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Figs3_4_mixed_integer_programming_solution.m
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Figs3_4_mixed_integer_programming_solution.m
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for seedd = 1:30
seedd
rng(seedd)
%Number of APs
L = 16;
%Number of antennas per AP
N = 4;
%Number of UEs in the network
K = 8;
%Number of DUs
W = 4;
SEAll = 0.25:0.25:10;
numberSetup = length(SEAll);
Axx = zeros(K,L,numberSetup);
Add = zeros(W,numberSetup);
Azz = zeros(L,numberSetup);
All = zeros(W,numberSetup);
Arho = zeros(K*L,numberSetup);
Bxx = zeros(K,L,numberSetup);
Bdd = zeros(W,numberSetup);
Bzz = zeros(L,numberSetup);
Bll = zeros(W,numberSetup);
Brho = zeros(K*L,numberSetup);
TotalPower = zeros(2,numberSetup);
%Number of channel realizations per setup
nbrOfRealizations = 500;
Nsmooth = 12;
Nslot = 16;
%Length of coherence block
tau_c = Nsmooth*Nslot;
%Length of pilot sequences
tau_p = K;
%Compute the prelog factor assuming only downlink data transmission
preLogFactor = (tau_c-tau_p)/tau_c;
%Angular standard deviation in the local scattering model (in radians)
ASD_varphi = deg2rad(15); %azimuth angle
ASD_theta = deg2rad(15); %elevation angle
%Total uplink transmit power per UE (mW)
p = 100;
%Total downlink transmit power per AP (mW)
rho_tot = 1000;
%Generate one setup with UEs at random locations
[gainOverNoisedB,R,pilotIndex,D,D_small,APpositions,UEpositions] = generateSetup(L,K,N,tau_p,1,0,ASD_varphi,ASD_theta);
%Generate channel realizations, channel estimates, and estimation
%error correlation matrices for all UEs to the cell-free APs
[Hhat,H,B,C] = functionChannelEstimates(R,nbrOfRealizations,L,K,N,tau_p,pilotIndex,p);
% Full uplink power for the computation of precoding vectors using
% virtual uplink-downlink duality
p_full = p*ones(K,1);
%Define the case when all APs serve all UEs
D_all = ones(L,K);
%Obtain the expectations
[signal_P_MMSE, signal2_P_MMSE, scaling_P_MMSE,...
signal_P_RZF, signal2_P_RZF, scaling_P_RZF,...
signal_LP_MMSE,signal2_LP_MMSE, scaling_LP_MMSE] = ...
functionComputeExpectationsV2(Hhat,H,D_all,C,nbrOfRealizations,N,K,L,p_full);
bk = zeros(L,K);
Ck = zeros(L,L,K,K);
%Go through all UEs
for k = 1:K
bk(:,k) = real(vec(signal_LP_MMSE(k,k,:)))./sqrt(scaling_LP_MMSE(:,k));
%Go through all UEs
for i = 1:K
if i==k
Ck(:,:,k,k) = bk(:,k)*bk(:,k)';
else
Ck(:,:,k,i) = diag(1./sqrt(scaling_LP_MMSE(:,i)))...
*(vec(signal_LP_MMSE(k,i,:))...
*vec(signal_LP_MMSE(k,i,:))')...
*diag(1./sqrt(scaling_LP_MMSE(:,i)));
end
for j = 1:L
Ck(j,j,k,i) = signal2_LP_MMSE(k,i,j)/scaling_LP_MMSE(j,i);
end
end
end
%Take the real part (in the SINR expression,the imaginary terms cancel
%each other)
Ck = real(Ck);
bb = zeros(L*K,K);
CC = zeros(L*K,L*K,K);
CC2 = zeros(L*K,L*K,K);
for k = 1:K
for i = 1:K
CC((i-1)*L+1:i*L,(i-1)*L+1:i*L,k) = Ck(:,:,k,i);
end
CC2(:,:,k) = sqrtm(CC(:,:,k));
bb((k-1)*L+1:k*L,k) = vec(bk(:,k));
end
%%
for sss = 1:numberSetup
sss
gamma = 2^(SEAll(sss)/preLogFactor)-1;
PAP0 = 6.8*N;
DeltaTr = 4;
PONU = 7.7;
sigmaCool = 0.9;
POLT = 20;
Pdisp = 120;
Pproc0 = 20.8;
DeltaProc = 74;
GOPSmax = 180;
fs = 30.72*10^6;
Ts = 71.4*10^(-6);
NDFT = 2048;
Nused = 1200;
Nbits = 12;
Cfilter = 40*N*fs/(10^9);
CDFT = (8*N*NDFT*log2(NDFT)/Ts)/(10^9);
SE0 = SEAll(sss);
CprecodingAP = Nused/(Ts*tau_c*10^9)*...
((8*N*tau_p+8*N^2)*tau_p + (4*N^2+4*N)*tau_p + 8*(N^3-N)/3);
CotherAP = ((Nbits/16)^(1.2))*(1.3*N) ...
+ ((Nbits/16)^(0.2))*(2.7*sqrt(N));
ZLP = Cfilter + CDFT + CprecodingAP + CotherAP;
CprecodingUE = Nused*(tau_c-tau_p)/(Ts*tau_c*10^9)*8*N ...
