中文名
瑞利分布
外文名
Rayleigh Distribution
所属领域
通信
应用
无线网络
在随机过程里，正弦（余弦）信号加窄带高斯随机信号的包络服从莱斯分布。莱斯分布指毕也称作广义瑞利分布。
阴影效应（Shadow Effect）：在无线通信系统中，移动台在运动的情况下，由唯察芹于大型建筑物和其他物体对电波的传输路径的阻挡而在传播接收区域上形成半盲区，从而形成电磁场阴影，这种没缓随移动台位置的不断变化而引起的接收点场强中值的起伏变化叫做阴影效应。阴影效应是产生慢衰落的主要原因。
下面共有两个程序，程序2 加入了图形显示程序竖握1
这个程序就是你要的。
# include "stdio.h"
# include "math.h"
# include "stdlib.h"
# include "math.h"
# include "dos.h"
# define MAX_N 3000 /*这个值为N可以定义的最大长度*/
# define N 100 /*产生随机序列的点数，注意不要大于MAX_N*/
/*产生均匀分布的随机变量*/
void randa(float *x,int num)
/*产生瑞利分布的随机变量*/
void randr(float *x,int num)
/*产生标准余袜庆高斯分布的随机变量*/
void randn(float *x,int num)
/*产生莱斯分布的随机变量*/
void randl(float *x, float a, float b, int num)
void fshow(char *name,float *x,int num)
main()
{
float x[N]
int i
/*
randa(&x,N)
randr(&x,N)
randl(&x,10,10,N)
*/
randn(&x,N)
/*此时x[N]就是所需要的高斯分布的序列*/
/*显示该序列*/
fshow("x",&x,N)
getch()
}
void randa(float *x,int num)
{
int i
struct time stime
unsigned seed
gettime(&stime)
seed=stime.ti_hund*stime.ti_min*stime.ti_hour
srand(seed)
for(i=0i<numi++)
{
x[i]=rand()
x[i]=x[i]/好租32768
}
}
void randr(float *x,int num)
{
float x1[MAX_N]
int i
struct time stime
unsigned seed
gettime(&stime)
seed=stime.ti_hund*stime.ti_min*stime.ti_hour
srand(seed)
for(i=0i<numi++)
{
x1[i]=rand()
x[i]=x1[i]/32768
x[i]=sqrt(-2*log(x[i]))
}
}
void randn(float *x,int num)
{
float x1[MAX_N],x2[MAX_N]
int i
struct time stime
unsigned seed
gettime(&stime)
seed=stime.ti_hund*stime.ti_min*stime.ti_hour
srand(seed)
for(i=0i<numi++)
{
x1[i]=rand()
x2[i]=rand()
x1[i]=x1[i]/32768
x2[i]=x2[i]/32768
x[i]=sqrt(-2*log(x1[i]))*cos(x2[i]*M_PI)
}
}
void randl(float *x, float a, float b, int num)
{
float x1[MAX_N],x2[MAX_N]
float temp[MAX_N]
int i
struct time stime
unsigned seed
gettime(&stime)
seed=stime.ti_hund*stime.ti_min*stime.ti_hour
srand(seed)
for(i=0i<numi++)
{
x1[i]=rand()
x2[i]=rand()
x1[i]=x1[i]/32768
x2[i]=x2[i]/32768
temp[i]=sqrt(-2*log(x1[i]))*cos(x2[i]*M_PI)
x2[i]=sqrt(-2*log(x1[i]))*sin(x2[i]*M_PI)
x1[i]=temp[i]
x[i]=sqrt((a+x1[i])*(a+x1[i])+(b+x2[i])*(b+x2[i]))
}
}
void fshow(char *name,float *x,int num)
{
int i,sign,L
float temp
printf("\n")
printf(name)
printf(" = ")
L=6
/*按照每行6个数据的格式显示*/
for(i=0i<numi++)
{
temp=i/L
sign=temp
if((i-sign*L)==0) printf("\n")
if(x[i]>0) printf(" %f ",x[i])
else printf("%f ",x[i])
}
}
程序 2
以下程序加入了图形显示的效果，因此更加直观，你可以参考一下。
/* 作者 Leo_nanjing
时间 2008.5.10
功能 生成各种分布的随机变量,并显示
*/
# include "stdio.h"
# include "math.h"
# include "graphics.h"
# include "math.h"
# include "dos.h"
# define MAX_N 3000
# define N 1000
void randa(float *x,int num)
void randr(float *x,int num)
void randn(float *x,int num)
void randl(float *x, float a, float b, int num)
void fshow(char *name,float *x,int num)
/*用于图形显示的部分*/
void init_graphic(unsigned color)
void plotxy(float *x, float *y, int num,int mode)
void plot(float *y,int num, int mode)
float max(float *x, int num)
float min(float *x, int num)
/*画出该随机序列的分布函数曲线*/
void plotpdf(float *x,int num,int part,int mode)
main()
{
