?? correlation.h
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/* **************************************************************************************** */
/* correlation.h ,C++ header file used in correlation_gen.gcc */
/* */
/* This file computes the correlation matrices RTx at Tx side */
/* and RRx at Rx side according to the PAS type(uniform, */
/* truncated Gaussian and truncated Laplacian) */
/* */
/* The following functions are included in this file: */
/* */
/* void normalisation_uniform(int cluster_number,float power_lin[],float AS_deg[],float *Q) */
/* void normalisation_gaussian(int cluster_number,float power_lin[],float AS_deg[], */
/* float delta_phi_deg[], float *Q, float *sigma_deg) */
/* void normalisation_laplacian(int cluster_number,float power_lin[],float AS_deg[], */
/* float delta_phi_deg[], float *Q, float *sigma_deg) */
/* cluster_number , the number of clusters */
/* power_lin[] , the power of clusters in linear values */
/* AS_deg[] , the Angular Spread of each cluster */
/* delta_phi_deg , the half domain definition of the PAS,being either 90 or 180 degrees */
/* *Q , the normalization coeffecient of PAS */
/* *sigma_deg[] , used later to derive Rxx_*() and Rxy_*() */
/* The above functions are used to derive the normalization coefficients of the PAS. */
/* */
/* float Rxx_uniform(float d_norm,float phi_0_deg,float AS_deg ) */
/* float Rxx_gaussian(float d_norm,float phi_0_deg,float sigma_deg,float delta_phi_deg) */
/* float Rxx_laplacian(float d_norm,float phi_0_deg,float sigma_deg,float delta_phi_deg) */
/* float Rxy_uniform(float d_norm,float phi_0_deg,float AS_deg ) */
/* float Rxy_gaussian(float d_norm,float phi_0_deg,float sigma_deg,float delta_phi_deg) */
/* float Rxy_laplacian(float d_norm,float phi_0_deg,float sigma_deg,float delta_phi_deg) */
/* d_norm , the spacing between antennas */
/* phi_0_deg , the AoA(Angle-of-Arrival) */
/* AS_deg , the Angular Spread */
/* sigma_deg , result returned by the normalisation_*() functions */
/* delta_phi-deg , the half domain definition of the PAS,being either 90 or 180 degrees */ */
/* The functions Rxx_*() of the above are used to compute the homogeneous part of the */
/* correlation function(between real or imaginary part) */
/* The functions Rxy_*() of the above are used to compute the cross part of the */
/* correlation function(between real and imaginary part) */
/* */
/* float **uniform_real(int N,float spacing,int cluster_number,float amplitude_cluster[], */
/* float phi_deg[],float AS_deg[],float delta_phi_deg[]) */
/* float **gaussian_real(int N,float spacing,int cluster_number,float amplitude_cluster[], */
/* float phi_deg[],float AS_deg[],float delta_phi_deg[]) */
/* float **laplacian_real(int N,float spacing,int cluster_number,float amplitude_cluster[], */
/* float phi_deg[],float AS_deg[],float delta_phi_deg[]) */
/* complex **uniform_cmpx(int N,float spacing,int cluster_number,float amplitude_cluster[], */
/* float phi_deg[],float AS_deg[],float delta_phi_deg[]) */
/* complex **gaussian_cmpx(int N,float spacing,int cluster_number,float amplitude_cluster[],*/
/* float phi_deg[],float AS_deg[],float delta_phi_deg[]) */
/* complex **laplacian_cmpx(int N,float spacing,int cluster_number,float amplitude_cluster[]*/
