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Optimal_Precoder_Selection_Comparison.m
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% Optimal 과 Proposed가 서로 같은 Precoder를 선택하는지 테스트해보는 실험
% nT = nR = nS = 4에서 진행하도록 설계
j = sqrt(-1);
comparison = false;
nS=4; %number of streams
nT=4; %number of transmit antenna
nR=4; %number of receive antenna
%LTE-A codebook
u=[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
-1, -j, 1, j, (-1-j)/sqrt(2), (1-j)/sqrt(2), (1+j)/sqrt(2), (-1+j)/sqrt(2), -1, -j, 1, j, -1, -1, 1, 1;
-1, 1, -1, 1, -j, j, -j, j, 1, -1, 1, -1, -1, 1, -1, 1;
-1, j, 1, -j, (1-j)/sqrt(2), (-1-j)/sqrt(2),(-1+j)/sqrt(2),(1+j)/sqrt(2), 1, -j, -1, j, 1, -1, -1, 1];
W=zeros(4,4,16);
for i=1:length(W)
a = u(:, i) * u(:, i)';
b = u(:, i)' * u(:, i);
W(:, :, i) = eye(4) - (2 * a) / b;
end
F4_matrix_order = ...
[[1 2 3 4];[1 2 3 4];[3 2 1 4];[3 2 1 4];
[1 2 3 4];[1 2 3 4];[1 3 2 4];[1 3 2 4];
[1 2 3 4];[1 2 3 4];[1 3 2 4];[1 3 2 4];
[1 2 3 4];[1 3 2 4];[3 2 1 4];[1 2 3 4]];
F4=zeros(4,4,16);
for i=1:length(W)
F4(:, :, i) = W(:, F4_matrix_order(i,:), i) / 2;
end
F2_matrix_order = ...
[[1 4];[1 2];[1 2];[1 2];
[1 4];[1 4];[1 3];[1 3];
[1 2];[1 4];[1 3];[1 3];
[1 2];[1 3];[1 3];[1 2]];
F2=zeros(4,2,16);
for i=1:length(W)
F2(:, :, i) = W(:, F2_matrix_order(i,:), i) / sqrt(2);
end
x = [[0,0,0,0]; [0,0,0,1]; [0,0,1,0]; [0,0,1,1];
[0,1,0,0]; [0,1,0,1]; [0,1,1,0]; [0,1,1,1];
[1,0,0,0]; [1,0,0,1]; [1,0,1,0]; [1,0,1,1];
[1,1,0,0]; [1,1,0,1]; [1,1,1,0]; [1,1,1,1]];
mapped_x = zeros(1, 16);
% QAM16 Mapping
parfor idx=1:16
cv = QAM_mapper(x(idx, :), 4);
mapped_x(idx) = cv;
end
possible_x = zeros(nS, 16^(nS));
x_idx = 0;
% 가능한 모든 x vector(possible_x)를 구함
if nS == 4
for a = mapped_x
for b = mapped_x
for c = mapped_x
for d = mapped_x
x_idx = x_idx + 1;
possible_x(:, x_idx) = [a, b, c, d];
end
end
end
end
% in case of F2
else
for a = mapped_x
for b = mapped_x
x_idx = x_idx + 1;
possible_x(:, x_idx) = [a, b];
end
end
end
time_a = clock;
filename = "selectionFile_"+ time_a(1)+ time_a(2)+ time_a(3) + ...
