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Copy pathSecondaryUserFDJointAllocVer2.m
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SecondaryUserFDJointAllocVer2.m
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classdef SecondaryUserFDJointAlloc < handle
%This class defines the properties and methods of the secondary user class
% OptX function optimizes w.r.t channel allocation
% OptP function optimizes w.r.t power allocation
% OptGamma function optimizes w.r.t the interference and noise
% dualMaster function optimizes w.r.t the price of the QoS constraint
% PriceOfSUInterRecevd function optimizes w.r.t the interference
% received at the given SU
properties
SUIndex %index of the secondary user pair
gainVecSUTrnsSURecv % channel gain from the given transmitting SU to its own receiver
gainVecSUTrnsMSRecv % max channel gains from the given transmitting SUs to the monitoring stations
X % channel allocation vec
P % Power allocation Vec
GammaInit % interference vec: addition of both SU int and PU int
alpha % fraction of residual power after SIC
maxiterations % maximum number of iterations
Pmax % Max power usable at an SU
J % interference caused at the PU by SUs in the previous slot
hs % the gain between the SU Tx antenna and Rx antenna
IntThreshold %interference threshold at PU
RxSensitivity % minimum detectable sinr at detector
rate %data rate of the pair
end
methods
function SU = SecondaryUserFDJointAlloc(SUIndex,gainVecSUTrnsSURecv,gainVecSUTrnsMSRecv,...
GammaInit,Pmax,maxiterations,hs,alpha,SUIntAtPU,IntThreshold,RxSensitivity)
SU.SUIndex = SUIndex;
SU.gainVecSUTrnsSURecv = gainVecSUTrnsSURecv;
SU.gainVecSUTrnsMSRecv = gainVecSUTrnsMSRecv;
SU.X = zeros(size(GammaInit,1)*2,1);
SU.P = zeros(size(GammaInit,1)*2,1);
SU.GammaInit = GammaInit;
SU.Pmax = Pmax;
SU.maxiterations = maxiterations;
SU.hs = hs;
SU.alpha = alpha;
SU.J = SUIntAtPU;
SU.IntThreshold = IntThreshold*ones(size(GammaInit,1),1);
SU.RxSensitivity = RxSensitivity;
SU.rate = 0;
end
function optXPGamma(SU)
numChannels =size(SU.GammaInit,1);
n=numChannels;
Xinit = ones(numChannels*2,1);
epsilon=0.1;
cbvPrev=-inf;
coeff = [SU.gainVecSUTrnsSURecv(2,SU.SUIndex), -SU.RxSensitivity*SU.hs*SU.alpha];
coeffMat = zeros(n*2);
rhsMat = zeros(n*2,1);
for i=1:2*n
if mod(i,2)~= 0
coeffMat(i,i:i+1)= coeff;
rhsMat(i) = SU.GammaInit(floor(i/2)+1,1);
else
coeffMat(i,i-1:i)= [-SU.RxSensitivity*SU.hs*SU.alpha, SU.gainVecSUTrnsSURecv(2,SU.SUIndex)];
rhsMat(i) = SU.GammaInit(i/2,2);
end
end
pfeasible = coeffMat\rhsMat;
totalPower = zeros(2,n);
powerUpperbound = zeros(2*n,1);
for i=1:n
totalPower(2,i)=pfeasible((i-1)*2+1); % group B
totalPower(1,i)=pfeasible((i)*2);% group A
end
if sum(totalPower(1,:))<=SU.Pmax && sum(totalPower(2,:))<=SU.Pmax
isFeasible = 1;
else
isFeasible = 0;
end
intAtPU=totalPower(1,:)*SU.gainVecSUTrnsMSRecv(1,1)+totalPower(2,:)*SU.gainVecSUTrnsMSRecv(2,1);
if isFeasible && all(intAtPU<=max(SU.IntThreshold'-SU.J',0))
isFeasible = 1;
else
isFeasible = 0;
end
A = zeros(3*n+2,2*n);
AUtopia = zeros(2*n,1);
b = zeros(3*n+2,1);
bUtopia = zeros(2*n,1);
xNew = zeros(2*n,1);
SU.X=zeros(2*n,1);
Ired = eye(n);
%% integer linear program
for iterations=1:100
f = zeros(1,2*n);
for i=1:n
for theta=1:2
if theta==2
f(1,(i-1)*2+1)= log2(1+totalPower(theta,i)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)/(SU.GammaInit(i,1)+totalPower(1,i)*SU.hs*SU.alpha));
% Xinit(i*2,1)*(SU.GammaInit(i,2)+Xinit((i-1)*2+1,1)*totalPower(theta,i)*SU.hs*SU.alpha)...
