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rate_allocation_simple_arrival.m
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function[served_rate, transmit_power] = rate_allocation_simple(vq, selectedaction, delay_r)
global N_Flow % number of flows
N_Flow = 2;
global N_SubF % number of each subflows for each flow, assume that each flow is divided equally
N_SubF = 4;
global N_BSs % the number of SC BSs
N_BSs = 6;
global N_Actions % The number of actions : Each user is assumed to choose two paths among 4 paths, then
% the number of actions is the combination of choosing 2 from 4.
N_Actions = 6;
global ops
% selectedaction = [1 1]';
% vq = 10*rand( N_SubF, 1 + N_BSs);
[nSF, nBS] = size(vq); % number of subflows and BSs
Delay_const = zeros(nBS, nSF);
indicator_BSs = routingtable(selectedaction);
arrival = zeros(nSF, 1);
for nbs = 1:nBS
% Transmit power constraints
for nsf = 1:nSF
Delay_const(nbs, nsf) = min(delay_r(nsf, nbs), log(1+5) );
end
end
% Routing table
RT.action(1).route1 = [1 2 3];
RT.action(1).route2 = [1 4 5];
RT.action(2).route1 = [1 2 3];
RT.action(2).route2 = [1 6];
RT.action(3).route1 = [1 2 3];
RT.action(3).route2 = [1 7];
RT.action(4).route1 = [1 4 5];
RT.action(4).route2 = [1 7];
RT.action(5).route1 = [1 4 5];
RT.action(5).route2 = [1 6];
RT.action(6).route1 = [1 7];
RT.action(6).route2 = [1 6];
%% 2 Solving Rate Allocation Problem, which uses SOCP method, Yalmip toolbox
% ops = sdpsettings('solver','mosek'); % fmincon set the interal solver to be mosek
ops = sdpsettings('solver','mosek','cachesolvers',1,'verbose',0,'debug',1,'beeponproblem',1,'saveduals',1); % set the interal solver to be mosek
% lowerbound = 0.5 * rand(nBS, nSF);
% lowerbound(1, :) = 0.2 *rand(1, nSF);
% Assign the lower bound
lowerbound = Delay_const;
% Declare the slack variables
u_next = ones(nBS, nSF);
tx_next = zeros(nBS, nSF);
n = 15; % ensuring that error accurancy is less than 10^-5
ObjFun = 1e-8;
lowerbound = lowerbound.* indicator_BSs;
while(1)
% Define variable
% rate = sdpvar(nBS, nSF);
tx = sdpvar(nBS, nSF);
x_max = sdpvar(nSF,1);
% Nonconvex variables
u = sdpvar(nBS, nSF);
kappa = sdpvar(n+4,nSF,'full'); % for convex approximation of exponential function
% Define constraints and Objectives
constraints = []; % contain all the constraints
constraints = [constraints, x_max >= 0];
constraints = [constraints, tx >= 0];
constraints = [constraints, u >= 1];
for nbs = 1:nBS
% Transmit power constraints
for nsf = 1:nSF
if indicator_BSs(nbs,nsf) == 0
constraints = [constraints, tx(nbs, nsf) == 0];
% constraints = [constraints, x_max(nsf, 1) == 0];
end
constraints = [constraints, tx(nbs, nsf) <= 5];
end
if nbs >= 2
constraints = [constraints, sum(tx(nbs, :)) <= 10]; % maximum power constraint
end
end
constraints = [constraints, sum(tx(1, :)) <= 20]; % maximum power constraint
% Here is to deal with the approximated convex constraints
for player = 1:N_Flow % rate_allocated = zeros(N_BSs+1, N_SubF);
if player == 1
UE = 8;
[~, sizea] = size(RT.action(selectedaction(player)).route1);
bs_list1 = RT.action(selectedaction(player)).route1;
for n1 = 1:sizea
if n1 == 1 % if MBS
