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Copy pathMIMO_IC.m
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MIMO_IC.m
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function MIMO_IC(varargin)
% % %
% The code is written to reproduce the results of paper:
% Gaurav Gupta and A.K. Chaturvedi, "User Selection in MIMO Interfering
% Broadcast Channels", IEEE TCOM 2014
% The code is open-access, and for using the code the user is required to
% cite the above paper.
% % %
% The following package is used for visual ease:
% progressbar, % Author:Steve Hoelzer
% % %
% sample input : (directive, n_t, n_r, SNR, BS, users)
% directive : code of algorithm to implement (see details of code below)
% n_t, n_r, SNR as usual
% BS : no of base stations comprising MIMO Interference channel
% users : users number vector
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
global n_t
global n_r
ii = 2;
n_t = varargin{ii};
n_r = varargin{ii+1};
SNR = varargin{ii+2};
BS = varargin{ii+3};
users_num = varargin{ii+4};
switch lower(varargin{1})
case 'ic'
R_F = SumCapacity_MIMO_IC_single_user(SNR, BS, users_num);
str = 'R_F_IC';
case 'ic_cap'
R_F = SumCapacity_MIMO_IC_capacity(SNR, BS, users_num);
str = 'R_F_IC_cap';
case 'optimal'
R_F = SumCapacity_optimal(SNR, BS, users_num);
str = 'R_F_opt_IC';
case 'capacity'
R_F = SumCapacity_capacity(SNR, BS, users_num);
str = 'R_F_cap_IC';
case 'conde'
R_F = SumCapacity_conditional_Ent(SNR, BS, users_num);
str = 'R_F_gg_IC';
case 'convention'
R_F = SumCapacity_conventional(SNR, BS, users_num);
str = 'R_F_conv_IC';
case 'tdma'
R_F = SumCapacity_TDMA(SNR, BS, users_num);
str = 'R_F_TDMA_IC';
case 'dist_iter'
% Here number of users are number of transmitter,Receiver pairs
R_F = SumCapacity_distributed_iterative(SNR, BS);
str = 'R_F_Diter';
case 'max_sinr'
R_F = SumCapacity_iterative_max_SINR(SNR, BS);
str = 'R_F_mSINR';
case 'group'
R_F = SumCapacity_grouping(SNR, BS, users_num);
str = 'R_F_grp';
case 'group_cap'
R_F = SumCapacity_grouping_Capacity(SNR, BS, users_num);
str = 'R_F_grp_cap';
case 'cap_test'
R_F = SumCapacity_grouping_CapacityTest(SNR, BS, users_num);
str = 'R_F_grp_capT';
case 'group_cho'
R_F = SumCapacity_grouping_Chordal(SNR, BS, users_num);
str = 'R_F_grp_cho1';
case 'group_opt'
R_F = SumCapacity_grouping_Optimal(SNR, BS, users_num);
str = 'R_F_grp_opt';
case 'three_cell'
R_F = SumCapacity_three_cell_alignment(SNR, BS, users_num);
str = 'R_F_3_cell';
case 'three_cell_cap'
R_F = SumCapacity_three_cell_Capacity(SNR, BS, users_num);
str = 'R_F_3_cell_cap';
case 'three_cell_cho'
R_F = SumCapacity_three_cell_Chordal(SNR, BS, users_num);
str = 'R_F_3_cell_cho';
case 'm2'
% select different models in the function itself
[R_F,appr] = SumCapacity_cyclic_model2(SNR, BS, users_num);
str = ['R_F_M2_' appr];
case 'm2_cap'
% select different models in the function itself
[R_F,appr] = SumCapacity_cyclic_model2_Capacity(SNR, BS, users_num);
str = ['R_F_M2_' appr '_cap'];
case 'hybrid'
R_F = SumCapacity_hybrid_grouping(SNR, BS, users_num);
str = 'R_F_hyb';
case 'gg'
R_F = SumCapacity_GG(SNR, BS, users_num);
str = 'R_F_gg';
case 'test'
R_F = SumCapacity_Test(SNR, BS, users_num);
str = 'R_F_test';
otherwise
disp('Wrong directive input, try again!');
return;
end
assignin('base', str, R_F);
function R_F = SumCapacity_MIMO_IC_single_user(SNR_vect, BS, users_num)
global n_t
global n_r
R_F = zeros(length(SNR_vect), length(users_num));