% /(SU.GammaInit(i,2)+Xinit((i-1)*2+1,1)*totalPower(theta,i)*SU.hs*SU.alpha+totalPower(1,i)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))...
% *totalPower(1,i)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)/((SU.GammaInit(i,2)+Xinit((i-1)*2+1,1)*totalPower(theta,i)*SU.hs*SU.alpha)^2) ...
% *totalPower(theta,i)*SU.hs*SU.alpha + log2(1+totalPower(theta,i)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)/(SU.GammaInit(i,1)+Xinit(i*2,1)*totalPower(1,i)*SU.hs*SU.alpha));
A((i-1)*2+1,(i-1)*2+1)= SU.RxSensitivity;
b((i-1)*2+1,1) =totalPower(theta,i)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)/(SU.GammaInit(i,1)+totalPower(1,i)*SU.hs*SU.alpha);
%
AUtopia((i-1)*2+1,1) = SU.gainVecSUTrnsMSRecv(2,1);
bUtopia((i-1)*2+1,1)= max(SU.IntThreshold(i,1)-SU.J(i,1),0);
else
f(1,i*2)= log2(1+totalPower(theta,i)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)/(SU.GammaInit(i,2)+totalPower(2,i)*SU.hs*SU.alpha));
% Xinit((i-1)*2+1,1)*(SU.GammaInit(i,1)+Xinit(i*2,1)*totalPower(theta,i)*SU.hs*SU.alpha)...
% /(SU.GammaInit(i,1)+Xinit(i*2,1)*totalPower(theta,i)*SU.hs*SU.alpha+totalPower(2,i)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))...
% *totalPower(2,i)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)/((SU.GammaInit(i,1)+Xinit(i*2,1)*totalPower(theta,i)*SU.hs*SU.alpha)^2)...
% *totalPower(theta,i)*SU.hs*SU.alpha + log2(1+totalPower(theta,i)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)/(SU.GammaInit(i,2)+Xinit((i-1)*2+1,1)*totalPower(2,i)*SU.hs*SU.alpha));
% A(i*2+2,i*2)= SU.RxSensitivity;
% b(i*2+2,1) = totalPower(theta,i)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)/(SU.GammaInit(i,2)+totalPower(2,i)*SU.hs*SU.alpha);
AUtopia(i*2,1) = SU.gainVecSUTrnsMSRecv(1,1);
bUtopia(i*2,1)= max(SU.IntThreshold(i,1)-SU.J(i,1),0);
end
end
A(2*n+i+2,(i-1)*2+1:(i-1)*2+2) = [totalPower(2,i)*SU.gainVecSUTrnsMSRecv(2,1),totalPower(1,i)*SU.gainVecSUTrnsMSRecv(1,1)];
b(2*n+i+2,1)=max(SU.IntThreshold(i,1)-SU.J(i,1),0);
end
% A(1,:)=-kron(ones(1,n),[1,0]);
% A(2,:)=-kron(ones(1,n),[0,1]);
% b(1:2,1) = 0;
A(1,:)=kron(totalPower(1,:),[0,1]);
A(2,:)=kron(totalPower(2,:),[1,0]);
b(1:2,1) = SU.Pmax;
% intcon = 1:2*n;
% lb=0;
% ub=1;
xNew = bintprog(-f,A,b,[],[],Xinit);
if norm(Xinit-xNew)<0.1
break;
end
Xinit=xNew;
end
%%lower and the upper bound of power
boxesupperbound = bUtopia./AUtopia.*xNew;
GammaInitlinear=[SU.GammaInit(:,1);SU.GammaInit(:,2)];
SU.P = zeros(2*n,1);
for i=1:n
powerUpperbound(n+i,1)=max(boxesupperbound((i-1)*2+1),0); % group B
powerUpperbound(i,1)=max(boxesupperbound((i)*2),0);% group A
SU.P(n+i,1)=max(pfeasible((i-1)*2+1),0); % group B
SU.P(i,1)=max(pfeasible((i)*2),0);% group A
SU.X(n+i,1)=xNew((i-1)*2+1); % group B
SU.X(i,1)=xNew(i*2); % group A
end
if isFeasible
cub = prod([(GammaInitlinear(1:n)+powerUpperbound(1:n)*SU.hs*SU.alpha+powerUpperbound(n+1:end)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(1:n)+powerUpperbound(1:n)*SU.hs*SU.alpha); ...
