl_complex_mul(double2complex(wKd,0.), gsl_matrix_complex_get(Derivative_val,i,j))));
        }
    }
    gsl_matrix_complex_free(Derivative_val);
    gsl_matrix_complex_free(error);
    return *new_val;
}

float PID(float a, float a0){
    float error=a-a0;
    snr_Intergral_val += error;
    float Derivative_val = error - snr_Previous_error;
    snr_Previous_error = error;
    double new_val =a0 + (Kp * error + Ki * snr_Intergral_val + Kd * Derivative_val);
    return new_val;
}

float SNR(fftwf_complex a[],double m_freq, double bandwidth){
    float noise_avg=0.;
    float signal_avg=0.;
    float power_spectrum[FRAME_BLOCK_LEN/2+1];
    int m_n = (int)(m_freq*FRAME_BLOCK_LEN/SAMPLING_RATE/2+1);
    int bandwidth_n = (int)(bandwidth*FRAME_BLOCK_LEN/SAMPLING_RATE);

    for (int i=0; i<FRAME_BLOCK_LEN/2+1; i++) {
        power_spectrum[i] = a[i][0] * a[i][0] + a[i][1] * a[i][1];
    }
    
    
    for(int i=0;i<FRAME_BLOCK_LEN/2+1;i++){
        noise_avg+=power_spectrum[i];
    }
    noise_avg/=(FRAME_BLOCK_LEN/2+1);

    for(int i=m_n-bandwidth_n;i<=m_n+bandwidth_n;i++){
        signal_avg+=power_spectrum[i];
    }
    //printf("%f\\n", signal_avg);
    signal_avg/=(bandwidth_n*2+1);

    //if((signal_avg/noise_avg)>3){
    //    printf("%f\\n",(signal_avg/noise_avg));
    //}
    
    //printf("%f\\t%f\\n",signal_avg,noise_avg);
    //printf("%f\\n",signal_avg/noise_avg);
    if(signal_avg/noise_avg>=snr_gate){
        return (signal_avg/noise_avg);
    }
    else{
        return (0);
    }
    
    //return (signal_avg);
}

void PrintMat(gsl_matrix_complex *m, char info[]){
    printf("Print Matrix %s: \\n",info);
    for(int i=0; i<m->size1;i++){
        for(int j=0;j<m->size2;j++){
            printf("%.6f+%.2fi\\t", gsl_matrix_complex_get(m,i,j).dat[0],gsl_matrix_complex_get(m,i,j).dat[1]);
        }
        printf("\\n");
    }
}

void autocorr(gsl_matrix_complex *Rxx, gsl_matrix_complex *m){
    gsl_matrix_complex *mH=gsl_matrix_complex_alloc(m->size2, m->size1);
    gsl_matrix_complex *Imat=gsl_matrix_complex_alloc(m->size1, m->size1);
    gsl_matrix_complex_set_identity(Imat);
    gsl_blas_zgemm(CblasConjTrans,CblasNoTrans,double2complex(1.,0.),m,Imat,double2complex(0.,0.),mH);
    //gsl_matrix_transpose_memcpy(mH, m);
    gsl_blas_zgemm (CblasNoTrans, CblasNoTrans,
                    double2complex(1./m->size2,0.), m, mH,
                    double2complex(0.,0.), Rxx);

    gsl_matrix_complex_free(mH);
    gsl_matrix_complex_free(Imat);

}

void invMat(gsl_matrix_complex *matrix,gsl_matrix_complex *inv){
    gsl_permutation *p = gsl_permutation_alloc(matrix->size1);
    int s;

    gsl_linalg_complex_LU_decomp(matrix, p, &s);
    gsl_linalg_complex_LU_invert(matrix, p, inv);
    gsl_permutation_free(p);
}

gsl_complex eulers_formula(double x){    //e^(xi) = cos(x) + i*sin(x)
    gsl_complex a;
    GSL_SET_COMPLEX(&a, cos(x), sin(x));
    return a;
}
float Compress(float n){
    float a, b, tmp;
    a=Ka*n;
    b=Kb*n+1;
    return a/b;
}
void Compress_Mat(gsl_matrix_complex *matrix){
    gsl_complex a, b, tmp;
    
    for(int i=0; i<matrix->size1; i++){
        for(int j=0; j<matrix->size2; j++){
            if (gsl_matrix_complex_get(matrix, i, j).dat[0]<=Ka){
                // do nothing
            }
            else{
                gsl_matrix_complex_set(matrix, i, j, double2complex(1., 0.));
            }
        }
    }
}

int audio_callback(const void *inputBuffer,
                   void *outputBuffer, 
                   unsigned long framesPerBuffer,
                   const PaStreamCallbackTimeInfo* timeInfo,
                   PaStreamCallbackFlags statusFlags,
                   void *userData){
    