"_" + time_a(4) + time_a(5) + ".mat";
k=4; %2,4,6
frame_size=nS*k; % frame_size = 8;
MAX_frame_NUM=1000;
EbNo_Start=28;%[dB]
EbNo_End=28;
EbNo_Step=1;
EbNo=EbNo_Start:EbNo_Step:EbNo_End; %[dB]
BER_target=5 * 10^(-6);
seed = 6807;
% nS = 4 or nS = 2
if nS == 4
F = F4;
else
F = F2;
end
if nS == 4
precoder_index=[1,2,5,6,13];
elseif nS == 2
precoder_index = 1:1:16;
end
% optimal_selection=zeros(1,MAX_frame_NUM);
% proposed_selection=zeros(1,MAX_frame_NUM);
% LR_selection=zeros(1,MAX_frame_NUM);
%
% i = 0;
%
% for EbNo_idx=EbNo % needs to modify
% i = i + 1;
% bit_error=0;
% rng('default');
% rng(seed);
% %noise variance calculation
% n_var=10^(-EbNo(i)/10)/k;
% tic
% for frame_idx=1:MAX_frame_NUM
% fprintf('[%d] \n', frame_idx);
% %random frame generation
% bits=randi([0 1],1,frame_size);
%
% %QAM mapping
% x=QAM_mapper(bits,k);
% x=transpose(x);%row->column
%
% %wireless transmission
% %Rayleigh fading channel
% H=1/sqrt(nS)*sqrt(1/2)*(randn(nR, nR)+j*randn(nR, nR));
%
% % parfor 로 수행시, precoder 당, 약 500초(8.3분) 정도 수행
%
% % GPU 로 수행시, precoder 당, 약 128초(2.13분) 정도 수행
% [opt_F, opt_idx] = optimal_precoder_select_with_GPUs(H, F4, nS, possible_x, precoder_index);
% [proposed_F, proposed_idx] = precoder_select_ML_kim_ver2(H, nS);
% [LR_F, LR_idx] = QRD_based_BT_E_Method(H, nS, nS-1, 0.99);
%
% optimal_selection(frame_idx) = find(precoder_index==opt_idx);
% proposed_selection(frame_idx) = find(precoder_index==proposed_idx);
% LR_selection(frame_idx) = find(precoder_index==LR_idx);
% % [proposed_F, proposed_idx] = precoder_select_ML_ver6_complex_ver1(H, nS);
% % [proposed_F, proposed_idx] = precoder_select_ML_ver4(H, nS);
% fprintf(' Optimal : %d, Proposed : %d\n', opt_idx, proposed_idx);
% fprintf(' Proposed : %d, LR : %d\n', proposed_idx, LR_idx);
%
% a = clock;
%
% save(filename,'optimal_selection','proposed_selection','LR_selection');
%
%
% end
% toc
%
% end
plotting_selections(optimal_selection(500:600), proposed_selection(500:600), LR_selection(500:600));
% plotting_accuracy(optimal_selection(200:300), proposed_selection(200:300), LR_selection(200:300));
function plotting_accuracy(optimal_selection, proposed_selection, LR_selection)
proposed_accuracy = sum(optimal_selection == proposed_selection) / length(optimal_selection) * 100;
LR_accuracy = sum(optimal_selection == LR_selection) / length(optimal_selection) * 100;
figure;
X = categorical({'Proposed', 'LR-based'});
bar(X,[proposed_accuracy LR_accuracy],'BarWidth', 0.4);
ylabel('Accuracy');
xlabel('Technique');
end
function plotting_selections(optimal, proposed, lr)
[~, trials] = size(optimal);
y = 1:trials;
figure;
plot(y,optimal,'ko', 'MarkerSize', 4, 'MarkerFaceColor', 'k');
hold on;
grid on;
grid minor;
plot(y,proposed,'ko', 'MarkerSize', 8);
hold on;
ylabel('Selected precoder index');
xlabel('Frame index');
xlim([0 trials + 1])
yticks('manual')
ylim([0 6])
yticklabels({'', '1', '2', '3', '4', '5', ''})
xbounds = ylim;
set(gca,'YTick',xbounds(1):xbounds(2));
hold off;
legend('Optimal','Proposed');
figure;
plot(y,optimal,'ko', 'MarkerSize', 4, 'MarkerFaceColor', 'k');
hold on;
grid on;
grid minor;
plot(y,lr,'ko', 'MarkerSize', 8);
hold on;
ylabel('Selected precoder index');
xlabel('Frame index');
xlim([0 trials + 1])
ylim([0 6])
yticklabels({'', '1', '2', '3', '4', '5', ''})
xbounds = ylim;
set(gca,'YTick',xbounds(1):xbounds(2));
hold off;
legend('Optimal','LR-based');
end
function [F_return, F_idx] = optimal_precoder_select(H, F, nS, possible_x, precoder_index)