(GammaInitlinear(n+1:end)+powerUpperbound(n+1:end)*SU.hs*SU.alpha+powerUpperbound(1:n)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(n+1:end)+powerUpperbound(n+1:end)*SU.hs*SU.alpha)]);
cbv = prod([(GammaInitlinear(1:n)+SU.P(1:n)*SU.hs*SU.alpha+SU.P(n+1:end)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(1:n)+SU.P(1:n)*SU.hs*SU.alpha); ...
(GammaInitlinear(n+1:end)+SU.P(n+1:end)*SU.hs*SU.alpha+SU.P(1:n)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(n+1:end)+SU.P(n+1:end)*SU.hs*SU.alpha)]);
SU.rate = log2(cbv);
else
pfeasible = pfeasible.*xNew;
for i=1:n
SU.P(n+i,1)=max(pfeasible((i-1)*2+1),0); % group B
SU.P(i,1)=max(pfeasible((i)*2),0);% group A
end
%cub = prod([(GammaInitlinear(1:n)+powerUpperbound(1:n)*SU.hs*SU.alpha+powerUpperbound(n+1:end)*SU.gainVecSUTrnsSURecv)./(GammaInitlinear(1:n)+powerUpperbound(1:n)*SU.hs*SU.alpha); ...
% (GammaInitlinear(n+1:end)+powerUpperbound(n+1:end)*SU.hs*SU.alpha+powerUpperbound(1:n)*SU.gainVecSUTrnsSURecv)./(GammaInitlinear(n+1:end)+powerUpperbound(n+1:end)*SU.hs*SU.alpha)]);
cbv = prod([(GammaInitlinear(1:n)+SU.P(1:n)*SU.hs*SU.alpha+SU.P(n+1:end)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(1:n)+SU.P(1:n)*SU.hs*SU.alpha); ...
(GammaInitlinear(n+1:end)+SU.P(n+1:end)*SU.hs*SU.alpha+SU.P(1:n)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(n+1:end)+SU.P(n+1:end)*SU.hs*SU.alpha)]);
SU.rate = log2(cbv);
end
cub = prod([(GammaInitlinear(1:n)+powerUpperbound(1:n)*SU.hs*SU.alpha+powerUpperbound(n+1:end)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(1:n)+powerUpperbound(1:n)*SU.hs*SU.alpha); ...
(GammaInitlinear(n+1:end)+powerUpperbound(n+1:end)*SU.hs*SU.alpha+powerUpperbound(1:n)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(n+1:end)+powerUpperbound(n+1:end)*SU.hs*SU.alpha)]);;
boxeslowerbound = SU.P;
boxesupperbound = max(min(powerUpperbound,SU.Pmax),0);
p_k = zeros(2*n,SU.maxiterations);
%%polyblock algorithm
initPowerFeasible=SU.P;
for k = 1:SU.maxiterations
%reduce the current boxes
eraseBoxes=[];
for boxNum=1:size(boxesupperbound,2)
intAtPU=boxeslowerbound(1:n,boxNum)*SU.gainVecSUTrnsMSRecv(1,1)+boxeslowerbound(n+1:end,boxNum)*SU.gainVecSUTrnsMSRecv(2,1);
objFuncUpperbound= prod([(GammaInitlinear(1:n)+boxesupperbound(1:n,boxNum)*SU.hs*SU.alpha+boxesupperbound(n+1:end,boxNum)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(1:n)+boxesupperbound(1:n,boxNum)*SU.hs*SU.alpha); ...