+ Nused/(Ts*tau_c*10^9)*8*N ...
+ Nused/(Ts*tau_c*10^9)*(8*N^2);
FLP = ((Nbits/16)^(1.2))*( 1.3*((SE0/6)^(1.5))*K )...
+ ((Nbits/16)^(1.2))*( 1.3*SE0/6*K )...
+ 8*SE0/6*K;
XLP = CprecodingUE;
Rmax = 10*10^9;
Rfronthaul = 2*fs*Nbits*N;
Wmax = floor(Rmax/Rfronthaul);
PPl = PAP0 + PONU + DeltaProc/GOPSmax*ZLP/sigmaCool;
%% Cell-free C-RAN
cvx_begin quiet
variable xx(K,L) binary
variable dd(W,1) binary
variable zz(L,1) binary
variable ll(W,1) binary
variable rho(K*L,1)
minimize Pdisp + PPl*sum(zz) + DeltaTr*quad_form(rho,eye(K*L))/10 ...
+ POLT*(1:W)*ll/sigmaCool + Pproc0*(1:W)*dd/sigmaCool ...
+ DeltaProc/GOPSmax*XLP*sum(sum(xx))/sigmaCool ...
+ DeltaProc/GOPSmax*FLP/sigmaCool
subject to
sum(xx,2) >= ones(K,1);
sum(zz) <= sum(sum(xx));
for k = 1:K
norm([CC2(:,:,k)*10*rho; 1]) <= sqrt((gamma+1)/gamma)*bb(:,k)'*10*rho;
end
sum(zz) <= Wmax*W;
zz <= (sum(xx,1)).';
K*zz >= (sum(xx,1)).';
sum(zz)/Wmax <= (1:W)*ll;
sum(zz)/Wmax >= (0:W-1)*ll;
ZLP*sum(zz) + XLP*sum(sum(xx)) + FLP <= GOPSmax*(1:W)*dd;
sum(dd) == 1;
sum(ll) == 1;
(1:W)*dd >= (1:W)*ll;
zeros(K*L,1) <= rho;
rho <= sqrt(rho_tot/100)*vec(xx.');
for ell = 1:L
norm(rho(ell:L:end,1)) <= sqrt(rho_tot/100)*zz(ell,1);
end
cvx_end
TotalPower(1,sss) = Pdisp + PPl*sum(zz) + DeltaTr*quad_form(rho,eye(K*L))/10 ...
+ POLT*(1:W)*ll/sigmaCool + Pproc0*(1:W)*dd/sigmaCool ...
+ DeltaProc/GOPSmax*XLP*sum(sum(xx))/sigmaCool ...
+ DeltaProc/GOPSmax*FLP/sigmaCool;
Axx(:,:,sss) = xx;
Add(:,sss) = dd;
Azz(:,sss) = zz;
All(:,sss) = ll;
Arho(:,sss) = rho;
if isnan(TotalPower(1,sss))
break
end
%% Small-cell C-RAN
cvx_begin quiet
variable xx(K,L) binary
variable dd(W,1) binary
variable zz(L,1) binary
variable ll(W,1) binary
variable rho(K*L,1)
minimize Pdisp + PPl*sum(zz) + DeltaTr*quad_form(rho,eye(K*L))/10 ...
+ POLT*(1:W)*ll/sigmaCool + Pproc0*(1:W)*dd/sigmaCool ...
+ DeltaProc/GOPSmax*XLP*sum(sum(xx))/sigmaCool ...
+ DeltaProc/GOPSmax*FLP/sigmaCool
subject to
sum(xx,2) == ones(K,1);
sum(zz) <= sum(sum(xx));
for k = 1:K
norm([CC2(:,:,k)*10*rho; 1]) <= sqrt((gamma+1)/gamma)*bb(:,k)'*10*rho;
end
sum(zz) <= Wmax*W;
zz <= (sum(xx,1)).';
K*zz >= (sum(xx,1)).';
sum(zz)/Wmax <= (1:W)*ll;
sum(zz)/Wmax >= (0:W-1)*ll;
ZLP*sum(zz) + XLP*sum(sum(xx)) + FLP <= GOPSmax*(1:W)*dd;
sum(dd) == 1;
sum(ll) == 1;
(1:W)*dd >= (1:W)*ll;
zeros(K*L,1) <= rho;
rho <= sqrt(rho_tot/100)*vec(xx.');
for ell = 1:L
norm(rho(ell:L:end,1)) <= sqrt(rho_tot/100)*zz(ell,1);
end
cvx_end
TotalPower(2,sss) = Pdisp + PPl*sum(zz) + DeltaTr*quad_form(rho,eye(K*L))/10 ...
+ POLT*(1:W)*ll/sigmaCool + Pproc0*(1:W)*dd/sigmaCool ...
+ DeltaProc/GOPSmax*XLP*sum(sum(xx))/sigmaCool ...
+ DeltaProc/GOPSmax*FLP/sigmaCool;
Bxx(:,:,sss) = xx;
Bdd(:,sss) = dd;
Bzz(:,sss) = zz;
Bll(:,sss) = ll;
Brho(:,sss) = rho;
end
save(strcat('MIPsim',num2str(seedd),'.mat'))
end