% constraints = [constraints, (1+ tx(bs_list1(n1), 1))
% >= exp(5+x_max(bs_list2(n1), 1)) ]; which is
% replaced by the below constraints, 20170213
k = 1;
constraints = [constraints, (1+ tx(bs_list1(n1), k)) >= exp(lowerbound(bs_list1(n1), k)) ];
constraints = [constraints, kappa(:,k) >= 0];
constraints = [constraints, (1+ tx(bs_list1(n1), k)) >= kappa(1,k) ];
constraints = [constraints, cone([2 + (arrival(k,1) + x_max(k, bs_list1(n1)) )/(2^(n-1)); 1-kappa(2,k)], kappa(2,k) +1)];
constraints = [constraints, cone([5/3 + (arrival(k,1) + x_max(k, bs_list1(n1)))/(2^(n)); 1-kappa(3,k)], kappa(3,k) +1)];
constraints = [constraints, cone([2*kappa(2,k); 1-kappa(4,k)],kappa(4,k) +1)];
constraints = [constraints, 19/72 + kappa(3,k) + 1/24*kappa(4,k) <= kappa(5,k)];
for mVar = 6:n+4
constraints = [constraints, cone([2*kappa(mVar-1,k);1-kappa(mVar,k)], kappa(mVar,k) +1)];
end
constraints = [constraints, cone([2*kappa(n+4,k); 1-kappa(1,k)], 1+kappa(1,k))];
else
% Cone constraint for SC BSs, and convex approximation
constraints = [constraints, cone( [ u(bs_list1(n1), 1); tx(bs_list1(n1), 1)./2], (2+ tx(bs_list1(n1), 1))./2 ) ];
constraints = [constraints, 2 * u(bs_list1(n1), 1)*u_next(bs_list1(n1), 1)./(1 + tx_next(bs_list1(n1-1), 1)) - (1+ tx(bs_list1(n1-1), 1)) * (u_next(bs_list1(n1), 1)./(1 + tx_next(bs_list1(n1-1), 1))).^2 >= exp(lowerbound(bs_list1(n1), 1)) ];
end
end
% 20170210 stop here
[~, sizeb] = size(RT.action(selectedaction(player)).route2);
bs_list2 = RT.action(selectedaction(player)).route2;
for n1 = 1:sizeb
if n1 == 1 % if MBS
k = 2;
constraints = [constraints, (1+ tx(bs_list2(n1), k)) >= exp(lowerbound(bs_list2(n1), k)) ];
constraints = [constraints, kappa(:,k) >= 0];
constraints = [constraints, (1+ tx(bs_list2(n1), k)) >= kappa(1,k) ];
constraints = [constraints, cone([2 + (arrival(k,1) + x_max(k, bs_list2(n1)) )/(2^(n-1)); 1-kappa(2,k)], kappa(2,k) +1)];
constraints = [constraints, cone([5/3 + (arrival(k,1) + x_max(k, bs_list2(n1)))/(2^(n)); 1-kappa(3,k)], kappa(3,k) +1)];
constraints = [constraints, cone([2*kappa(2,k); 1-kappa(4,k)],kappa(4,k) +1)];
constraints = [constraints, 19/72 + kappa(3,k) + 1/24*kappa(4,k) <= kappa(5,k)];
for mVar = 6:n+4
constraints = [constraints, cone([2*kappa(mVar-1,k);1-kappa(mVar,k)], kappa(mVar,k) +1)];
end
constraints = [constraints, cone([2*kappa(n+4,k); 1-kappa(1,k)], 1+kappa(1,k))];
else
% Cone constraint for SC BSs, and convex approximation
constraints = [constraints, cone( [ u(bs_list2(n1), 2); tx(bs_list2(n1), 2)./2], (2+ tx(bs_list2(n1), 2))./2) ];
constraints = [constraints, 2* u(bs_list2(n1), 2) * u_next(bs_list2(n1), 2)./(1 + tx_next(bs_list2(n1-1), 2)) - (1+ tx(bs_list2(n1-1), 2)) * (u_next(bs_list2(n1), 2)./(1+tx_next(bs_list2(n1-1), 2))).^2 >= exp(lowerbound(bs_list2(n1), 2)) ];
end
end
else % if player 2, then update subflow 3 & 4
UE = 9;
[~, sizea] = size(RT.action(selectedaction(player)).route1);
bs_list1 = RT.action(selectedaction(player)).route1;
for n1 = 1:sizea
if n1 == 1 % if MBS
k = 3;
constraints = [constraints, x_max(3, bs_list1(n1))>= (lowerbound(bs_list1(n1), k)) ];
constraints = [constraints, kappa(:,k) >= 0];
