MATLAB code to calculate spectral efficiency

Please I need help on the code or guideline to calculate spectral efficency of an OFDM waveform.

[KALYAN ACHARJYA]

You asked for Mathematical Analysis or Matlab Implementation?

[Mordecai Raji]

Actually both, the materials I have read does not provide a straight forward guide I can follow. I already have my OFDM signal coded in matlab, transmitted and recieved succssfully. (fourier and wavelet) problem is how to actually calculate the spectral efficiency in each case. Can't find it in matlab documentation.

thanks for the material you provided.

[Aschalew Ambelu]

i went to find spectral efficiency improvement polar code Matlab code

[Aschalew Ambelu]

i need matlab code implementation not matihmatical analysis

Answer 1

[Aschalew Ambelu]

%% Create Precoder based on the LTE-A Codebook
j = sqrt(-1);
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]];

% Precoder Matrix 'F4' For QAM-16
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

%% HyperParameter setting

% 4x4 MIMO, 4 Streams
nS=4;   %number of streams
nT=4;   %number of transmit antenna
nR=4;   %number of receive antenna

% 4x2 MIMO, 2 Streams
nS=2;   %number of streams
nT=2;   %number of transmit antenna
nR=4;   %number of receive antenna

k=4;    %2,4,6

frame_size=nS*k;                    %bits
if nS == 4
    MAX_frame_NUM=79000000;
else 
    MAX_frame_NUM=165250000;
end

EbNo_Start=1;%[dB]
EbNo_End=20;
EbNo_Step=1;
EbNo=EbNo_Start:EbNo_Step:EbNo_End;       %[dB]
BER_target=8 * 10^(-7);
bit_error_target=1000;
threshold =  bit_error_target / (frame_size * BER_target) ; 
seed = 6807;   
file_name = 'MIMO_4x2_QAM16_nS2';
disp(threshold);

   156250000

disp(seed);

        6807

NO_BER = zeros(1,length(EbNo));
SML_BER = zeros(1,length(EbNo));
ML_BER = zeros(1,length(EbNo));
QRD_BER = zeros(1,length(EbNo));
QRD_BTP_BER =zeros(1,length(EbNo));
QRD_BTC_BER =zeros(1,length(EbNo));
QRD_BTE_BER =zeros(1,length(EbNo));
SVD_BER = zeros(1, length(EbNo));

%% Read Figure which is already exists (SEED: 6807)
fig_name = 'MIMO_4x2_QAM16_nS2';
try
    fig = openfig(fig_name);
    h = findobj(gca,'Type','line');
    y_data_cell = get(h,'Ydata');
    y_data_mat = cell2mat(y_data_cell);
    Loaded_NO_BER = y_data_mat(8, :);
    Loaded_ML_BER = y_data_mat(7, :);
    Loaded_SML_BER = y_data_mat(6, :);
    Loaded_QRD_BER = y_data_mat(5, :);
    Loaded_QRD_BTP_BER = y_data_mat(4, :);
    Loaded_QRD_BTC_BER = y_data_mat(3, :);
    Loaded_QRD_BTE_BER = y_data_mat(2, :);
    Loaded_SVD_BER =y_data_mat(1, :);
catch
    disp('Cannot find the figure : set all BER value to zero (list)');
    Loaded_NO_BER = zeros(1,length(EbNo));
    Loaded_SML_BER = zeros(1,length(EbNo));
    Loaded_ML_BER = zeros(1,length(EbNo));
    Loaded_QRD_BER = zeros(1,length(EbNo));
    Loaded_QRD_BTP_BER =zeros(1,length(EbNo));
    Loaded_QRD_BTC_BER =zeros(1,length(EbNo));
    Loaded_QRD_BTE_BER =zeros(1,length(EbNo));
    Loaded_SVD_BER =zeros(1,length(EbNo));
end

Cannot find the figure : set all BER value to zero (list)

precoder_selection_name = ["No_Precoder", "SPS", "Proposed", "QRD", "QRD_BT_P", "QRD_BT_C", "QRD_BT_E", "SVD"];
BER_list = zeros(length(precoder_selection_name),length(EbNo));