time = zeros(length(SNR_vect), length(users_num));
N_sim = 1000;
% dlg = ProgressDialog();
for SNR_ind = 1:length(SNR_vect)
for mi = 1:length(users_num)
nusers = users_num(mi);
R_final = zeros(N_sim,1);
str = sprintf('Channel_Mat/H_all_%d_%d_%d_%d',n_t,n_r,nusers,BS);
eval(['load ' str]);
% dlg.FractionComplete = 0;
% dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f, %d%% done', nusers,SNR_vect(SNR_ind),0);
progress(0);
tic
comb = ones(2,1);
for avg_sim_ind = 1:N_sim
% H = (randn(n_r,n_t,2,2,nusers) + 1i*randn(n_r,n_t,2,2,nusers))/sqrt(2);
H = H_all(:,:,:,:,:,avg_sim_ind); %#ok<*NODEF>
R_final(avg_sim_ind) = Sum_capacity_MIMO_IC(H, SNR_vect(SNR_ind),comb);
if ~rem(avg_sim_ind,10)
% dlg.FractionComplete = avg_sim_ind / N_sim;
% dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f dB, %d%% done',nusers,SNR_vect(SNR_ind),avg_sim_ind*100/N_sim);
progress(avg_sim_ind / N_sim);
end
end
R_F(SNR_ind, mi) = mean(R_final);
time(SNR_ind) = toc;
fprintf('Simulation for no. of users = %d at SNR = %2.1f dB done, time taken = %f\n', nusers, SNR_vect(SNR_ind), time(SNR_ind));
end
end
if numel(time) > 1
fprintf('Total time taken = %f\n', sum(sum(time)));
end
function R_F = SumCapacity_conditional_Ent(SNR_vect, BS, users_num)
global n_t
global n_r
R_F = zeros(length(SNR_vect), length(users_num));
time = zeros(length(SNR_vect), length(users_num));
N_sim = 1000;
dlg = ProgressDialog();
for SNR_ind = 1:length(SNR_vect)
for mi = 1:length(users_num)
nusers = users_num(mi);
R_final = zeros(N_sim,1);
str = sprintf('Channel_Mat/H_all_%d_%d_%d_%d',n_t,n_r,nusers,BS);
eval(['load ' str]);
dlg.FractionComplete = 0;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f, %d%% done', nusers,SNR_vect(SNR_ind),0);
tic
for avg_sim_ind = 1:N_sim
H = H_all(:,:,:,:,:,avg_sim_ind); %#ok<*NODEF>
K_set = zeros(1,BS);
for cell_ind = 1:BS
Frob_temp = 0;
for user_ind = 1:nusers
Frob_Norm = norm(H(:,:,user_ind,cell_ind,cell_ind), 'fro')^2;
if Frob_Norm > Frob_temp
Frob_temp = Frob_Norm;
maxValInd = user_ind;
end
end
K_set(cell_ind) = maxValInd;
end
SNR_tmp = 10^(SNR_vect(SNR_ind)/10) / n_t;
for i = 1:BS
Ent_temp = 0;
for j = 1:nusers
H1 = H(:,:,j,i,i);
H2 = [];
for ui = 1:BS
if ui == i, continue;end
if ~isempty(H2)
H3 = H(:,:,j,i,ui);
break;
end
H2 = H(:,:,j,i,ui);
end
Ent123 = log2(real(det(eye(n_t) + SNR_tmp*((H1'*H1) + (H2'*H2) + (H3'*H3)))));
Ent23 = log2(real(det(eye(n_t) + SNR_tmp*((H2'*H2) + (H3'*H3)))));
Ent = Ent123 - Ent23;
T = eye(n_t);
% for k = 1:3
% if k == i, continue;end
% H1 = H(:,:,K_set(k), k, k);
% H2 = [];
% for ui = 1:BS
% if ui == k, continue;end
% if ~isempty(H2),
% % T = H(:,:,j,i,k) \ H(:,:,j,i,ui);
% % T = H(:,:,j,i,ui) \ H(:,:,j,i,k);
% % T = inv(H(:,:,j,i,ui));
% % T = inv(H(:,:,j,ui,k));
% % ind_3 = ui;
% H3 = T * H(:,:,K_set(k),k,ui);
% % H3 = H(:,:,K_set(k),k,ui);
% break;
% end
% % T = inv(H(:,:,j,i,ui));
% % T = inv(H(:,:,j,ui,k));
% % ind_2 = ui;
% H2 = T * H(:,:,K_set(k),k,ui);
% end
% % T = H(:,:,j,i,ind_2) \ H(:,:,j,i,ind_3);
% % H2 = T * H2;
% % T = H(:,:,j,i,ind_3) \ H(:,:,j,i,ind_2);
% % H3 = T*H3;
% % H1 = T * H1;
% % H2 = T * H2;
% Ent123 = log2(real(det(eye(n_t) + SNR_tmp*((H1'*H1) + (H2'*H2) + (H3'*H3)))));
% Ent23 = log2(real(det(eye(n_t) + SNR_tmp*((H2'*H2) + (H3'*H3)))));
% Ent = Ent + Ent123 - Ent23;
% % Ent = Ent + Ent123;
% end
% sz = 1;
% mat = cell(1,2);
% for cell_ind = 1:BS
% if cell_ind == i, continue;end
% mat{sz} = H(:,:,j,i,cell_ind)'*H(:,:,j,i,cell_ind)*SNR_tmp;
% sz = sz + 1;
