NR - CSI Codebook

Followings are the code that I wrote in  Matlab 2019b and Phased Array System Toolbox  to creates all the plots shown in this page. You may copy these code and play with these codes. Change variables and try yourself until you get your own intuitive understanding.

It will be helpful for you to understand the code here if you take a look at this page and understand how the radiation daigram for ULA (Uniform Linear Array). Make some practice until you are able to draw a radiation pattern of linear array antenna on your own.

The highlighted part in the code is for drawing the radiation pattern, W_5_2_2_2_1_5() is to calculate the weight vector based on 3GPP NR Codebook Calculation Algorithm explained in this page.

NOTE : At first look, it may not make much of sense, but a couple of things that would seem obvious are

• whenever i₁₁changes the direction of the beam changes

• whenever i₂changes the direction of the beam does not changes. only phase value for each antenna element changes

• Once you get this high level observation, check out the mathematics of this table and try to associate the observation with the math part if you are interested.

< Code 1 >

function main

    c = 3e8;        % propagation speed

    fc = 26e9;      % carrier frequency

    lambda = c/fc;  % wavelength

    NoOfTxAntenna = 8;

    antennaElement = phased.CrossedDipoleAntennaElement;

    txarray = phased.ULA('NumElements',NoOfTxAntenna,'ElementSpacing',lambda/2,'Element',antennaElement);

    txmipos = getElementPosition(txarray)/lambda;

    txarraystv = phased.SteeringVector('SensorArray',txarray,'PropagationSpeed',c);

    P_CSIRS = 16;

    N1 = 8;

    N2 = 1;

    O1 = 4;

    O2 = 1;

    i2List = [0 1 2 3;4 5 6 7;8 9 10 11;12 13 14 15];

    fidx = 1;

    for i2si = 1:4

        for i11 = 0 : (N1*O1-1)  

            for i12 = 0 : (N2*O2-1)

               %for i2 = i2List(:,i2si)'   

               for i2 = i2List(i2si,:)     

                    i_11 = i11;

                    i_12 = i12;

                    i_2 = i2;

                    W = W_5_2_2_2_1_5(2,P_CSIRS,N1,O1,N2,O2,i_11,i_12,i_2);

                    tStr = sprintf('i_{11} = %d, i_{12} = %d, i_2 = %d',i_11,i_12,i_2);

                    wStr = sprintf('i_11 = %d, i_12 = %d, i_2 = %d',i_11,i_12,i_2);

                    for i = 1:15

                       wStr = sprintf('%s ,%0.4f+%0.4fi',wStr,real(W(i)),imag(W(i)));

                    end

                    wStr = sprintf('%s\r\n',wStr);

                    disp(wStr);

                    disp(W);

                    %wt = W.';

                    wt = W;

                    wt1 = wt(1:numel(wt)/2);

                    wt2 = wt(numel(wt)/2+1:end);

                    txbeam_ang = -90:90;

                    txbeam_ang_rad = (pi*txbeam_ang)/180;

                    txbeam1 = (wt1*steervec(txmipos,txbeam_ang));  

                    txbeamMag1 = abs(txbeam1)/max(abs(txbeam1));

                    txbeamArg1 = angle(txbeam1)/max(angle(txbeam1));

                    txbeam2 = (wt2*steervec(txmipos,txbeam_ang));  

                    txbeamMag2 = abs(txbeam2)/max(abs(txbeam2));

                    txbeamArg2 = angle(txbeam2)/max(angle(txbeam2));

                    hFig = figure(1);

                    set(hFig, 'Position', [100 100 600 500]);

                    set(gcf,'color','w');

                    subplot(3,2,1);

                    polarplot(txbeam_ang_rad,txbeamMag1,'r');

                    set(gca,'RTickLabels',[]);

                    title(tStr);

                    subplot(3,2,2);  

                    polarplot(txbeam_ang_rad,txbeamMag2,'r');

                    set(gca,'RTickLabels',[]);

                    title(tStr);

                    subplot(3,2,3);

                    polarplot(txbeam_ang_rad,txbeamArg1,'b');

                    set(gca,'RTickLabels',[]);

                    title('Phase');

                    subplot(3,2,4);  

                    polarplot(txbeam_ang_rad,txbeamArg2,'b');

                    set(gca,'RTickLabels',[]);

                    title('Phase');

                    subplot(3,2,5);

                    plot(real(wt1),imag(wt1),'ro');

                    axis([-1.0 1.0 -1.0 1.0]);

                    pbaspect([1 1 1]);

                    title("W - pol 1");

                    subplot(3,2,6);

                    plot(real(wt2),imag(wt2),'ro');

                    axis([-1.0 1.0 -1.0 1.0]);

                    pbaspect([1 1 1]);

                    title("W - pol 2");

                    pause(0.2);

                end

            end

        end

    end

    fclose(fileID);

end

function W = W_5_2_2_2_1_5(CBtype,P_CSIRS,N1,O1,N2,O2,i_11,i_12,i_2)

    if CBtype == 1

        l = i_11;

        m = i_12;

        n = i_2;

    elseif CBtype == 2 & N2 == 1

        if ismember(i_2, [0 1 2 3])

           l = 2 * i_11 + 0;

        elseif ismember(i_2, [4 5 6 7])

           l = 2 * i_11 + 1;

        elseif ismember(i_2, [8 9 10 11])

           l = 2 * i_11 + 2;   

        elseif ismember(i_2, [12 13 14 15])

           l = 2 * i_11 + 3;

        end   

        m = 0;

        n = mod(i_2,4);    

        %disp(n);

    elseif CBtype == 2 & N2 > 1

       % l = i_11;

       % m = i_12;

       % n = i_2;

    end

    Vlm = CalcVlm(l,N1,O1,m,N2,O2);

    Pn = PhiN(n);

    %W = (1/sqrt(P_CSIRS)) * [Vlm Pn*Vlm].';

    W = (1/sqrt(P_CSIRS)) * [Vlm Pn.*Vlm];

end

function Pn = PhiN(n)

     Pn = exp(j*pi*n/2);

end

function Vlm = CalcVlm(l,N1,O1,m,N2,O2)

    Vlm = [1];

    Um = CalcUm(m,N2,O2);

    for n = 1 : N1-1

        Vlm = [Vlm exp(j*(2*pi*l*n)/(O1*N1))*Um];  

    end

end

function Um = CalcUm(m,N2,O2)

    if N2 == 1

       Um = 1;

    else

       Um = [];

       for n = 0 : N2-1

           Um = [Um exp(j*(2*pi*m*n)/(O2*N2))];  

       end

    end   

end