分式规划和波束成形（MATLAB代码）Dinkelbach_type_algorthm

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我是靠谱客的博主殷勤画板，最近开发中收集的这篇文章主要介绍分式规划和波束成形（MATLAB代码）Dinkelbach_type_algorthm，觉得挺不错的，现在分享给大家，希望可以做个参考。

概述

Dinkelbach_type_algorthm

q1=20
q2=30
q3=35
q4=28
N=4
m=4
k=1

h=abs(rand(N,m+2))
g=abs(rand(N,m+2))
v=abs(randn(N,1,k))
x=abs(randn(N,m,k))
t2=1
while t2~=0
 for i=1:m
    temp0=0
    for j=1:m
        if i==j
            continue
        else
            s=temp0+h(:,i)'*x(:,j,k)*x(:,j,k)'*h(:,i)
            temp0=s
        end
    end
    u(i)=(-h(:,i)'*x(:,i,k)*x(:,i,k)'*h(:,i))/(s+g(:,i)'*v(:,:,k)*v(:,:,k)'*g(:,i))
 end
u_value(k)=max(u)




cvx_begin sdp
variable W(N,N,m+1) complex hermitian
variable V(N,N) complex hermitian 
variable t 
minimize t;
subject to;

temp1=0
for i=1:m+1
            s1=trace(W(:,:,i))+temp1
            temp1=s1
             W(:,:,i) == hermitian_semidefinite(N)
end
temp1<=q1                        %信息发射端的功率小于q1
trace(V(:,:))<=q2  
 V  == hermitian_semidefinite(N) %是半定矩阵
 
 temp2=0
 for i=1:m+1
s2= trace( h(:,4)'*W(:,:,i)*h(:,4))+temp2
temp2=s2
 end
 temp2+trace(g(:,4)'*V(:,:)*g(:,4))>=q3
 
 temp3=0
  for i=1:m+1
s3=  trace(h(:,5)'*W(:,:,i)*h(:,5))+temp3
temp3=s3
 end
temp3+trace(g(:,5)'*V(:,:)*g(:,5))<=q4



for i=1:m
    
    temp5=0
    for j=1:m
        if i==j
            continue
        else
           
            s2=-h(:,i)'*W(:,:,j)*h(:,i)+temp5
            temp5=s2
        end
    end
 trace(s2*u_value(k))-trace(h(:,i)'*W(:,:,i)*h(:,i))-trace(g(:,i)'*V(:,:)*g(:,i)*u_value(k))<=t
end
cvx_end 
mine(k)=cvx_optval
k=k+1
for i=1:m
    for j=1:N
    a(j)=sqrt(W(j,j,i))
    end
    b(:,i)=a'
end
x(:,:,k)=b
for i=1:N
    c(i)=sqrt(V(i,i))
end
v(:,:,k)=c'

t2(k-1)=-cvx_optval
if k<=18
    continue
else
    break
end

end

对原问题进行一点改进：

Dinkelbach_type_2algorthm

q1=20
q2=30
q3=35
q4=28
N=4
m=4
k=1

h=abs(rand(N,m+2))
g=abs(rand(N,m+2))
v=abs(randn(N,1,k))
x=abs(randn(N,m,k))
t2=1
while t2~=0
 for i=1:m
    temp0=0
    for j=1:m
        if i==j
            continue
        else
            s=temp0+h(:,i)'*x(:,j,k)*x(:,j,k)'*h(:,i)
            temp0=s
        end
    end
    u(i)=(-h(:,i)'*x(:,i,k)*x(:,i,k)'*h(:,i))/(s+g(:,i)'*v(:,:,k)*v(:,:,k)'*g(:,i))
 end
u_value(k)=max(u)




cvx_begin sdp
variable W(N,N,m+1) complex hermitian
variable V(N,N) complex hermitian 
variable t 
minimize t;
subject to;

temp1=0
for i=1:m+1
            s1=trace(W(:,:,i))+temp1
            temp1=s1
             W(:,:,i) == hermitian_semidefinite(N)
end
temp1<=q1                        %信息发射端的功率小于q1
trace(V(:,:))<=q2  
 V  == hermitian_semidefinite(N) %是半定矩阵
 
 temp2=0
 for i=1:m+1
s2= trace( h(:,4)'*W(:,:,i)*h(:,4))+temp2
temp2=s2
 end
 temp2+trace(g(:,4)'*V(:,:)*g(:,4))>=q3
 
 temp3=0
  for i=1:m+1
s3=  trace(h(:,5)'*W(:,:,i)*h(:,5))+temp3
temp3=s3
 end
temp3+trace(g(:,5)'*V(:,:)*g(:,5))<=q4



for i=1:m
    temp4=0
    temp5=0
    for j=1:m
        if i==j
            continue
        else
            s1=temp4+h(:,i)'*x(:,j,k)*x(:,j,k)'*h(:,i)
            temp4=s1
            s2=-h(:,i)'*W(:,:,j)*h(:,i)+temp5
            temp5=s2
        end
    end
 trace(s2*u_value(k))-trace(h(:,i)'*W(:,:,i)*h(:,i))-trace(g(:,i)'*V(:,:)*g(:,i)*u_value(k))<=trace((s1+g(:,i)'*v(:,:,k)*v(:,:,k)'*g(:,i)))*t
end
cvx_end 
mine(k)=cvx_optval
k=k+1
for i=1:m
    for j=1:N
    a(j)=sqrt(W(j,j,i))
    end
    b(:,i)=a'
end
x(:,:,k)=b
for i=1:N
    c(i)=sqrt(V(i,i))
end
v(:,:,k)=c'

t2(k-1)=-cvx_optval
if k<=18
    continue
else
    break
end

end