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precoder_select_ML_ver6.m
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precoder_select_ML_ver6.m
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function [F, F_index]=precoder_select_ML_ver6(H,nS)
% Input parameters
% H: Channel matrix (4 x 4 Complex matrix),
% nS: number of Tx antennas (default = 4)
% Output parameter
% F : Precoder itself(when getIndex==0), or precoder index (when getIndex==1)
% radius_scores : Calculated minimum radius of all(16) precoder
%% Default Value
if nargin < 1
rng('default');
rng(2254);
disp('[Message] Proposed_Precoder_Selection : Default set H, nS');
nT = 4; nR = 4;
nS = 4;
H = 1/sqrt(nS)*sqrt(1/2)*(randn(nT,nR)+1i*randn(nT,nR));
elseif nargin < 2
disp('[Message] Proposed_Precoder_Selection : Default set only nS');
nS = 4;
end
%%
j= sqrt(-1);
%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]];
% 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
delta_x_set=[-3 -2 -1 0 1 2 3]; plus_cond = logical([0 0 0 1 1 1 1]);
% delta_x_set=[0 1 -1 2 -2 3 -3]; plus_cond = [1 1 0 1 0 1 0];
YES=1; NO=0;
termination_idx=100;
x_list_init=ones(2*nS,length(delta_x_set)).*100;
x_now_init =ones(2*nS,1).*100;
max_of_min_radius=0;
if nS == 4
precoder_index=[1,2,5,6,13];
elseif nS == 2
precoder_index = 1:1:16;
end
for precoder_idx=precoder_index
candidate_count = zeros(nS * 2, 1);
candidate_idx = ones(nS, 1);
zero_count = 0;
if nS == 4
HF=H*F4(:,:,precoder_idx);
elseif nS == 2
HF=H*F2(:,:,precoder_idx);
end
H_R =[real(HF) -(imag(HF)); imag(HF) real(HF)]; % complex system -> real system
[~,R_R] = qr(H_R); % QR Decomposition
min_radius = min(vecnorm(R_R)); %initialize min_radius
if min_radius<=max_of_min_radius
continue;
end
stage_idx=1;
Is_New_Stage=YES;
x_list=x_list_init;
x_now=x_now_init;
while stage_idx~=termination_idx
if stage_idx==2*nS+1 %if a vector of length 2xnT is found
if zero_count == 2 * nS
stage_idx=stage_idx-1;
zero_count = zero_count - 1;
Is_New_Stage=NO; % if metric_temp is zero vector
else
metric_temp=norm(R_R*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=YES;
zero_count = 0;
x_list=x_list_init;
x_now=x_now_init;
else
if x_now(1) == 0
zero_count = zero_count - 1;
end
stage_idx=stage_idx-1;
Is_New_Stage=NO;
end
end
else %if the length of the vector x_now is shorter than 2nT
if Is_New_Stage==YES % In case of a new stage, we choose candidate symbols for the stage
%tic
RR_mul_x_now = R_R(2 *nS-stage_idx+1:end, 2 *nS-stage_idx+2:end)*...
x_now(2 *nS-stage_idx+2:end);
if stage_idx == 1
middle = min_radius^2;
else
middle = min_radius^2-sum(abs(RR_mul_x_now(2:end)).^2);
end
R_value_stage = R_R(2*nS-stage_idx+1,2*nS-stage_idx+1);
if R_value_stage > 0
bound_lower=(-sqrt(middle)-RR_mul_x_now(1))/R_value_stage;
bound_upper=(sqrt(middle)-RR_mul_x_now(1))/R_value_stage;
else
bound_lower=(sqrt(middle)-RR_mul_x_now(1))/R_value_stage;
bound_upper=(-sqrt(middle)-RR_mul_x_now(1))/R_value_stage;
end
delta_x_cond = (bound_lower <= delta_x_set)&(delta_x_set <= bound_upper);
if stage_idx==1
delta_x_cond(1:3) = false;
end %if stage_idx is 1, delta_x_set->delta_x_set+
len_B = sum(delta_x_cond);
x_list(end-stage_idx+1, 1:len_B) = delta_x_set(delta_x_cond);
candidate_count(stage_idx) = len_B;
candidate_idx(stage_idx) = 1;
%time_temp = time_temp + toc;
% time_curr = time_curr + 1;
end
if candidate_count(stage_idx) == 0
%if the stage does not contain any candidate symbol
if stage_idx==1
stage_idx=termination_idx;
else
Is_New_Stage=NO;
stage_idx=stage_idx-1;
if x_now(end - stage_idx + 1) == 0
zero_count = zero_count - 1;
end
end
else % candidates exist
candidate_entry = x_list(end-stage_idx+1,candidate_idx(stage_idx));
x_now(end -stage_idx+1)= candidate_entry ;
if candidate_entry == 0
zero_count = zero_count + 1;
end
Is_New_Stage=YES;
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 ~any(x_list(2*nS-stage_idx+1,:) - 100)
end % if stage_idx==2*nS+1
end % while
if min_radius > max_of_min_radius
max_of_min_radius = min_radius;
opt_precoder_idx = precoder_idx;
end
% precoder_score(precoder_idx) = min_radius;
end % for
if nS == 4
F = F4(:,:,opt_precoder_idx);
F_index = opt_precoder_idx;
elseif nS == 2
F = opt_precoder_idx;
end
% disp(time_temp / time_curr);
% radius_scores = precoder_score;