(GammaInitlinear(n+1:end)+boxesupperbound(n+1:end,boxNum)*SU.hs*SU.alpha+boxesupperbound(1:n,boxNum)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(n+1:end)+boxesupperbound(n+1:end,boxNum)*SU.hs*SU.alpha)]);
if sum(boxeslowerbound(1:n,boxNum))<=SU.Pmax && sum(boxeslowerbound(n+1:end,boxNum))<=SU.Pmax && all(intAtPU<=max(SU.IntThreshold-SU.J,0))
if all(boxesupperbound(n+1:end,boxNum)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)./(GammaInitlinear(1:n)+boxesupperbound(1:n,boxNum)*SU.hs*SU.alpha)>=SU.RxSensitivity.*SU.X(n+1:end,1)) && ...
all(boxesupperbound(1:n,boxNum)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)./(GammaInitlinear(n+1:end)+boxesupperbound(n+1:end,boxNum)*SU.hs*SU.alpha)>=SU.RxSensitivity.*SU.X(1:n,1)) && objFuncUpperbound>cbv
%do the reduction
alphaVec=[];
for individual=1:2
for row=1:n
if individual==1 && SU.X(row,1)>0
cvx_begin quiet
variable alphaOpt nonnegative
maximize alphaOpt
subject to
sum(boxeslowerbound(1:n,boxNum)+alphaOpt*(boxesupperbound(row,boxNum)-boxeslowerbound(row,boxNum))*Ired(:,row))<=SU.Pmax;
%sum(boxeslowerbound(n+1:end,boxNum)+alphaOpt*(boxesupperbound(n+1:end,boxNum)-boxeslowerbound(n+1:end,boxNum))'*Ired(:,row))<=SU.Pmax;
(boxeslowerbound(row,boxNum)+boxeslowerbound(n+row,boxNum)+alphaOpt*(boxesupperbound(row,boxNum)-boxeslowerbound(row,boxNum))*Ired(:,row))*max(SU.gainVecSUTrnsMSRecv(1,:))<=max(SU.IntThreshold(row,1)-SU.J(row,1),0);
%(boxeslowerbound(n+1:end,boxNum)+alphaOpt*(boxesupperbound(n+1:end,boxNum)-boxeslowerbound(n+1:end,boxNum))'*Ired(:,row))*max(SU.gainVecSUTrnsMSRecv(2,:))<=SU.IntThreshold-SU.J;
alphaOpt <= 1;
cvx_end
if ~isnan(alphaOpt)
alphaVec=[alphaVec,alphaOpt];
else
alphaVec=[alphaVec,1];
end
boxesupperbound(row,boxNum)=boxeslowerbound(row,boxNum)+alphaVec(row)*(boxesupperbound(row,boxNum)-boxeslowerbound(row,boxNum));
elseif individual==1 && SU.X(row,1)== 0
alphaVec=[alphaVec,1];
boxesupperbound(row,boxNum)=boxeslowerbound(row,boxNum)+alphaVec(row)*(boxesupperbound(row,boxNum)-boxeslowerbound(row,boxNum));
elseif individual==2 && SU.X(n+row,1)>0
cvx_begin quiet
variable alphaOpt nonnegative
maximize alphaOpt
subject to
%sum(boxeslowerbound(1:n,boxNum)+alphaOpt*(boxesupperbound(1:n,boxNum)-boxeslowerbound(1:n,boxNum))'*Ired(:,row))<=SU.Pmax;
sum(boxeslowerbound(n+1:end,boxNum)+alphaOpt*(boxesupperbound(n+row,boxNum)-boxeslowerbound(n+row,boxNum))*Ired(:,row))<=SU.Pmax;
%(boxeslowerbound(1:n,boxNum)+alphaOpt*(boxesupperbound(1:n,boxNum)-boxeslowerbound(1:n,boxNum))'*Ired(:,row))*max(SU.gainVecSUTrnsMSRecv(1,:))<=SU.IntThreshold-SU.J;
(boxeslowerbound(row,boxNum)+boxeslowerbound(n+row,boxNum)+alphaOpt*(boxesupperbound(n+row,boxNum)-boxeslowerbound(n+row,boxNum))*Ired(:,row))*max(SU.gainVecSUTrnsMSRecv(2,:))<=max(SU.IntThreshold(row,1)-SU.J(row,1),0);
alphaOpt <= 1;
cvx_end
if ~isnan(alphaOpt)
alphaVec=[alphaVec,alphaOpt];
else
alphaVec=[alphaVec,1];
end
boxesupperbound(n+row,boxNum)=boxeslowerbound(n+row,boxNum)+alphaVec(n+row)*(boxesupperbound(n+row,boxNum)-boxeslowerbound(n+row,boxNum));
elseif individual==2 && SU.X(n+row,1)== 0