%%
parfor function_idx = 0:0
    tic
    BER_Bucket = zeros(1, length(EbNo));
    if function_idx == 1     % No Precoder
        BER_Bucket(1:length(Loaded_NO_BER)) = Loaded_NO_BER;
    elseif function_idx == 2 % SML
        BER_Bucket(1:length(Loaded_SML_BER)) = Loaded_SML_BER;
    elseif function_idx == 3 % ML
        BER_Bucket(1:length(Loaded_ML_BER)) = Loaded_ML_BER;
    elseif function_idx == 4 % QRD
        BER_Bucket(1:length(Loaded_QRD_BER)) = Loaded_QRD_BER;
    elseif function_idx == 5 % QRD_BT_P
        BER_Bucket(1:length(Loaded_QRD_BTP_BER)) = Loaded_QRD_BTP_BER;
    elseif function_idx == 6 % QRD_BT_C
        BER_Bucket(1:length(Loaded_QRD_BTC_BER)) = Loaded_QRD_BTC_BER;
    elseif function_idx == 7 % QRD_BT_E
        BER_Bucket(1:length(Loaded_QRD_BTE_BER)) = Loaded_QRD_BTE_BER;
    elseif function_idx == 8 % SVD
        BER_Bucket(1:length(Loaded_SVD_BER)) = Loaded_SVD_BER;
    end
    
    for EbNo_idx=1:length(EbNo)
        bit_error=0;
        rng('default');
        rng(seed);
        
        % For saving execute time, if BER value already exists, then skip.
        
        if BER_Bucket(EbNo_idx) ~= 0 
            fprintf(strcat(precoder_selection_name(function_idx), ' : EbNo_idx %d) is already exist -> %g\n'), EbNo_idx, BER_Bucket(EbNo_idx));
            continue;
        end
        for frame_idx=1:MAX_frame_NUM
            %random frame generation
            bits=randi([0 1],1,frame_size);
            %             bits=randn(1,frame_size);
            %             neg_idx=find(bits<0);
            %             bits=ones(1,frame_size);
            %             bits(neg_idx)=0;
            
            %QAM mapping
            x=QAM_mapper(bits,k);
            x=transpose(x);%row->column
            
            %noise variance calculation
            n_var=10^(-EbNo(EbNo_idx)/10)/k;
            
            %wireless transmission
            %Rayleigh fading channel
            % H=1/sqrt(nS)*sqrt(1/2)*(randn(nR,nT)+j*randn(nR,nT));
            H=1/sqrt(nS)*sqrt(1/2)*(randn(nR,nR)+j*randn(nR,nR));
            
            if function_idx == 1        % No Precoder
                if nS == 2
                    F = F2(:, :, 1);             
                else                % nS == 4
                    F = F4(:, :, 1);
                end
            elseif function_idx == 2 % SML
                [F, ~] = Simplified_ML_Precoder_Selection(H, nS);
            elseif function_idx == 3    % ML
                F = precoder_select_ML_kim_ver1(H, nS);
            elseif function_idx == 4  % QRD
                [F, ~] = QRD_based_Method(H, nS);
            elseif function_idx == 5   % QRD_BT_P
                [F, ~] = QRD_based_BT_P_Method(H, nS);
            elseif function_idx == 6 % QRD_BT_C
                [F, ~] = QRD_based_BT_C_Method(H, nS, 0.99);
            elseif function_idx == 7 % QRD_BT_E
                if nS ~= 2
                    [F, ~] = QRD_based_BT_E_Method(H, nS, 2, 0.99);
                else
                    [F, ~] = QRD_based_BT_E_Method(H, nS, 1, 0.99);
                end
            elseif function_idx == 8 % SVD
                [F, ~] = SVD_based_Method(H, nS);
            end
            % Use selected Random Precoder
            % n : Gaussian noise
            n=sqrt(n_var/2)*(randn(nR,1)+j*randn(nR,1));
            y=H*F*x+n;
            
            %receiver
            %Rayleigh fading channel
            %If F is selected by ML algorithm, then use sphere decoder to get
            % original stream(signal).
            
