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precoder_select_ML_kim_ver3.m
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function [F, F_idx]=precoder_select_ML_kim_ver3(H,nS)
%PRECODER_SELECT_ML_VER6_COMPLEX
j= sqrt(-1);
%% Default Value
if nargin < 1
rng('default');
rng(5656);
disp('[Message] Proposed_Precoder_Selection : Default set H, nS');
nT = 4; nR = 4;
nS = 4;
H = 1/sqrt(nS)*sqrt(1/2)*(randn(nR,nT)+j*randn(nR,nT));
elseif nargin < 2
disp('[Message] Proposed_Precoder_Selection : Default set only nS');
nS = 4;
end
%%
%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 ii=1:length(W)
a = u(:, ii) * u(:, ii)'; b = u(:, ii)' * u(:, ii); W(:, :, ii) = 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]];
% Precoder Matrix 'F2' For QAM-16
F2=zeros(4,2,16);
for i=1:length(W)
F2(:, :, i) = W(:, F2_matrix_order(i,:), i) / sqrt(2) ;
end
%%
x_set = [-3:1:3];
delta_x_set = zeros(49, 1);
% plus_cond = false((2 * nS - 1)^2, 1);
curr_delta_x_idx = 1;
max_of_min_radius = 0;
x_list_init= complex(ones(nS,length(delta_x_set)).*(100));
x_now_init = complex(ones(nS,1).*(100));
% for rx = x_set
% for ix = x_set
% delta_x_set(curr_delta_x_idx) = rx + j * ix;
% % if rx >= 0
% if ix >= -rx
% plus_cond(curr_delta_x_idx) = true;
% end
% curr_delta_x_idx = curr_delta_x_idx + 1;
% end
% end
delta_x_set=[ -3.0000 - 3.0000i;
-3.0000 - 2.0000i;
-3.0000 - 1.0000i;
-3.0000 + 0.0000i;
-3.0000 + 1.0000i;
-3.0000 + 2.0000i;
-3.0000 + 3.0000i;%7
-2.0000 - 3.0000i;
-2.0000 - 2.0000i;
-2.0000 - 1.0000i;
-2.0000 + 0.0000i;
-2.0000 + 1.0000i;
-2.0000 + 2.0000i;
-2.0000 + 3.0000i;%14
-1.0000 - 3.0000i;
-1.0000 - 2.0000i;
-1.0000 - 1.0000i;
-1.0000 + 0.0000i;
-1.0000 + 1.0000i;
-1.0000 + 2.0000i;
-1.0000 + 3.0000i;%21
0.0000 - 3.0000i;
0.0000 - 2.0000i;
0.0000 - 1.0000i;
0.0000 + 0.0000i;%25 o
0.0000 + 1.0000i;%26 o
0.0000 + 2.0000i;%27 o
0.0000 + 3.0000i;%28 o
1.0000 - 3.0000i;
1.0000 - 2.0000i;
1.0000 - 1.0000i;
1.0000 + 0.0000i;
1.0000 + 1.0000i;%33 o
1.0000 + 2.0000i;%34 o
1.0000 + 3.0000i;%35 o
2.0000 - 3.0000i;
2.0000 - 2.0000i;
2.0000 - 1.0000i;
2.0000 + 0.0000i;
2.0000 + 1.0000i;%40 o
2.0000 + 2.0000i;%41 o
2.0000 + 3.0000i;%42 o
3.0000 - 3.0000i;
3.0000 - 2.0000i;
3.0000 - 1.0000i;
3.0000 + 0.0000i;
3.0000 + 1.0000i;%47 o
3.0000 + 2.0000i;%48 o
3.0000 + 3.0000i];%49 o
% for first stage
delta_x_set_fs = [
0.0000 + 0.0000i;%25 o
0.0000 + 1.0000i;%26 o
0.0000 + 2.0000i;%27 o
0.0000 + 3.0000i;%28 o
1.0000 + 1.0000i;%33 o
1.0000 + 2.0000i;%34 o
1.0000 + 3.0000i;%35 o
2.0000 + 1.0000i;%40 o
2.0000 + 2.0000i;%41 o
2.0000 + 3.0000i;%42 o
3.0000 + 1.0000i;%47 o
3.0000 + 2.0000i;%48 o
3.0000 + 3.0000i];%49 o
if nS == 4
precoder_index=[1,2,5,6,13];
elseif nS == 2
precoder_index = 1:1:16;
end
%%
% abs_delta_x_set = abs(delta_x_set);
time_temp = 0;
time_curr = 0;
%%
for precoder_idx=precoder_index
candidate_count = zeros(nS, 1); candidate_idx = ones(nS, 1);
searchOver = false;
if nS == 4
HF=H*F4(:,:,precoder_idx) ;