alphaVec=[alphaVec,1];
boxesupperbound(n+row,boxNum)=boxeslowerbound(n+row,boxNum)+alphaVec(n+row)*(boxesupperbound(n+row,boxNum)-boxeslowerbound(n+row,boxNum));
end
end
end
betaVec=[];
for individual=1:2
for row=1:n
if individual==1 && SU.X(row,1)>0
cvx_begin quiet
variable betaOpt nonnegative
maximize betaOpt
subject to
sum(boxesupperbound(1:n,boxNum)-betaOpt*(boxesupperbound(row,boxNum)-boxeslowerbound(row,boxNum))*Ired(:,row))>=SU.Pmax;
%sum(boxesupperbound(n+1:end,boxNum)-betaOpt*(boxesupperbound(n+1:end,boxNum)-boxeslowerbound(n+1:end,boxNum))'*Ired(:,row))>=SU.Pmax;
(boxesupperbound(row,boxNum)+boxesupperbound(n+row,boxNum))*max(SU.gainVecSUTrnsMSRecv(1,:))-betaOpt*(boxesupperbound(row,boxNum)-boxeslowerbound(row,boxNum))*Ired(:,row)*max(SU.gainVecSUTrnsMSRecv(1,:))>=max(SU.IntThreshold(row,1)-SU.J(row,1),0);
%(boxesupperbound(n+1:end,boxNum)-betaOpt*(boxesupperbound(n+1:end,boxNum)-boxeslowerbound(n+1:end,boxNum))'*Ired(:,row))*max(SU.gainVecSUTrnsMSRecv(2,:))>=SU.IntThreshold-SU.J;
(boxesupperbound(row,boxNum)-betaOpt*(boxesupperbound(row,boxNum)-boxeslowerbound(row,boxNum))*Ired(:,row))*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)./(GammaInitlinear(n+row)+(boxesupperbound(n+row,boxNum))*SU.hs*SU.alpha)>=SU.RxSensitivity;
%(boxesupperbound(n+1:end,boxNum)-betaOpt*(boxesupperbound(n+1:end,boxNum)-boxeslowerbound(n+1:end,boxNum))'*Ired(:,row))*SU.gainVecSUTrnsSURecv-(GammaInitlinear(1:n)+(boxesupperbound(1:n,boxNum)-betaOpt*(boxesupperbound(1:n,boxNum)-boxeslowerbound(1:n,boxNum))'*Ired(:,row))*SU.hs*SU.alpha)*SU.RxSensitivity>=0;
betaOpt <= 1;
cvx_end
if ~isnan(betaOpt)
betaVec=[betaVec,betaOpt];
else
betaVec=[betaVec,1];
end
boxeslowerbound(row,boxNum)=boxesupperbound(row,boxNum)-betaVec(row)*(boxesupperbound(row,boxNum)-boxeslowerbound(row,boxNum));
elseif individual==1 && SU.X(row,1)==0
betaVec=[betaVec,1];
boxeslowerbound(row,boxNum)=boxesupperbound(row,boxNum)-betaVec(row)*(boxesupperbound(row,boxNum)-boxeslowerbound(row,boxNum));
elseif individual==2 && SU.X(n+row,1)>0
cvx_begin quiet
variable betaOpt nonnegative
maximize betaOpt
subject to
%sum(boxesupperbound(1:n,boxNum)-betaOpt*(boxesupperbound(1:n,boxNum)-boxeslowerbound(1:n,boxNum))'*Ired(:,row))>=SU.Pmax;
sum(boxesupperbound(n+1:end,boxNum)-betaOpt*(boxesupperbound(n+row,boxNum)-boxeslowerbound(n+row,boxNum))*Ired(:,row))>=SU.Pmax;
(boxesupperbound(row,boxNum)+boxesupperbound(n+row,boxNum)-betaOpt*(boxesupperbound(n+row,boxNum)-boxeslowerbound(n+row,boxNum))'*Ired(:,row))*max(SU.gainVecSUTrnsMSRecv(2,:))>=max(SU.IntThreshold(row,1)-SU.J(row,1),0);
%(boxesupperbound(n+1:end,boxNum)-betaOpt*(boxesupperbound(n+1:end,boxNum)-boxeslowerbound(n+1:end,boxNum))'*Ired(:,row))*max(SU.gainVecSUTrnsMSRecv(2,:))>=SU.IntThreshold-SU.J;
(boxesupperbound(n+row,boxNum)-betaOpt*(boxesupperbound(n+row,boxNum)-boxeslowerbound(n+row,boxNum))'*Ired(:,row))*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)./(GammaInitlinear(row)+(boxesupperbound(row,boxNum))*SU.hs*SU.alpha)>=SU.RxSensitivity;