            HF = H*F;
            s_hat=Sphere_Decoder_Complex(y,HF,nS,k,n_var);
            bits_hat=QAM_demapper(s_hat,k);
            
            %BER calculation
            bit_error=bit_error+sum(xor(bits,bits_hat));
            if bit_error > bit_error_target
                BER_Bucket(EbNo_idx)=bit_error/(frame_idx*frame_size);
                fprintf(strcat(precoder_selection_name(function_idx), ' : EbNo_idx %d) is over -> %g\n'),EbNo_idx, bit_error/(frame_idx*frame_size));
                break;
            end
            
            if bit_error_target /(frame_idx*frame_size) < BER_target
                BER_Bucket(EbNo_idx)=bit_error/(frame_idx*frame_size);
                fprintf(strcat(precoder_selection_name(function_idx), ' : EbNo_idx %d) is over -> %g\n'),EbNo_idx, bit_error/(frame_idx*frame_size));
                break;
            end
        end
        if BER_Bucket(EbNo_idx) < BER_target
            break; 
        end
    end
    
    disp(strcat('---------------', precoder_selection_name(function_idx), ...
        ' Precoder Selection performance measurement is over ---------------'));
    if function_idx == 1        % No Precoder
        NO_BER = NO_BER + BER_Bucket;
    elseif function_idx == 2 % SML
        SML_BER =  SML_BER + BER_Bucket;
    elseif function_idx == 3    % ML
        ML_BER = ML_BER + BER_Bucket;
    elseif function_idx == 4  % QRD
        QRD_BER = QRD_BER + BER_Bucket;
    elseif function_idx == 5   % QRD_BT_P
        QRD_BTP_BER = QRD_BTP_BER + BER_Bucket;
    elseif function_idx == 6 % QRD_BT_C
        QRD_BTC_BER = QRD_BTC_BER + BER_Bucket;
    elseif function_idx == 7 % QRD_BT_E
        QRD_BTE_BER = QRD_BTE_BER + BER_Bucket;
    elseif function_idx == 8 % QRD_BT_E
        SVD_BER = SVD_BER + BER_Bucket;
    end
    toc
end

Warning: The temporary variable 'F' will be cleared at the beginning of each iteration of the parfor-loop. If 'F' is used before it is set, a runtime error will occur. For more information, see Parallel for Loops in MATLAB, "Uninitialized Temporaries".

Starting parallel pool (parpool) using the 'Processes' profile ...
Parallel pool using the 'Processes' profile is shutting down.

Error using solution>(parfor supply)
Array indices must be positive integers or logical values.

disp('All over');
figure;
semilogy(EbNo,NO_BER, 'rx-');  hold on;
semilogy(EbNo, ML_BER, 'bo-');         hold on;
semilogy(EbNo, SML_BER, 'm*--');      hold on;
semilogy(EbNo, QRD_BER, 'k+-');        hold on;
semilogy(EbNo, QRD_BTP_BER, 'k^-');    hold on;
semilogy(EbNo, QRD_BTC_BER, 'ks-');    hold on;
semilogy(EbNo, QRD_BTE_BER, 'kd-.');    hold on;
semilogy(EbNo, SVD_BER, 'k>--');    hold on;
title('BER Performance comparison for precoder selection');
xlabel('SNR[dB]');
ylabel('BER');
lgd = legend('No precoder','ML precoder', 'SML precoder', 'QRD precoder', ...
    'QRD BT-P precoder', 'QRD BT-C precoder', 'QRD BT-E precoder', 'SVD precoder','Location','southwest');
lgd.NumColumns = 2;
saveas(gcf,file_name);


figure;
semilogy(EbNo,NO_BER, 'rx-');  hold on;
semilogy(EbNo, ML_BER, 'bo-');         hold on;
semilogy(EbNo, SML_BER, 'm*--');      hold on;
semilogy(EbNo, QRD_BER, 'k+-');        hold on;
% semilogy(EbNo, QRD_BTP_BER, 'k^-');    hold on;
% semilogy(EbNo, QRD_BTC_BER, 'ks-');    hold on;
semilogy(EbNo, SVD_BER, 'k>--');    hold on;
semilogy(EbNo, QRD_BTE_BER, 'kd-.');    hold on;

xlabel('SNR[dB]');
ylabel('BER');
lgd = legend('No precoder','ML precoder', 'Simplified', 'QRD'...
    ,'SVD','LR','Location','southwest');
lgd.NumColumns = 2;
saveas(gcf,file_name);