/* ,float phi_deg[],float AS_deg[],float delta_phi_deg[]) */
/* N , the number of antennas */
/* spacing , the normalized spacing between antennas ,in wavelength */
/* cluster_number , the number of clusters */
/* amplitude_cluster[] , the power of each cluster in linear values */
/* phi_deg[] , AoAs at Rx side or AoDs at Tx side, in degrees */
/* AS_deg[] , the Angular Spread of each cluster */
/* delta_phi_deg , the half domain definition of the PAS,being either 90 or 180 degrees */
/* The *_real functions of the above are used to compute the correlation matrix with */
/* real power coeffecients */
/* The *_cmpx functions of the above are used to compute the correlation matrix with */
/* complex field coeffecients */
/* */
/* Created by : Xu Xiaojun, Zeng Meng */
/* National Communications Lab,UESTC */
/* 16 April 2005 */
/* Revised on : 25 Aptil,10 May, 2005 */
/* Version 1.0 */
/* (c) Xu Xiaojun,ZengMeng 2005, NCL-UESTC */
/* **************************************************************************************** */
#include "float.h" /* function _isnan() in it is used to judge if a number is NaN */
#include "complex.h" /* operation of complex numbers */
#include "numerical_recipes.h" /* functions of numerical recipes */
#define sqrt3 1.7320508
#define sqrt2 1.4142136
#define PI 3.1415926536
/*********************/
/* Uniform PAS */
/*********************/
/********************************/
/* Normalization of uniform PAS */
/********************************/
/** compute the power normalisation coef Q such that the PAS can be regarded as probability distribution **/
void normalisation_uniform(int cluster_number, float power_lin[], float AS_deg[],float *Q)
{
int i,j,k;
float *delta_phi_rad,*b;
float **A;
delta_phi_rad=vector(1,cluster_number);
b = vector(1,cluster_number);
A = matrix(1,cluster_number,1,cluster_number);
/** initialize A=zeros(cluster_number) **/
for(i=1;i<=cluster_number;i++)
{
for(j=1;j<=cluster_number;j++)
A[i][j] = 0.0;
}
/** initialize b=zeros(cluster_number,1) **/
for(j=1;j<=cluster_number;j++)
{
b[j]=0.0;
}
/** set b=[0,0,0.5] **/
b[cluster_number] = 0.5;
/** convert AS from degree to rad **/
for(i=1;i<=cluster_number;i++)
{
delta_phi_rad[i] = (AS_deg[i-1]*PI/180)*sqrt3;
}
if(cluster_number==1)
{
Q[1] = 1/(2*delta_phi_rad[1]);
}
else
{
for(i=1;i<=cluster_number-1;i++)
{
A[i][1] = 1/power_lin[0];
}
for(k=2;k<=cluster_number;k++)
{
A[k-1][k] = (-1.0)/power_lin[k-1];
}
for(i=1;i<=cluster_number;i++)
{
A[cluster_number][i] = delta_phi_rad[i];
}
/** compute AQ=b, and Q is saved in b **/
inverse(A,cluster_number,b);
for(i=1;i<=cluster_number;i++)
{
Q[i] = b[i];
}
}
}
/******************************/
/* Computation of Rxx_uniform */
/******************************/
/** compute the correlation of the real/imaginary parts of signals in the case of uniform PAS
/* at the spacing given by d_norm. **/
/** The PAS is charaterised by the AOA phi_0_deg and by AS AS_deg
/* result is a 1*3 vector, and by toeplitz transformation, it is turned into the desired Rxx **/
float Rxx_uniform(float d_norm,float phi_0_deg,float AS_deg )
{
float D,phi_0_rad,AS_rad,result,delta_phi_uniform_rad,temp_xx_uniform;
int m;
/** Convert parameters from degree to rad **/
D = 2*PI*d_norm;