float x[N]
int i
randn(&x,N)
fshow("x",&x,N)
getch()
/*以下为图形显示部分*/
init_graphic(0)
/*显示随机序列*/
plot(&x,N,1)
getch()
/*显示其分布函数*/
plotpdf(&x,N,20,0)
getch()
}
void randa(float *x,int num)
{
int i
struct time stime
unsigned seed
gettime(&stime)
seed=stime.ti_hund*stime.ti_min*stime.ti_hour
srand(seed)
for(i=0i<numi++)
{
x[i]=rand()
x[i]=x[i]/32768
}
}
void randr(float *x,int num)
{
float x1[MAX_N]
int i
struct time stime
unsigned seed
gettime(&stime)
seed=stime.ti_hund*stime.ti_min*stime.ti_hour
srand(seed)
for(i=0i<numi++)
{
x1[i]=rand()
x[i]=x1[i]/32768
x[i]=sqrt(-2*log(x[i]))
}
}
void randn(float *x,int num)
{
float x1[MAX_N],x2[MAX_N]
int i
struct time stime
unsigned seed
gettime(&stime)
seed=stime.ti_hund*stime.ti_min*stime.ti_hour
srand(seed)
for(i=0i<numi++)
{
x1[i]=rand()
x2[i]=rand()
x1[i]=x1[i]/32768
x2[i]=x2[i]/32768
x[i]=sqrt(-2*log(x1[i]))*cos(x2[i]*M_PI)
}
}
void randl(float *x, float a, float b, int num)
{
float x1[MAX_N],x2[MAX_N]
float temp[MAX_N]
int i
struct time stime
unsigned seed
gettime(&stime)
seed=stime.ti_hund*stime.ti_min*stime.ti_hour
srand(seed)
for(i=0i<numi++)
{
x1[i]=rand()
x2[i]=rand()
x1[i]=x1[i]/32768
x2[i]=x2[i]/32768
temp[i]=sqrt(-2*log(x1[i]))*cos(x2[i]*M_PI)
x2[i]=sqrt(-2*log(x1[i]))*sin(x2[i]*M_PI)
x1[i]=temp[i]
x[i]=sqrt((a+x1[i])*(a+x1[i])+(b+x2[i])*(b+x2[i]))
}
}
void fshow(char *name,float *x,int num)
{
int i,sign,L
float temp
printf("\n")
printf(name)
printf(" = ")
L=6
for(i=0i<numi++)
{
temp=i/L
sign=temp
if((i-sign*L)==0) printf("\n")
if(x[i]>0) printf(" %f ",x[i])
else printf("%f ",x[i])
}
}
/*以下为图形显示的函数*/
void init_graphic(unsigned color)
{
int graphicdriver,graphicmode
graphicdriver=DETECT
graphicmode=1
initgraph(&graphicdriver,&graphicmode,"E:\\turboc2\\")
setbkcolor(color)
}
void plotxy(float *x, float*y, int num,int mode)
{
int i
float max_x,max_y,min_x,min_y
float x0,y0,x1,y1
clrscr(0)
cleardevice()
setbkcolor(0)
max_x=max(x,num)
max_y=max(y,num)
min_x=min(x,num)
min_y=min(y,num)
setlinestyle(0,2,1)
line(65,35,65,445)
line(65,445,575,445)
setlinestyle(3,0,1)
line(65,35,575,35)
line(575,35,575,445)
setlinestyle(0,2,1)
if(max_x==min_x)
x0=320
else
x0=(x[0]-min_x)*500/(max_x-min_x)+70
if(max_y==min_y)
y0=240
else
y0=480-((y[0]-min_y)*400/(max_y-min_y)+40)
if(mode==0) circle(x0,y0,2)
for(i=1i<numi++)
{
if(max_x==min_x)
x1=320
else
x1=(x[i]-min_x)*500/(max_x-min_x)+70
if(max_y==min_y)
y1=240
else
y1=480-((y[i]-min_y)*400/(max_y-min_y)+40)
if(mode==0) circle(x1,y1,2)
line(x0,y0,x1,y1)
x0=x1y0=y1
}
printf("\n\n")
printf("%f",max_y)
printf("\n\n\n\n\n\n\n\n\n\n")
printf("\n\n\n")
printf("%f",(max_y+min_y)/2)
printf("\n\n\n\n\n\n\n\n\n\n")
printf("\n\n")
printf("%f",min_y)
printf("\n %f",min_x)
printf(" ")
printf("%f",(max_x+min_x)/2)
printf(" ")
printf("%f",max_x)
}
void plot(float*y, int num,int mode)
{
int i
float max_x,max_y,min_x,min_y
float x0,y0,x1,y1
float x[MAX_N]
clrscr(0)
cleardevice()
setbkcolor(0)
for(i=0i<numi++) x[i]=i+1
max_x=max(x,num)
