exp-svm.m

通常情况下是线性的分类,但在复杂情况下,要把他转换到另一空间来,以便线性的分类, SVM有其优势,还能做非线性的波束形成.

close all;
clear all;
N=5;
M=8;
j=sqrt(-1);
len=100;

theta=[-45*pi/180,-30*pi/180,0*pi/180,10*pi/180,40*pi/180];
s0=2*(rand(1,len)>0.5)-1;
s1=2*(rand(1,len)>0.5)-1;
s2=2*(rand(1,len)>0.5)-1;
s3=2*(rand(1,len)>0.5)-1;
s4=2*(rand(1,len)>0.5)-1;

for i=1:len
   x_bpsk1(i)=sqrt(10.^(-5/10))*s0(i);
    x_bpsk2(i)=sqrt(10.^(8/10))*s1(i);
     x_bpsk3(i)=sqrt(10.^(5/10))*s2(i);
      x_bpsk4(i)=sqrt(10.^(5/10))*s3(i); 
       x_bpsk5(i)=sqrt(10.^(-8/10))*s4(i);
end
s=[x_bpsk1;x_bpsk2;x_bpsk3;x_bpsk4;x_bpsk5];
for i=1:M
    for k=1:N
        A1(i,k)=exp(-j*pi*(i-1)*sin(theta(k)));%array responce
    end
end

rp.mean_v  = 0; % mean of complex-valued AWGN
rp.var_v   = 1; % variance of complex-valued AWGN
vr = sqrt(rp.var_v/2) * randn(M,len) + rp.mean_v;
vi = sqrt(rp.var_v/2) * randn(M,len) + rp.mean_v;
v  = vr + j*vi;
X_nn=A1*s;
X=X_nn+v;
L=100;
a=zeros(1,L);
C=0.1;
y=s2;
Xt=zeros(M.^2,L);
lb=1;
for i=1:L
    sum=0;
   for k=1:L
       K=exp(-((X(:,i)-X(:,k))'*(X(:,i)-X(:,k)))/(lb.^2));
        sum=sum+a(k)*y(k)*K;
    end
    u=1/exp(-((X(:,i)-X(:,i))'*(X(:,i)-X(:,i)))/(lb.^2));
    a(i)=a(i)+u*(1-y(i)*sum);
    if a(i)<0
        a(i)=0;
    else if a(i)>C
            a(i)=C;
        end
    end
end
max=0;
min=0;

for i=1:L%得到-1和1出现的首位置
    if y(i)==-1
        r=i;break
    end
end
for i=1:L
     if y(i)==1
         p=i;break
     end
 end
 K1=0;
 K2=0;
for i=1:L%max/min初始化
        K1=exp(-((X(:,i)-X(:,r))'*(X(:,i)-X(:,r)))/(lb.^2));
        K2=exp(-((X(:,i)-X(:,p))'*(X(:,i)-X(:,p)))/(lb.^2));
        max=max+a(i)*y(i)*K1;
        min=min+a(i)*y(i)*K2;
 end
 
 
for i=1:L
     sum2=0;
    for k=1:L
        K=exp(-((X(:,i)-X(:,k))'*(X(:,i)-X(:,k)))/(lb.^2));
        sum2=sum2+a(k)*y(k)*K;
    end
    if y(i)==-1&&max<sum2
        max=sum2;
    end
    if y(i)==1&&min>sum2
        min=sum2;
    end
end
b=-(max+min)/2;
f=zeros(1,L);%输出BPSK信号
for i=1:L
    sum=0;
    for k=1:L
         K=exp(-((X(:,i)-X(:,k))'*(X(:,i)-X(:,k)))/(lb.^2));
        sum=sum+a(k)*y(k)*K;
    end
    f(i)=sign(real(sum+b));
end
y_to_f=0;
for i=1:L%求判断正确的BPSK信号个数
    if f(i)==y(i)
        y_to_f=y_to_f+1;
    end
end
% w=zeros(9,1);
% i=1;
% for i=1:L
%    w=w+a(i)*y(i)*Xt(:,i);
% end

sita1=[-90:2:90];
sita=sita1*pi/180;
G_sita=zeros(1,length(sita));
a_sita_i=zeros(M,length(sita));
for i=1:length(sita)
     Gsita=0;
     a_sita_i(:,i)=[1;exp(-j*pi*sin(sita(i)));exp(-j*2*pi*sin(sita(i)));exp(-j*3*pi*sin(sita(i)));exp(-j*4*pi*sin(sita(i)));exp(-j*5*pi*sin(sita(i)));exp(-j*6*pi*sin(sita(i)));exp(-j*7*pi*sin(sita(i)))];
       for k=1:L
         K=exp(-((a_sita_i(:,i)-X(:,k))'*(a_sita_i(:,i)-X(:,k)))/(lb.^2));
         Gsita= Gsita+a(k)*y(k)*K;
      end
     G_sita(i)=Gsita;
    
end


figure;
plot(sita1,10*log10(abs(G_sita)));
grid on ;