% end
% Ent12 = log2(real(det(eye(n_t) + mat{1} + mat{2})));
% Ent1 = log2(real(det(eye(n_t) + mat{1})));
% Ent2 = log2(real(det(eye(n_t) + mat{2})));
% Ent = 2*Ent12 - Ent1 - Ent2;
% Ent = log2(real(det(eye(n_t) + H(:,:,j,i,i)'*H(:,:,j,i,i)*SNR_tmp)));
% K_set_tmp = K_set;
% K_set_tmp(i) = j;
% [U, V] = compute_post_pre_processing_matrices_MMSE_opt(H, K_set_tmp, SNR_vect(SNR_ind));
% A = [];
% for ui = 1:BS
% if ui == i, continue;end
% if ~isempty(A),
% B = H(:,:,j,i,ui)*V{ui};
% break;
% end
% A = H(:,:,j,i,ui)*V{ui};
% end
% Ent = cho_dist(A, B);
if Ent > Ent_temp
Ent_temp = Ent;
maxValInd = j;
end
end
K_set(i) = maxValInd;
end
R_final(avg_sim_ind) = sum_capacity_R_sigma(H, SNR_vect(SNR_ind), K_set);
if ~rem(avg_sim_ind,10)
dlg.FractionComplete = avg_sim_ind / N_sim;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f dB, %d%% done',nusers,SNR_vect(SNR_ind),avg_sim_ind*100/N_sim);
end
end
R_F(SNR_ind,mi) = mean(R_final);
time(SNR_ind,mi) = toc;
fprintf('Simulation for no. of users = %d at SNR = %2.1f dB done, time taken = %f\n', users_num(mi), SNR_vect(SNR_ind), time(SNR_ind,mi));
end
end
if numel(time) > 1
fprintf('Total time taken = %f\n', sum(sum(time)));
end
function R_F = SumCapacity_capacity(SNR_vect, BS, users_num)
global n_t
global n_r
R_F = zeros(length(SNR_vect), length(users_num));
time = zeros(length(SNR_vect), length(users_num));
N_sim = 1000;
dlg = ProgressDialog();
for SNR_ind = 1:length(SNR_vect)
for mi = 1:length(users_num)
nusers = users_num(mi);
R_final = zeros(N_sim,1);
str = sprintf('Channel_Mat/H_all_%d_%d_%d_%d',n_t,n_r,nusers,BS);
eval(['load ' str]);
dlg.FractionComplete = 0;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f, %d%% done', nusers,SNR_vect(SNR_ind),0);
tic
for avg_sim_ind = 1:N_sim
H = H_all(:,:,:,:,:,avg_sim_ind); %#ok<*NODEF>
K_set = zeros(1,BS);
for cell_ind = 1:BS
Frob_temp = 0;
for user_ind = 1:nusers
Frob_Norm = norm(H(:,:,user_ind,cell_ind,cell_ind), 'fro')^2;
if Frob_Norm > Frob_temp
Frob_temp = Frob_Norm;
maxValInd = user_ind;
end
end
K_set(cell_ind) = maxValInd;
end
for cell_ind = 1:BS
R_temp = 0;
for user_ind = 1:nusers
K_set_temp = K_set;
K_set_temp(cell_ind) = user_ind;
R_S = sum_capacity_R_sigma(H, SNR_vect(SNR_ind), K_set_temp);
if R_S > R_temp
R_temp = R_S;
maxValInd = user_ind;
end
end
K_set(cell_ind) = maxValInd;
R_final(avg_sim_ind) = max(R_final(avg_sim_ind),R_temp);
end
if ~rem(avg_sim_ind,10)
dlg.FractionComplete = avg_sim_ind / N_sim;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f dB, %d%% done',nusers,SNR_vect(SNR_ind),avg_sim_ind*100/N_sim);
end
end
R_F(SNR_ind,mi) = mean(R_final);
time(SNR_ind,mi) = toc;
fprintf('Simulation for no. of users = %d at SNR = %2.1f dB done, time taken = %f\n', users_num(mi), SNR_vect(SNR_ind), time(SNR_ind,mi));
end
end
if numel(time) > 1
fprintf('Total time taken = %f\n', sum(sum(time)));
end
function R_F = SumCapacity_MIMO_IC_capacity(SNR_vect, BS, users_num)
global n_t
global n_r
R_F = zeros(length(SNR_vect), length(users_num));
time = zeros(length(SNR_vect), length(users_num));
N_sim = 1000;
% dlg = ProgressDialog();
for SNR_ind = 1:length(SNR_vect)
for mi = 1:length(users_num)
nusers = users_num(mi);
R_final = zeros(N_sim,1);
str = sprintf('Channel_Mat/H_all_%d_%d_%d_%d',n_t,n_r,nusers,BS);
eval(['load ' str]);
% dlg.FractionComplete = 0;
% dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f, %d%% done', nusers,SNR_vect(SNR_ind),0);
progress(0);
tic