    float *in = (float*) inputBuffer, *out = (float*)outputBuffer;
    float y_arr_f_to_t_domain[FRAME_BLOCK_LEN];
    float *y_arr_p = y_arr_f_to_t_domain;
    float *snr_p = &snr;
    float *snr0_p = &snr0;
    static double phase = 0;
    float in_unsort[INPUT_CHANNEL][FRAME_BLOCK_LEN];
    float in_sort[USED_CH][FRAME_BLOCK_LEN];
    fftwf_complex input_fft_data[USED_CH][FRAME_BLOCK_LEN/2+1];
    fftwf_plan plan;
    fftwf_complex output_fft_data[FRAME_BLOCK_LEN/2+1];
    float output[USED_CH][FRAME_BLOCK_LEN];
    int printmat=0;
    gsl_matrix_complex *fft_data_mat=gsl_matrix_complex_alloc(USED_CH, FRAME_BLOCK_LEN/2+1);
    gsl_matrix_complex *in_sort_mat=gsl_matrix_complex_alloc(USED_CH, FRAME_BLOCK_LEN);
    //printf("\\n\\n-----------start print------------\\n");
    int ch_tag=0;
    int zero_count=0;
    for (int i=0;i<INPUT_CHANNEL;i++){
        float is_zero=0.;
        for (int j=0;j<FRAME_BLOCK_LEN;j++){
            in_unsort[i][j]=in[INPUT_CHANNEL*j+i];
            is_zero+=in[INPUT_CHANNEL*j+i];
            //printf("%f\\t",in[INPUT_CHANNEL*j+i]);
        }
        //printf("\\n\\n");
        if(is_zero==0. && zero_count!=2){
            //printf("WHAT THE HECK DID YOU DOl?");
            zero_count++;
            continue;
        }
        //printf("\\n---DONE!---\\n");
        if(zero_count>=2){
            for(int j=0;j<FRAME_BLOCK_LEN;j++){
                in_sort[ch_tag][j] = in_unsort[i][j];
            }
            //printf("\\n\\n");
            ch_tag++;
        }
    }
    for(int i=ch_tag;i<USED_CH;i++){
        for(int j=0;j<FRAME_BLOCK_LEN;j++){
            in_sort[i][j] = in_unsort[i-ch_tag][j];
        }
        //printf("\\n\\n");
    }
    for(int i=0;i<USED_CH;i++){
        for(int j=0;j<FRAME_BLOCK_LEN;j++){
            gsl_matrix_complex_set (in_sort_mat, i, j, double2complex(in_sort[i][j], 0.));
        }
        //printf("\\n\\n");
    }

    for(int i=0;i<USED_CH;i++){
        //printf("\\n");
        plan = fftwf_plan_dft_r2c_1d(FRAME_BLOCK_LEN, in_sort[i], input_fft_data[i], FFTW_ESTIMATE);
        fftwf_execute(plan);

        //gsl_fft_complex_radix2_forward(input_fft_data[i], 1, FRAME_BLOCK_LEN);
        for(int k=0;k<FRAME_BLOCK_LEN/2+1;k++){
            gsl_matrix_complex_set (fft_data_mat, i, k, double2complex(input_fft_data[i][k][0], input_fft_data[i][k][1]));
        }
    }
 
    //-------Processing in f domain-------
    gsl_matrix_complex *Rxx=gsl_matrix_complex_alloc(fft_data_mat->size1, fft_data_mat->size1);
    gsl_matrix_complex *invR=gsl_matrix_complex_alloc(fft_data_mat->size1, fft_data_mat->size1);
    gsl_matrix_complex *AA=gsl_matrix_complex_alloc(1,USED_CH);
    gsl_matrix_complex *tempww=gsl_matrix_complex_alloc(1,USED_CH);
    gsl_matrix_complex *ww=gsl_matrix_complex_alloc(1,1);
    gsl_matrix_complex *w=gsl_matrix_complex_alloc(USED_CH,1);
    gsl_matrix_complex *y=gsl_matrix_complex_alloc(1, FRAME_BLOCK_LEN);
    
    float doa=0.;
    autocorr(Rxx,fft_data_mat);
    invMat(Rxx,invR);
    Compress_Mat(invR);
    for(int i=0;i<USED_CH;i++){
        float tempaa = (float) (sin(M_PI/2)*cos(DEG2RAD((double)doa)-2*i*M_PI/USED_CH));
        gsl_matrix_complex_set (AA, 0, i, eulers_formula(-1*2*M_PI*Radii*tempaa/(LDA)));
    }
    