phi_0_rad = phi_0_deg*PI/180;
AS_rad = AS_deg*PI/180;
delta_phi_uniform_rad = AS_rad*sqrt3;
/** initialisation **/
result = 0.0;
temp_xx_uniform = 1.0;
/** Computation of Rxx **/
m = 0;
while(m<100)
{
m++;
temp_xx_uniform = 2*bessj(2*m,D)*sin(2*m*delta_phi_uniform_rad)*cos(2*m*phi_0_rad)/m;
result += temp_xx_uniform;
}
return result;
}
/******************************/
/* Computation of Rxy_uniform */
/******************************/
/** compute the correlation of the real and imaginary parts of signals in the case of uniform PAS
/* at the spacing given by d_norm. **/
/** The PAS is charaterised by the AOA phi_0_deg and by AS AS_deg
/* result is a 1*3 vector, and by toeplitz transformation, it is turned into the desired Rxy **/
float Rxy_uniform(float d_norm,float phi_0_deg,float AS_deg)
{
float D,phi_0_rad,AS_rad,result,delta_phi_uniform_rad,temp_xx_uniform;
int m;
/** Convert parameters from degree to rad **/
D = 2*PI*d_norm;
phi_0_rad = phi_0_deg*PI/180;
AS_rad = AS_deg*PI/180;
delta_phi_uniform_rad = AS_rad*sqrt3;
/** Initialization **/
result = 4*bessj1(D)*sin(delta_phi_uniform_rad)*sin(phi_0_rad);;
temp_xx_uniform = 1.0;
/** Computation of Rxy **/
m = 0;
while(m<100)
{
m++;
temp_xx_uniform = 4*bessj(2*m+1,D)*sin((2*m+1)*delta_phi_uniform_rad)*sin((2*m+1)*phi_0_rad)/(2*m+1);
result += temp_xx_uniform;
}
return result;
}
/******************************/
/* correlation of real matrix */
/******************************/
float **uniform_real(int N,float spacing,int cluster_number,float amplitude_cluster[],float phi_deg[],
float AS_deg[],float delta_phi_deg[])
{
int i,j,k;
float *d_norm;
d_norm = vector(1,N);
/** Computation of d_norm in case of ULA **/
for(i=1;i<=N;i++)
d_norm[i] = (i-1)*spacing;
float *Rxx,*Rxy;
float *temp;
float result_x,result_y;
float *Q;
float **R;
Rxx = vector(1,N);
Rxy = vector(1,N);
temp = vector(1,N);
Q = vector(1,cluster_number);
R = matrix(1,N,1,N);
/** Computation of real correlation of uniform PAS **/
if(N==1)
{
R[N][N] = 1;
}
else
{
for(i=1;i<=N;i++)
{
Rxx[i] = bessj0(2*PI*d_norm[i]);
Rxy[i] = 0.0;
}
normalisation_uniform(cluster_number,amplitude_cluster,AS_deg,Q);
for(i=1;i<=N;i++)
{
for(k=1;k<=cluster_number;k++)
{
result_x = Rxx_uniform(d_norm[i],phi_deg[k-1],AS_deg[k-1]);
result_y = Rxy_uniform(d_norm[i],phi_deg[k-1],AS_deg[k-1]);
Rxx[i] += Q[k]*result_x;
Rxy[i] += Q[k]*result_y;
}
}
for(i=1;i<=N;i++)
{
temp[i] = Rxx[i]*Rxx[i]+Rxy[i]*Rxy[i];
}
/** Toeplitz operation **/
for(i=1;i<=N;i++)
for(j=i,k=1;j<=N;j++,k++)
{
R[i][j] = temp[k];
R[j][i] = R[i][j];
}
}
return R;
}
/*********************************/
/* Correlation of complex matrix */
/*********************************/
complex **uniform_cmpx(int N,float spacing,int cluster_number,float amplitude_cluster[],float phi_deg[],
float AS_deg[],float delta_phi_deg[])
{
int i,j,k;
float *d_norm;
d_norm = vector(1,N);
for(i=1;i<=N;i++)
{
d_norm[i] = (i-1)*spacing;
}
float *Rxx,*Rxy;
complex *temp;
float result_x,result_y,*Q;
complex **R;
Rxx = vector(1,N);
Rxy = vector(1,N);
temp = cvector(1,N);
Q = vector(1,cluster_number);
R = cmatrix(1,N*N,1,N*N);
/** Compute compelx correlation of uniform PAS **/
if(N==1)
{
R[N][N] = complex(1.0,0.0);
}
else
{
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