for avg_sim_ind = 1:N_sim
% H = H_all(:,:,:,:,:,avg_sim_ind); %#ok<*NODEF>
H = (randn(n_r,n_t,2,2,nusers) + 1i*randn(n_r,n_t,2,2,nusers))/sqrt(2);
K_set = zeros(1,2);
for cell_ind = 1:2
Frob_temp = 0;
for user_ind = 1:nusers
Frob_Norm = norm(H(:,:,cell_ind,cell_ind,user_ind), 'fro')^2;
if Frob_Norm > Frob_temp
Frob_temp = Frob_Norm;
maxValInd = user_ind;
end
end
K_set(cell_ind) = maxValInd;
end
R_temp = 0;
maxValInd_exist = 0;
for cell_ind = 1:2
for user_ind = 1:nusers
K_set_temp = K_set;
K_set_temp(cell_ind) = user_ind;
R_S = Sum_capacity_MIMO_IC(H, SNR_vect(SNR_ind), K_set_temp);
if R_S > R_temp
R_temp = R_S;
maxValInd = user_ind;
maxValInd_exist = 1;
end
end
if maxValInd_exist
K_set(cell_ind) = maxValInd;
end
maxValInd_exist = 0;
end
R_final(avg_sim_ind) = R_temp;
if ~rem(avg_sim_ind,10)
% dlg.FractionComplete = avg_sim_ind / N_sim;
% dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f dB, %d%% done',nusers,SNR_vect(SNR_ind),avg_sim_ind*100/N_sim);
progress(avg_sim_ind / N_sim);
end
end
R_F(SNR_ind,mi) = mean(R_final);
time(SNR_ind,mi) = toc;
fprintf('Simulation for no. of users = %d at SNR = %2.1f dB done, time taken = %f\n', users_num(mi), SNR_vect(SNR_ind), time(SNR_ind,mi));
end
end
if numel(time) > 1
fprintf('Total time taken = %f\n', sum(sum(time)));
end
function R_F = SumCapacity_optimal(SNR_vect, BS, users_num)
global n_t
global n_r
R_F = zeros(length(SNR_vect), length(users_num));
time = zeros(length(SNR_vect), length(users_num));
N_sim = 1000;
dlg = ProgressDialog();
for SNR_ind = 1:length(SNR_vect)
for mi = 1:length(users_num)
nusers = users_num(mi);
R_final = zeros(N_sim,1);
str = sprintf('Channel_Mat/H_all_%d_%d_%d_%d',n_t,n_r,nusers,BS);
eval(['load ' str]);
dlg.FractionComplete = 0;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f, %d%% done', nusers,SNR_vect(SNR_ind),0);
tic
for avg_sim_ind = 1:N_sim
H = H_all(:,:,:,:,:,avg_sim_ind); %#ok<*NODEF>
R_temp = 0;
for i = 1:nusers
for j = 1:nusers
for k = 1:nusers
R_S = sum_capacity_R_sigma(H, SNR_vect(SNR_ind), [i,j,k]);
if R_S > R_temp
R_temp = R_S;
end
end
end
end
R_final(avg_sim_ind) = R_temp;
if ~rem(avg_sim_ind,10)
dlg.FractionComplete = avg_sim_ind / N_sim;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f dB, %d%% done',nusers,SNR_vect(SNR_ind),avg_sim_ind*100/N_sim);
end
end
R_F(SNR_ind,mi) = mean(R_final);
time(SNR_ind,mi) = toc;
fprintf('Simulation for no. of users = %d at SNR = %2.1f dB done, time taken = %f\n', nusers, SNR_vect(SNR_ind), time(SNR_ind,mi));
end
end
if numel(time) > 1
fprintf('Total time taken = %f\n', sum(sum(time)));
end
function R_F = SumCapacity_hybrid_grouping(SNR_vect, BS, users_num)
global n_t
global n_r
R_F = zeros(length(SNR_vect), length(users_num));
time = zeros(length(SNR_vect), length(users_num));
fprintf('Enter the value of DoF for each user in each cell :\n');
DoF_str = input('','s');
[DoF,status] = str2num(DoF_str);
if ~status
fprintf('Wrong value input, program will terminate!\n');
return
end
N_sim = 1000;
dlg = ProgressDialog();
for SNR_ind = 1:length(SNR_vect)
for mi = 1:length(users_num)
nusers = users_num(mi);
R_final = zeros(N_sim,1);
str = sprintf('Channel_Mat/H_all_%d_%d_%d_%d',n_t,n_r,nusers,BS);
eval(['load ' str]);
dlg.FractionComplete = 0;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f, %d%% done', nusers,SNR_vect(SNR_ind),0);
tic
for avg_sim_ind = 1:N_sim
H = H_all(:,:,:,:,:,avg_sim_ind); %#ok<*NODEF>