    gsl_blas_zgemm(CblasNoTrans, CblasNoTrans, double2complex(1.,0.), AA, invR, double2complex(0.,0.), tempww);
    gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, double2complex(1.,0.), tempww, AA, double2complex(0.,0.), ww);
    gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, gsl_complex_div(double2complex(1.,0.),gsl_matrix_complex_get(ww,0,0)), invR, AA, double2complex(0.,0.), w);
    gsl_blas_zgemm(CblasConjTrans, CblasNoTrans, double2complex(GAIN*(*snr_p),0.), w, in_sort_mat, double2complex(0.,0.), y);
    for(int i=0;i<FRAME_BLOCK_LEN;i++){
        // y_arr_f_to_t_domain[i] = (float) gsl_complex_abs(gsl_matrix_complex_get(y,0,i));
        y_arr_f_to_t_domain[i] = (float) gsl_matrix_complex_get(y,0,i).dat[0];
    }
    float original[FRAME_BLOCK_LEN];  // original audio using complex form
    float *p_original=original;

    for(int i=0;i<FRAME_BLOCK_LEN;i++){
        float tmp=0;
        for(int j=0;j<USED_CH;j++){
            tmp+=(in_sort[j][i]/6);
            //tmp+=output[j][i];
        }
        original[i]=tmp;
        *out++ = *y_arr_p++;
    }
    plan = fftwf_plan_dft_r2c_1d(FRAME_BLOCK_LEN, y_arr_f_to_t_domain, output_fft_data, FFTW_ESTIMATE);
    fftwf_execute(plan);
    *snr_p = SNR(output_fft_data, 343./(LDA), 10.);
    *snr_p = PID(*snr_p,*snr0_p);

    //Free these all Fucking things
    *snr0_p = *snr_p;
    gsl_matrix_complex_free(Rxx);
    gsl_matrix_complex_free(invR);
    gsl_matrix_complex_free(AA);
    gsl_matrix_complex_free(tempww);
    gsl_matrix_complex_free(ww);
    gsl_matrix_complex_free(w);
    gsl_matrix_complex_free(y);
    gsl_matrix_complex_free(fft_data_mat);
    gsl_matrix_complex_free(in_sort_mat);
    fftwf_destroy_plan(plan);
    return paContinue;
}

void init_stuff(){
    int i,id;
    const PaDeviceInfo *info;
    const PaHostApiInfo *hostapi;
    PaStreamParameters outputParameters, inputParameters;
    w0 = gsl_matrix_complex_alloc(USED_CH, 1);
    w_Intergral_val = gsl_matrix_complex_alloc(USED_CH, 1);
    w_Previous_error = gsl_matrix_complex_alloc(USED_CH, 1);
    gsl_matrix_complex_set_zero(w0);
    gsl_matrix_complex_set_zero(w_Intergral_val);
    gsl_matrix_complex_set_zero(w_Previous_error);

    Pa_Initialize(); // initialize portaudio

    id = Pa_GetDefaultOutputDevice();
    info = Pa_GetDeviceInfo(id);
    hostapi = Pa_GetHostApiInfo(info->hostApi);
    printf("output device [%s] %s\\n",hostapi->name, info->name);
    outputParameters.device = id;
    outputParameters.channelCount = OUTPUT_CHANNEL;
    outputParameters.sampleFormat = paFloat32;
    outputParameters.suggestedLatency = 0;
    outputParameters.hostApiSpecificStreamInfo = NULL; /*no specific info*/

    sleep(0.5);
    id = Pa_GetDefaultInputDevice();
    info = Pa_GetDeviceInfo(id); /* get chosen device information struct */
    hostapi = Pa_GetHostApiInfo(info->hostApi); /* get host API struct */
    printf("input device [%s] %s\\n",
    hostapi->name, info->name);
    inputParameters.device = id; /* chosen device id */
    inputParameters.channelCount = INPUT_CHANNEL; /* stereo input */
    inputParameters.sampleFormat = paFloat32; /* 32 bit float input */
    inputParameters.suggestedLatency = 0;
    inputParameters.hostApiSpecificStreamInfo = NULL;

    Pa_OpenStream(
        &audioStream,
        &inputParameters,       // output parameters
        &outputParameters,      // input parameters
        SAMPLING_RATE,          // set sampling rate
        FRAME_BLOCK_LEN,        // set frames per buffer
        paClipOff,              // set no clip
        audio_callback,         // callback function
        NULL );                 // provide no data for the callback
    
    Pa_StartStream(audioStream); /* start the callback mechanism */
    printf("running. . . press space bar and enter to exit\\n");
    printf("Latency: %f\\n",info->defaultLowInputLatency);
}

void terminate_stuff(){
    gsl_matrix_complex_free(w_Intergral_val);
    gsl_matrix_complex_free(w_Previous_error);

    Pa_StopStream( audioStream ); /* stop the callback mechanism */
    Pa_CloseStream( audioStream ); /* destroy the audio stream object */
    Pa_Terminate(); /* terminate portaudio */
}

int main(){
    init_stuff();
    while(getchar() != ' ') Pa_Sleep(100);
    terminate_stuff();
    return 0;
}

# complie and link

gcc callback_in_C.c -lportaudio -lgsl -lgslcblas -lfftw3f -lm