max_y=max(y,num)
min_x=min(x,num)
min_y=min(y,num)
setlinestyle(0,2,1)
line(65,35,65,445)
line(65,445,575,445)
setlinestyle(3,0,1)
line(65,35,575,35)
line(575,35,575,445)
setlinestyle(0,2,1)
if(max_x==min_x)
x0=320
else
x0=(x[0]-min_x)*500/(max_x-min_x)+70
if(max_y==min_y)
y0=240
else
y0=480-((y[0]-min_y)*400/(max_y-min_y)+40)
if(mode==0) circle(x0,y0,2)
for(i=1i<numi++)
{
if(max_x==min_x)
x1=320
else
x1=(x[i]-min_x)*500/(max_x-min_x)+70
if(max_y==min_y)
y1=240
else
y1=480-((y[i]-min_y)*400/(max_y-min_y)+40)
if(mode==0) circle(x1,y1,2)
line(x0,y0,x1,y1)
x0=x1y0=y1
}
printf("\n\n")
printf("%f",max_y)
printf("\n\n\n\n\n\n\n\n\n\n")
printf("\n\n\n")
printf("%f",(max_y+min_y)/2)
printf("\n\n\n\n\n\n\n\n\n\n")
printf("\n\n")
printf("%f",min_y)
printf("\n %f",min_x)
printf(" ")
printf("%f",(max_x+min_x)/2)
printf(" ")
printf("%f",max_x)
}
void plotpdf(float *x,int num,int part,int mode)
{
int i,j
float max_x,min_x,round,deltax,up,down,sum
float xl[MAX_N],yl[MAX_N]
sum=0
max_x=max(x,num)
min_x=min(x,num)
round=max_x-min_x
deltax=round/part
xl[0]=min_x
for(i=1i<=parti++)
{
xl[i]=min_x+deltax*i
yl[i-1]=0
up=xl[i]
down=xl[i-1]
for(j=0j<numj++)
{
if((x[j]<up) &&(x[j]>=down)) yl[i-1]=yl[i-1]+1
}
yl[i-1]=yl[i-1]/num/deltax
}
for(i=0i<parti++) sum=sum+yl[i]
plotxy(&xl,&yl,part,mode)
}
float max(float *x, int num)
{
int i
float max
max=x[0]
for(i=1i<numi++)
{
if(x[i]>max) max=x[i]
}
return max
}
float min(float *x, int num)
{
int i
float min
min=x[0]
for(i=1i<numi++)
{
if(x[i]<min) min=x[i]
}
return min
}
%----------Input Section----------------
N=1000000 %Number of samples to generate
variance = 1% Variance of underlying Gaussian random variables
%---------------------------------------
%Independent Gaussian random variables with zero mean and unit variance
x = randn(1, N)
y = randn(1, N)
%Rayleigh fading envelope with the desired variance
r = sqrt(variance*(x.^2 + y.^2))
%Define bin steps and range for histogram plotting
step = 0.1range = 0:step:5
%Get histogram values and approximate it to get the pdf curve
h = hist(r, range)
approxPDF = h/(step*sum(h))%Simulated PDF from the x and y samples
%Theoritical PDF from the Rayleigh Fading equation
theoretical = (range/variance).*exp(-range.^2/(2*variance))
plot(range, approxPDF,'b*'耐吵, range, theoretical,'r')
title('方差1.0时瑞利悔亩巧概率密度函数仿真值和理论值')
legend('概率密度仿真碧键值','概率密度函数理论值')
xlabel('r')
ylabel('P(r)')
grid
%PDF of phase of the Rayleigh envelope
theta = atan(y./x)
figure(2)
hist(theta)%Plot histogram of the phase part
%Approximate the histogram of the phase part to a nice PDF curve
[counts,range] = hist(theta,100)
step=range(2)-range(1)
approxPDF = counts/(step*sum(counts))%Simulated PDF from the x and y samples
bar(range, approxPDF,'b')
hold on
plotHandle=plot(range, approxPDF,'r')
set(plotHandle,'LineWidth',3.5)
axis([-2 2 0 max(approxPDF)+0.2])
hold off
title('瑞利概率密度函数相位分布仿真 ')
xlabel('\theta ')
ylabel('P(\theta)')
grid
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