R_final(avg_sim_ind) = Sum_capacity_hybrid_grouping(H, SNR_vect(SNR_ind), nusers, BS, DoF);
if ~rem(avg_sim_ind,10)
dlg.FractionComplete = avg_sim_ind / N_sim;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f dB, %d%% done',nusers,SNR_vect(SNR_ind),avg_sim_ind*100/N_sim);
end
end
R_F(SNR_ind) = mean(R_final);
time(SNR_ind) = toc;
fprintf('Simulation for no. of users = %d at SNR = %2.1f dB done, time taken = %f\n', nusers, SNR_vect(SNR_ind), time(SNR_ind));
end
end
if numel(time) > 1
fprintf('Total time taken = %f\n', sum(sum(time)));
end
function R_S = Sum_capacity_hybrid_grouping(H, SNR, K, L, dof)
global n_t
global n_r
SNR = 10^(SNR/10);
sz = n_t - ((K(L-2)+1)*dof);
U = zeros(n_r,dof,K,L);
V = zeros(n_t,sz,K,L);
G = zeros(n_t,dof,L);
for cell_ind = 1:L
next_cell_ind = cell_ind + 1;
if cell_ind + 1 > L, next_cell_ind = 1;end
if K <= 3
mat_req = zeros(K*n_t,n_t + K*n_r);
sz_eye = 1;
sz_H_colm = n_t;
sz_H_row = 1;
for i = 1:K
mat_req(sz_eye:sz_eye+n_t-1,1:n_t) = eye(n_t);
mat_req(sz_H_row:sz_H_row+n_t-1,sz_H_colm+1:sz_H_colm+n_r) = -H(:,:,i,next_cell_ind,cell_ind)';
sz_eye = sz_eye + n_t;
sz_H_row = sz_H_row + n_t;
sz_H_colm = sz_H_colm + n_r;
end
X = null(mat_req);
G(:,:,cell_ind) = X(1:n_t,:);
sz = n_t;
for i = 1:K
U(:,:,i,next_cell_ind) = X(sz+1:sz+n_r,:);
sz = sz + n_r;
end
else
disp('bye');
end
end
for cell_ind = 1:L
next_cell_ind = cell_ind + 1;
if next_cell_ind > L, next_cell_ind = 1;end
for user_ind = 1:K
mat_req = zeros((K*(L-2)+1)*dof,n_t);
mat_req(1:dof,:) = G(:,:,cell_ind)';
req_cell_ind = 1:L;
req_cell_ind(req_cell_ind == cell_ind) = [];
req_cell_ind(req_cell_ind == next_cell_ind) = [];
sz = dof;
for i = req_cell_ind
for j = 1:K
mat_req(sz + 1:sz + dof,:) = U(:,:,j,i)'*H(:,:,j,i,cell_ind);
sz = sz + dof;
end
end
V(:,:,user_ind,cell_ind) = null(mat_req);
end
end
sz = size(V,2);
% R_S = 0;
R = zeros(1);
for cell_ind = 1
H_tilda = zeros(dof,sz,K);
for k = 1:K
H_tilda(:,:,k) = U(:,:,k,cell_ind)'*H(:,:,k,cell_ind,cell_ind)*V(:,:,k,cell_ind);
end
R(cell_ind) = SumCapacityOfUserSet_DPC(1:K, H_tilda, SNR, sz, dof);
end
R_S = mean(R);
function R_S = SumCapacityOfUserSet_DPC(comb, H, SNR, n_t, n_r)
% R_S = 0;
set_card = length(comb);
P = getMACCovMat(comb, H, SNR, set_card, n_t, n_r);
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
% Note: While solving dual MAC problem it is assumed that decoding order is
% 1,2,...,K while the eqn for BC capacity (3) in "Duality, Achievable Rates,
% and Sum-Rate Capacity of Gaussian MIMO Broadcast Channels" is written
% assuming encoding order 1,2,...,K. Therefore here after solving dual
% problem the encoding order will reverse i.e. in BC K,K-1,..,1 and the
% capacity eqn will change as below:
% Q = getMACToBCCovMat(comb, P, H, set_card, n_t, n_r);
% for j = 1:set_card
% mat = zeros(n_t,n_t);
% for i = 1:j-1
% mat = mat + Q(:,:,i);
% end
% mat_num = mat + Q(:,:,j);
% num = real(det(eye(n_r) + H(:,:,comb(j))*mat_num*H(:,:,comb(j))'));
% den = real(det(eye(n_r) + H(:,:,comb(j))*mat*H(:,:,comb(j))'));
% R_S = R_S + log2(num/den);
% end
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
% Alternate way to evaluate capacity (MAC)
mat = eye(n_t);
for j = 1:set_card
mat = mat + H(:,:,comb(j))'*P(:,:,j)*H(:,:,comb(j));
end
R_S = log2(real(det(mat)));
% function Q_bar = getMACToBCCovMat(comb, P, H, K, n_t, n_r)
%
% Q_bar = zeros(n_t,n_t,K);
%
% for j = 1:K
% mat = zeros(n_t,n_t);
% for l = 1:j-1
% mat = mat + Q_bar(:,:,l);
% end
%
% D = eye(n_r) + H(:,:,comb(j))*mat*H(:,:,comb(j))';