if nS == 2
F_dist_list = zeros(1, 16);
parfor F_idx = 1:16
min_val = intmax;
for x_1 = 1:length(possible_x)
temp_possible_x = possible_x;
picked_possible_x = possible_x(:, x_1);
temp_possible_x(:, x_1) = [];
diff_x = temp_possible_x - picked_possible_x;
dist = vecnorm(H * F(:, :, F_idx) * (diff_x),2);
[min_dist, min_idx] = min(dist);
if min_val > min_dist
min_val = min_dist;
% fprintf('%d th precoder Min value changed : %f\n', F_idx, min_val);
% min_x_list (:, F_idx) = diff_x(:, min_idx);
end
end
F_dist_list(F_idx) = min_val;
% fprintf('%d th precoder is over. %f\n', F_idx, min_val);
end
else
% parfor 로 수행시, precoder 당, 약 500초(8.3분) 정도 수행
F_dist_list = zeros(1, length(precoder_index));
parfor idx = 1:length(precoder_index)
tic
F_idx = precoder_index(idx);
min_val = intmax;
for x_1 = 1:(nS * nS) ^4
temp_possible_x = possible_x;
picked_possible_x = possible_x(:, x_1);
temp_possible_x(:, x_1) = [];
diff_x = temp_possible_x - picked_possible_x;
dist = vecnorm(H * F(:, :, F_idx) * (diff_x),2);
[min_dist, ~] = min(dist);
if min_val > min_dist
min_val = min_dist;
end
end
F_dist_list(idx) = min_val;
% fprintf('%d th precoder is over. %f\n', F_idx, min_val);
toc
end
end
disp(F_dist_list);
[~, max_idx] = max(F_dist_list);
F_return = F(:, :, max_idx);
F_idx = precoder_index(max_idx);
end
function [F_return, F_idx] = optimal_precoder_select_with_GPUs(H, F, nS, possible_x, precoder_index)
matrix_step_size = 150;
if nS == 4
% possible_x_device = possible_x;
% F_device = F;
% H_device = H;
possible_num = length(possible_x);
F_dist_list = zeros(1, length(precoder_index));
parfor idx = 1:length(precoder_index)
possible_x_device = gpuArray(possible_x);
F_device = gpuArray(F);
H_device = gpuArray(H);
tic
F_idx = precoder_index(idx);
min_val = intmax;
for idx_x = 1:floor(possible_num / matrix_step_size) + 1
if idx_x ~= floor(possible_num / matrix_step_size) + 1
repeated_x = repmat(possible_x_device, 1, 1, matrix_step_size);
[x_1, x_2, x_3]=size(repeated_x);
repeated_x(:,1 + (idx_x - 1) * matrix_step_size:x_2+1:end)=[];
repeated_x = reshape(repeated_x, x_1, [], x_3);
temp_repelemed = repelem(possible_x_device(:,1 + (idx_x - 1) * matrix_step_size:(idx_x) * matrix_step_size), ...
1,possible_num - 1);
single_repeated_x = reshape(temp_repelemed,[],possible_num-1,matrix_step_size);
subbed_repeated_x = repeated_x - single_repeated_x;
else
remained_size = mod(possible_num, matrix_step_size);
repeated_x = repmat(possible_x, 1, 1, remained_size);
[x_1, x_2, x_3]=size(repeated_x);
repeated_x(:,1 + (idx_x - 1) * matrix_step_size:x_2+1:end)=[];
repeated_x = reshape(repeated_x, x_1, [], x_3);
temp_repelemed = repelem(possible_x_device(:,1 + (idx_x - 1) * matrix_step_size:end), ...
1,possible_num - 1);
single_repeated_x = reshape(temp_repelemed,[],possible_num-1,remained_size);
subbed_repeated_x = repeated_x - single_repeated_x;
end
Y = H_device * F_device(: , : , F_idx);
celled_repeated_x = cellfun(@(x) Y * x, num2cell(subbed_repeated_x, [1 2]),'UniformOutput',false);
celled_repeated_x = cat(3, celled_repeated_x{:});
dist = vecnorm(celled_repeated_x, 2);
min_dist = min(dist,[],'all');
if min_val > min_dist
min_val = min_dist;
end
% fprintf('%d %d %f\n',F_idx, x_1, min_dist);
F_dist_list(idx) = gather(min_val);
end
toc
end
disp(F_dist_list);
[max_val, ~] = max(F_dist_list);
max_idx = find(F_dist_list==max_val, 1, 'last');
F_return = F(:, :, max_idx);
F_idx = precoder_index(max_idx);
end
end