%(boxesupperbound(n+1:end,boxNum)-betaOpt*(boxesupperbound(n+1:end,boxNum)-boxeslowerbound(n+1:end,boxNum))'*Ired(:,row))*SU.gainVecSUTrnsSURecv-(GammaInitlinear(1:n)+(boxesupperbound(1:n,boxNum)-betaOpt*(boxesupperbound(1:n,boxNum)-boxeslowerbound(1:n,boxNum))'*Ired(:,row))*SU.hs*SU.alpha)*SU.RxSensitivity>=0;
betaOpt <= 1;
cvx_end
if ~isnan(betaOpt)
betaVec=[betaVec,betaOpt];
else
betaVec=[betaVec,1];
end
boxeslowerbound(n+row,boxNum)=boxesupperbound(n+row,boxNum)-betaVec(n+row)*(boxesupperbound(n+row,boxNum)-boxeslowerbound(n+row,boxNum));
elseif individual==2 && SU.X(n+row,1)==0
betaVec=[betaVec,1];
boxeslowerbound(n+row,boxNum)=boxesupperbound(n+row,boxNum)-betaVec(n+row)*(boxesupperbound(n+row,boxNum)-boxeslowerbound(n+row,boxNum));
end
end
end
else
eraseBoxes=[eraseBoxes,boxNum];
end
end
end
boxeslowerbound(:,eraseBoxes)=[];
boxesupperbound(:,eraseBoxes)=[];
cub(eraseBoxes)=[];
if isempty(boxesupperbound)
break
end
powerUpperbound=boxesupperbound;
%find the maximum feasible
%a_prime = a-norm(boxesupperbound-boxeslowerbound)/4*ones(n*2,1);
[maxCUB,maxUpperBoundIndex] =max(cub);
z = powerUpperbound(:,maxUpperBoundIndex);
a=boxeslowerbound(:,maxUpperBoundIndex);
%a_prime = a-norm(boxesupperbound-boxeslowerbound)/4*ones(n*2,1);
% disp(maxUpperBoundIndex);
% disp(z);
%check if z is feasible if so stop
intAtPU=z(1:n,1)*SU.gainVecSUTrnsMSRecv(1,1)+z(n+1:end,1)*SU.gainVecSUTrnsMSRecv(2,1);
objFuncUpperbound= prod([(GammaInitlinear(1:n)+z(1:n,1)*SU.hs*SU.alpha+z(n+1:end,1)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(1:n)+z(1:n,1)*SU.hs*SU.alpha); ...
(GammaInitlinear(n+1:end)+z(n+1:end,1)*SU.hs*SU.alpha+z(1:n,1)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(n+1:end)+z(n+1:end,1)*SU.hs*SU.alpha)]);
if sum(z(1:n,1))<=SU.Pmax && sum(z(n+1:end,1))<=SU.Pmax && all(intAtPU<=max(SU.IntThreshold-SU.J,0))
if all(z(n+1:end,1)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)./(GammaInitlinear(1:n)+z(1:n,1)*SU.hs*SU.alpha)>=SU.RxSensitivity.*SU.X(n+1:end,1)) && ...
all(z(1:n,1)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex)./(GammaInitlinear(n+1:end)+z(n+1:end,1)*SU.hs*SU.alpha)>=SU.RxSensitivity.*SU.X(1:n,1)) && objFuncUpperbound>cbv
SU.P=z;
break;
end
end
cvx_begin quiet
variable lambda
minimize lambda
subject to
%z-lambda*(z-a_prime)-SU.P<=0
sum(z(1:n)-lambda*(z(1:n)-a(1:n)))<=SU.Pmax;
sum(z(n+1:end)-lambda*(z(n+1:end)-a(n+1:end)))<=SU.Pmax;
(z(1:n)-lambda*(z(1:n)-a(1:n)))*max(SU.gainVecSUTrnsMSRecv(1,:))+ (z(n+1:end)-lambda*(z(n+1:end)-a(n+1:end)))*max(SU.gainVecSUTrnsMSRecv(2,:))<=max(SU.IntThreshold-SU.J,0);
%
%(z_vec(1,:)-lambda*(z_vec(1,:)-a_prime_vec(1,:)))'>=zeros(n,1)
%(z_vec(2,:)-lambda*(z_vec(2,:)-a_prime_vec(2,:)))'>=zeros(n,1)
cvx_end
p_k(:,k) = max([(z(1:n)-lambda*(z(1:n)-a(1:n)));(z(n+1:end)-lambda*(z(n+1:end)-a(n+1:end)))],0);
%powerUpperbound(:,maxUpperBoundIndex) = p_k(:,k);
SU.P = max(p_k(:,k),0);
cbvPrev=cbv;
cbv = prod([(GammaInitlinear(1:n)+SU.P(1:n)*SU.hs*SU.alpha+SU.P(n+1:end)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(1:n)+SU.P(1:n)*SU.hs*SU.alpha); ...