constraints = [constraints, (1+ tx(bs_list1(n1), 3)) >= kappa(1,k) ];
constraints = [constraints, cone([2 + (arrival(k,1) + x_max(3, bs_list1(n1)) )/(2^(n-1)); 1-kappa(2,k)], kappa(2,k) +1)];
constraints = [constraints, cone([5/3 + (arrival(k,1) + x_max(3, bs_list1(n1)))/(2^(n)); 1-kappa(3,k)], kappa(3,k) +1)];
constraints = [constraints, cone([2*kappa(2,k); 1-kappa(4,k)],kappa(4,k) +1)];
constraints = [constraints, 19/72 + kappa(3,k) + 1/24*kappa(4,k) <= kappa(5,k)];
for mVar = 6:n+4
constraints = [constraints, cone([2*kappa(mVar-1,k);1-kappa(mVar,k)], kappa(mVar,k) +1)];
end
constraints = [constraints, cone([2*kappa(n+4,k); 1-kappa(1,k)], 1+kappa(1,k))];
else
% Cone constraint for SC BSs, and convex approximation
constraints = [constraints, cone( [ u(bs_list1(n1), 3); tx(bs_list1(n1), 3)./2], (2+ tx(bs_list1(n1), 3))./2) ];
constraints = [constraints, 2* u(bs_list1(n1), 3) * u_next(bs_list1(n1), 3)./(1 + tx_next(bs_list1(n1-1), 3)) - (1+ tx(bs_list1(n1-1), 3)) * (u_next(bs_list1(n1), 3)./(1+tx_next(bs_list1(n1-1), 3))).^2 >= exp(lowerbound(bs_list1(n1), 3)) ];
end
end
% 20170210 stop here
[~, sizeb] = size(RT.action(selectedaction(player)).route2);
bs_list2 = RT.action(selectedaction(player)).route2;
for n1 = 1:sizeb
if n1 == 1 % if MBS
k = 4;
constraints = [constraints, x_max(4, bs_list2(n1)) >= (lowerbound(bs_list2(n1), k)) ];
constraints = [constraints, kappa(:,k) >= 0];
constraints = [constraints, (1+ tx(bs_list2(n1), 4)) >= kappa(1,k) ];
constraints = [constraints, cone([2 + (arrival(k,1) + x_max(4, bs_list2(n1)) )/(2^(n-1)); 1-kappa(2,k)], kappa(2,k) +1)];
constraints = [constraints, cone([5/3 + (arrival(k,1) + x_max(4, bs_list2(n1)))/(2^(n)); 1-kappa(3,k)], kappa(3,k) +1)];
constraints = [constraints, cone([2*kappa(2,k); 1-kappa(4,k)],kappa(4,k) +1)];
constraints = [constraints, 19/72 + kappa(3,k) + 1/24*kappa(4,k) <= kappa(5,k)];
for mVar = 6:n+4
constraints = [constraints, cone([2*kappa(mVar-1,k);1-kappa(mVar,k)], kappa(mVar,k) +1)];
end
constraints = [constraints, cone([2*kappa(n+4,k); 1-kappa(1,k)], 1+kappa(1,k))];
else
% Cone constraint for SC BSs, and convex approximation
constraints = [constraints, cone( [ u(bs_list2(n1), 4); tx(bs_list2(n1), 4)./2], (2+ tx(bs_list2(n1), 4))./2 ) ];
constraints = [constraints, 2* u(bs_list2(n1), 4) * u_next(bs_list2(n1), 4)./(1 + tx_next(bs_list2(n1-1), 4)) - (1+ tx(bs_list2(n1-1), 4)) * (u_next(bs_list2(n1), 4)./(1+tx_next(bs_list2(n1-1), 4))).^2 >= exp(lowerbound(bs_list2(n1), 4)) ];
end
end
end
end
% Objective function
obj = -sum(vq(:,1)' * x_max);
% Solve the problem
sol = optimize(constraints, obj, ops); % solve the problem optimize replaced sdpsolve
x_max = value(x_max);
tx = value(tx);
u = value(u);
obj = value(obj);
% Check the results
sol.info;
if sol.problem == 0
tx_next = tx;
u_next = u;
temp = - obj;
if temp <= ObjFun + 1e-2 % abs(temp - ObjFun) <= 1e-2
transmit_power = tx;
% calculate the serving rate
for nbs = 1:nBS
for nsf = 1:nSF
served_rate(nsf,nbs) = log(1 + tx(nbs,nsf));
end
end
break;
end
ObjFun = temp;
else
disp('wrong!');
sol.info;
yalmiperror(sol.problem)
end
end % end while
end % end function