% E = eye(n_t);
% for l = j+1 : K
% E = E + H(:,:,comb(l))' * P(:,:,l) * H(:,:,comb(l));
% end
% [F,~,G] = svd(E^-0.5 * H(:,:,comb(j))' * D^-0.5, 0);
% Q_bar(:,:,j) = (E^-0.5)*F*(G')*(D^0.5)*P(:,:,j)*(D^0.5)*G*(F')*(E^-0.5);
% end
function P = getMACCovMat(comb,H, Pow, K, n_t, n_r)
G = zeros(n_r,n_t,K);
P = zeros(n_r,n_r,K);
for j = 1:K
P(:,:,j) = eye(n_r)*Pow/(K*n_r);
end
for n = 1:75
for j = 1:K
mat = eye(n_t);
for i = 1:K
if i == j, continue;end
mat = mat + H(:,:,comb(i))' *P(:,:,i)* H(:,:,comb(i));
end
G(:,:,j) = H(:,:,comb(j)) * (mat^-0.5);
end
S = getWaterFillCovMat(G,n_r,K, Pow);
P_nM1 = P;
MSE = zeros(1,K);
for j = 1:K
if K <= 2
P(:,:,j) = S(:,:,j);
else
P(:,:,j) = 1/K * S(:,:,j) + (K-1)/K * P(:,:,j);
end
MSE(j) = sum(sum((P(:,:,j) - P_nM1(:,:,j)).^2))/(n_t*n_r);
end
if sum(MSE)/K < 1e-7, break;end
end
function S = getWaterFillCovMat(G,n_r,K, Pow)
S = zeros(n_r,n_r,K);
lambda = zeros(n_r*K,1);
for i = 1:K
lambda((i-1)*n_r+1:i*n_r,1) = real(eig(G(:,:,i)*G(:,:,i)'));
end
pl = Water_filling(lambda, Pow);
for i = 1:K
[U,~] = eig(G(:,:,i)*G(:,:,i)');
Lam = diag(pl((i-1)*n_r+1:i*n_r));
S(:,:,i) = U*Lam*U';
end
function R_F = SumCapacity_grouping_Optimal(SNR_vect, BS, users_num)
global n_t
global n_r
R_F = zeros(length(SNR_vect), length(users_num));
time = zeros(length(SNR_vect), length(users_num));
fprintf('Enter the value of DoF for each user in each cell :\n');
DoF_str = input('','s');
[DoF,status] = str2num(DoF_str);
if ~status
fprintf('Wrong value input, program will terminate!\n');
return
end
K = min(floor((n_t/DoF-1)/(BS-1)), 1+floor((n_r/DoF-1)/(BS-1)));
N_sim = 1000;
% dlg = ProgressDialog();
for SNR_ind = 1:length(SNR_vect)
for mi = 1:length(users_num)
nusers = users_num(mi);
R_final = zeros(N_sim,1);
str = sprintf('Channel_Mat/H_all_%d_%d_%d_%d',n_t,n_r,nusers,BS);
eval(['load ' str]);
% dlg.FractionComplete = 0;
% dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f, %d%% done', nusers,SNR_vect(SNR_ind),0);
progress(0);
tic
for avg_sim_ind = 1:N_sim
H = H_all(:,:,:,:,:,avg_sim_ind); %#ok<*NODEF>
comb = combntns(1:nusers,K);
all_perm = allcomb_gg(1:size(comb,1), BS);
for k = 1:size(all_perm,1)
user_comb = comb(all_perm(k,:)',:);
R_S = Sum_capacity_grouping(H, SNR_vect(SNR_ind), user_comb, K,BS, DoF);
if R_S > R_final(avg_sim_ind)
R_final(avg_sim_ind) = R_S;
end
end
if ~rem(avg_sim_ind,10)
% dlg.FractionComplete = avg_sim_ind / N_sim;
% dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f dB, %d%% done',nusers,SNR_vect(SNR_ind),avg_sim_ind*100/N_sim);
progress(avg_sim_ind / N_sim);
end
end
R_F(SNR_ind,mi) = mean(R_final);
time(SNR_ind,mi) = toc;
fprintf('Simulation for no. of users = %d at SNR = %2.1f dB done, time taken = %f\n', nusers, SNR_vect(SNR_ind), time(SNR_ind,mi));
end
end
if numel(time) > 1
fprintf('Total time taken = %f\n', sum(sum(time)));
end
function R_F = Sum_capacity_MIMO_IC(H, SNR,comb)
global n_t
global n_r
U = zeros(n_r,n_r,2);
V = zeros(n_t,n_t,2);
[U(:,:,1),~,V(:,:,1)] = svd(H(:,:,2,1,comb(1)));
[U(:,:,2),~,V(:,:,2)] = svd(H(:,:,1,2,comb(2)));
% For H_1 we will take the last N columns
H_1_tmp = U(:,:,1)'*H(:,:,1,1,comb(1))*V(:,:,2);
H_1 = H_1_tmp(:,n_t-n_r+1:end);
% For H_2 we will take the first min(M-N,N) inputs
H_2_tmp = U(:,:,2)'*H(:,:,2,2,comb(2))*V(:,:,1);
H_2 = H_2_tmp(1:min(n_t-n_r,n_r),n_r+1:end);
Pow = 10^(SNR / 10);
lambda1 = eig(H_1*H_1');
pl1 = Water_filling(lambda1, Pow);
lambda2 = eig(H_2*H_2');
pl2 = Water_filling(lambda2, Pow);