(GammaInitlinear(n+1:end)+SU.P(n+1:end)*SU.hs*SU.alpha+SU.P(1:n)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(n+1:end)+SU.P(n+1:end)*SU.hs*SU.alpha)]);
SU.rate = log2(cbv);
% if k>3 && abs(cbvPrev-cbv)<=0.00001
% break;
% end
powerUpperbound(:,maxUpperBoundIndex)=p_k(:,k);
totalPower(1,:)=SU.P(1:n);
totalPower(2,:)=SU.P(n+1:end);
if abs(maxCUB-cbv)<=epsilon
break;
end
%% new polyblock generation
colVecz=[];
colVecy=[];
rowVector=zeros(2*n,1);
for col=1:size(powerUpperbound,2)
for row=1:2*n
if powerUpperbound(row,col)>p_k(row,k)
rowVector(row,1)=1;
elseif powerUpperbound(row,col)==p_k(row,k) && SU.X(row,1)==0
rowVector(row,1)=1;
end
end
if sum(rowVector)==2*n
colVecz=[colVecz,col];
colVecy=[colVecy,col];
elseif all(powerUpperbound(:,col)>=p_k(:,k))
colVecy=[colVecy,col];
end
end
if isempty(colVecz)
disp(p_k(:,k))
break;
else
I = eye(2*n);
for col=fliplr(colVecz)
rowVec=[];
z = powerUpperbound(:,col);
for ycol=fliplr(colVecy)
comp=find(z>boxesupperbound(:,ycol),2);
if ~isempty(comp)&& size(comp,1)==1
rowVec=[rowVec,comp];
end
end
powerUpperbound(:,col)=[];
boxeslowerbound(:,col)=[];
cub(col)=[];
for row=1:2*n
if (any(rowVec~=row) || isempty(rowVec))&& SU.X(row,1)==1
newVertex=z+(p_k(:,k)-z).*I(:,row);
upperBoundObj= prod([(GammaInitlinear(1:n)+newVertex(1:n)*SU.hs*SU.alpha+newVertex(n+1:end)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(1:n)+newVertex(1:n)*SU.hs*SU.alpha); ...
(GammaInitlinear(n+1:end)+newVertex(n+1:end)*SU.hs*SU.alpha+newVertex(1:n)*SU.gainVecSUTrnsSURecv(2,SU.SUIndex))./(GammaInitlinear(n+1:end)+newVertex(n+1:end)*SU.hs*SU.alpha)]);
if upperBoundObj>cbv
powerUpperbound = [powerUpperbound,newVertex];
boxeslowerbound = [boxeslowerbound,initPowerFeasible.*SU.X];
cub = [cub,upperBoundObj];
end
end
end
end
end
removableCols=[];
for index=1:size(cub,2)
if all(removableCols~=index)
for compareIndex=2:size(cub,2)
if all(powerUpperbound(:,index)>=powerUpperbound(:,compareIndex))
removableCols=[removableCols,compareIndex];
end
end
end
end
cub(removableCols)=[];
boxeslowerbound(:,removableCols) =[];
powerUpperbound(:,removableCols) =[];
%[~,indices]=sort(cub,'descend');
if size(cub,2)>=100
cub=cub(1:100);
boxeslowerbound =boxeslowerbound(:,1:100);
powerUpperbound= powerUpperbound(:,1:100);
boxesupperbound= powerUpperbound;
else
boxesupperbound= powerUpperbound;
end
end
end
end
end