[~,RR] = qr(HF);
min_radius = min([norm(RR(:,1)) norm(RR(:,2)) norm(RR(:,3)) norm(RR(:,4))]);
else
HF=H*F2(:,:,precoder_idx);
[~,RR] = qr(HF);
min_radius = min([norm(RR(:,1)) norm(RR(:,2))]);
end
% RR = complex(RR);
% min_radius = min([norm(RR(:,1)) norm(RR(:,2)) norm(RR(:,3)) norm(RR(:,4))]);
%min_radius = min(vecnorm(RR));
if min_radius<=max_of_min_radius
continue;
end
stage_idx = 1; Is_New_Stage = true; x_now = x_now_init; x_list = x_list_init;
while ~searchOver
% if stage_idx == nS+1
if stage_idx == nS
x_1_temp=round(-RR(1,[2:end])*x_now(2:end)/RR(1,1));
x_now(1)=min(max(real(x_1_temp),-3),3)+j*min(max(imag(x_1_temp),-3),3);
% disp(sum(x_list-100 ~=0, 2));
if ~any(x_now)
stage_idx=stage_idx-1; Is_New_Stage=false; % if metric_temp is zero vector
else
metric_temp=norm(RR*x_now); % calculate the radius
% if metric_temp is less than max_of_min_radius, stop and start next procoder_idx
if metric_temp <= max_of_min_radius, min_radius=metric_temp; break; end
if metric_temp < min_radius
min_radius=metric_temp; stage_idx=1; Is_New_Stage=true;
else
stage_idx=stage_idx-1; Is_New_Stage=false;
end
end
else
if Is_New_Stage
% Refer "MIMO-OFDM Wireless Communications with MATLAB" 332p
R_value_stage = RR(nS-stage_idx+1,nS-stage_idx+1);
RR_mul_x_now = RR(nS-stage_idx+1:end, nS-stage_idx+2:end)*x_now(nS-stage_idx+2:end);
if stage_idx == 1, middle = min_radius^2; coord = 0;
else
middle = min_radius^2-sum(abs(RR_mul_x_now(2:end)).^2);
coord = RR_mul_x_now(1) / R_value_stage;
end
if stage_idx == 1
squared_x_set = abs(delta_x_set_fs + coord).^2 ;
else
squared_x_set = abs(delta_x_set + coord).^2 ;
end
range = middle / (R_value_stage^2);
another_delta_x_cond = squared_x_set <= range;
len_B = sum(another_delta_x_cond);
if stage_idx == 1
x_list(nS-stage_idx+1, 1:len_B)=delta_x_set_fs(another_delta_x_cond);
else
x_list(nS-stage_idx+1, 1:len_B)=delta_x_set(another_delta_x_cond);
end
candidate_count(stage_idx) = len_B;
candidate_idx(stage_idx) = 1;
end
if candidate_count(stage_idx) == 0
%if the stage does not contain any candidate symbol
if stage_idx==1, searchOver=true;
else Is_New_Stage=false; stage_idx=stage_idx-1;
end
else % candidates exist
x_now(nS-stage_idx+1)=x_list(nS-stage_idx+1, candidate_idx(stage_idx));
Is_New_Stage=true;
candidate_idx(stage_idx) = candidate_idx(stage_idx) + 1;
candidate_count(stage_idx) = candidate_count(stage_idx) - 1;
stage_idx=stage_idx+1;
end % if candidate_count(stage_idx) == 0
end
end % While
% disp(min_radius);
%fprintf('%d) %20.30f\n',precoder_idx, min_radius)
if min_radius > max_of_min_radius
max_of_min_radius = min_radius;
opt_precoder_idx = precoder_idx;
end
end
if nS == 4
F = F4(:,:,opt_precoder_idx);
F_idx = opt_precoder_idx;
elseif nS == 2
F = F2(:,:,opt_precoder_idx);
F_idx = opt_precoder_idx;
end
end
function [ q,r ] = vpa_qr( x )
result = feval(symengine,'linalg::factorQR',x);
q=result(1);
r=result(2);
end
%max_of_min_radius
% disp(time_temp / time_curr);