R_F = sum(log2(1 + lambda1.*pl1)) + sum(log2(1 + lambda2.*pl2));
function R_F = SumCapacity_grouping(SNR_vect, BS, users_num)
global n_t
global n_r
R_F = zeros(length(SNR_vect), length(users_num));
time = zeros(length(SNR_vect), length(users_num));
fprintf('Enter the value of DoF for each user in each cell :\n');
DoF_str = input('','s');
[DoF,status] = str2num(DoF_str);
if ~status
fprintf('Wrong value input, program will terminate!\n');
return
end
N_sim = 1000;
dlg = ProgressDialog();
for SNR_ind = 1:length(SNR_vect)
for mi = 1:length(users_num)
nusers = users_num(mi);
R_final = zeros(N_sim,1);
% str = sprintf('Channel_Mat/H_all_%d_%d_%d_%d',n_t,n_r,nusers,BS);
% eval(['load ' str]);
dlg.FractionComplete = 0;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f, %d%% done', nusers,SNR_vect(SNR_ind),0);
tic
comb = repmat(1:nusers,BS,1);
for avg_sim_ind = 1:N_sim
% H = H_all(:,:,:,:,:,avg_sim_ind); %#ok<*NODEF>
H = (randn(n_r,n_t,nusers,BS,BS) + 1i*randn(n_r,n_t,nusers,BS,BS))/sqrt(2);
R_final(avg_sim_ind) = Sum_capacity_grouping(H, SNR_vect(SNR_ind),comb, nusers, BS, DoF);
if ~rem(avg_sim_ind,10)
dlg.FractionComplete = avg_sim_ind / N_sim;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f dB, %d%% done',nusers,SNR_vect(SNR_ind),avg_sim_ind*100/N_sim);
end
end
R_F(SNR_ind) = mean(R_final);
time(SNR_ind) = toc;
fprintf('Simulation for no. of users = %d at SNR = %2.1f dB done, time taken = %f\n', nusers, SNR_vect(SNR_ind), time(SNR_ind));
end
end
if numel(time) > 1
fprintf('Total time taken = %f\n', sum(sum(time)));
end
function R_F = SumCapacity_three_cell_alignment(SNR_vect, BS, users_num)
global n_t
global n_r
R_F = zeros(length(SNR_vect), length(users_num));
time = zeros(length(SNR_vect), length(users_num));
fprintf('Enter the value of DoF for each user in each cell :\n');
DoF_str = input('','s');
[DoF,status] = str2num(DoF_str);
if ~status
fprintf('Wrong value input, program will terminate!\n');
return
end
N_sim = 1000;
dlg = ProgressDialog();
for SNR_ind = 1:length(SNR_vect)
for mi = 1:length(users_num)
nusers = users_num(mi);
R_final = zeros(N_sim,1);
% str = sprintf('Channel_Mat/H_all_%d_%d_%d_%d',n_t,n_r,nusers,BS);
% eval(['load ' str]);
dlg.FractionComplete = 0;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f, %d%% done', nusers,SNR_vect(SNR_ind),0);
tic
comb = repmat(1:nusers,BS,1);
for avg_sim_ind = 1:N_sim
% H = (randn(n_r,n_t,3,3,nusers) + 1i*randn(n_r,n_t,3,3,nusers))/sqrt(2);
H = (randn(n_r,n_t,3,3,nusers) + 1i*randn(n_r,n_t,3,3,nusers))/sqrt(2);
% H = H_all(:,:,:,:,:,avg_sim_ind); %#ok<*NODEF>
R_final(avg_sim_ind) = Sum_capacity_three_cell(H, SNR_vect(SNR_ind),comb, nusers, DoF);
if ~rem(avg_sim_ind,10)
dlg.FractionComplete = avg_sim_ind / N_sim;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f dB, %d%% done',nusers,SNR_vect(SNR_ind),avg_sim_ind*100/N_sim);
end
end
R_F(SNR_ind) = mean(R_final);
time(SNR_ind) = toc;
fprintf('Simulation for no. of users = %d at SNR = %2.1f dB done, time taken = %f\n', nusers, SNR_vect(SNR_ind), time(SNR_ind));
end
end
if numel(time) > 1
fprintf('Total time taken = %f\n', sum(sum(time)));
end
function [R_F,input_approach] = SumCapacity_cyclic_model2(SNR_vect, BS, nusers)
global n_t
global n_r
R_F = zeros(length(SNR_vect), 1);
time = zeros(length(SNR_vect), 1);
input_approach = [];
fprintf('Enter the value of DoF for each user in each cell :\n');
DoF_str = input('','s');
[DoF,status] = str2num(DoF_str);
if ~status
fprintf('Wrong value input, program will terminate!\n');
return
end
fprintf('Enter the type of approach in Model 2, curretly available [b, c] :\n');
input_approach = input('','s');
err_flag = 0;
switch input_approach
case 'b'
if n_t < nusers*n_r || n_r < (nusers+1)*DoF
err_flag = 1;
end
Sum_capacity = @ Sum_capacity_cyclic_model2_b;
case 'c'
if n_t < 2*nusers*DoF || n_r < (nusers+1)*DoF
err_flag = 1;
end
Sum_capacity = @ Sum_capacity_cyclic_model2_c;
otherwise
fprintf('Input approach doesn''t exist, program will terminate!\n');
return
end
if err_flag
fprintf('Antenna values doesn''t met constraints, program will terminate!\n');
return
end
N_sim = 1000;
dlg = ProgressDialog();
for SNR_ind = 1:length(SNR_vect)
R_final = zeros(N_sim,1);
% str = sprintf('Channel_Mat/H_all_%d_%d_%d_%d',n_t,n_r,nusers,BS);
% eval(['load ' str]);
dlg.FractionComplete = 0;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f, %d%% done', nusers,SNR_vect(SNR_ind),0);
tic
comb = repmat(1:nusers,BS,1);
for avg_sim_ind = 1:N_sim
H = (randn(n_r,n_t,BS,BS,nusers) + 1i*randn(n_r,n_t,BS,BS,nusers))/sqrt(2);
% H = H_all(:,:,:,:,:,avg_sim_ind); %#ok<*NODEF>
R_final(avg_sim_ind) = Sum_capacity(H, SNR_vect(SNR_ind),comb, BS, nusers, DoF);
if ~rem(avg_sim_ind,10)
dlg.FractionComplete = avg_sim_ind / N_sim;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f dB, %d%% done',nusers,SNR_vect(SNR_ind),avg_sim_ind*100/N_sim);
end
end
R_F(SNR_ind) = mean(R_final);
time(SNR_ind) = toc;
fprintf('Simulation for no. of users = %d at SNR = %2.1f dB done, time taken = %f\n', nusers, SNR_vect(SNR_ind), time(SNR_ind));
end
if numel(time) > 1
fprintf('Total time taken = %f\n', sum(time));
end
function [R_F,input_approach] = SumCapacity_cyclic_model2_Capacity(SNR_vect, L, users_num)
global n_t
global n_r
R_F = zeros(length(SNR_vect), length(users_num));
time = zeros(length(SNR_vect), length(users_num));
input_approach = [];
fprintf('Enter the value of DoF for each user in each cell :\n');
DoF_str = input('','s');
[DoF,status] = str2num(DoF_str);
if ~status
fprintf('Wrong value input, program will terminate!\n');
return
end
fprintf('Enter the type of approach in Model 2, curretly available [b, c] :\n');
input_approach = input('','s');
% err_flag = 0;
switch input_approach
case 'b'
% if n_t < users_num*n_r || n_r < (users_num+1)*DoF,
% err_flag = 1;
% end
K = n_t / n_r;
Sum_capacity = @ Sum_capacity_cyclic_model2_b;
case 'c'
% if n_t < 2*users_num*DoF || n_r < (users_num+1)*DoF,
% err_flag = 1;
% end
K = n_t / 2 / DoF;
Sum_capacity = @ Sum_capacity_cyclic_model2_c;
otherwise
fprintf('Input approach doesn''t exist, program will terminate!\n');
return
end
% if err_flag,
% fprintf('Antenna values doesn''t met constraints, program will terminate!\n');
% return
% end
N_sim = 1000;
dlg = ProgressDialog();
for SNR_ind = 1:length(SNR_vect)
for mi = 1:length(users_num)
nusers = users_num(mi);
R_final = zeros(N_sim,1);
% str = sprintf('Channel_Mat/H_all_%d_%d_%d_%d',n_t,n_r,nusers,L);
% eval(['load ' str]);
dlg.FractionComplete = 0;
dlg.StatusMessage = sprintf('Number of users = %d, SNR = %2.1f, %d%% done', nusers,SNR_vect(SNR_ind),0);
tic
comb = repmat(1:nusers,L,1);
for avg_sim_ind = 1:N_sim
H = (randn(n_r,n_t,L,L,nusers) + 1i*randn(n_r,n_t,L,L,nusers))/sqrt(2);
user_comb = zeros(L,K);
for cell_ind = 1:L
user_comb(cell_ind,:) = getInitialUserSet('new',H(:,:,cell_ind,cell_ind,:), K, 1:nusers);
end
R_temp = 0;
maxValInd_exist = 0;