Writing mathematical equations in MATLAB

[EngWiPy]

Hello,

I have the attached paper, and I want to write equations 4, 5 and the equation in the first line after equation 5 in MATLAB. I did it as following:

Np=24;
L=19;
TapsL=[1 19 20];
S=length(TapsL);

Index=zeros(S,1);%Tap Locations   
    c=zeros(L+1,1);
    cHatMP=zeros(L+1,1);
    hHatMP=zeros(S,1);%Taps CS Estimates
    
    h=(1/sqrt(2.*(S))).*(randn(S,1)+1i.*randn(S,1));
    c(TapsL)=h;
   
    
    %Channel Estimation
    np=(1/sqrt(2*SNR(ii))).*(randn(Np+L,1)+1i.*randn(Np+L,1));
    n=(1/sqrt(2*SNR(ii))).*(randn(Nd+L,1)+1i.*randn(Nd+L,1));
    
    xpCP=[xp(end-L+1:end);xp];
    
    yp=filter(c,1,xpCP)+np;
    
    yp(1:L)=[]; At this point we have y=Ac+n
    
    cHatLS=inv(transpose(conj(A))*A)*transpose(conj(A))*yp;%Least square channel estimation
    
    
    for ss=1:S
        max=0;
        for pp=1:L+1
            if ss>1
                set=0;
                for mm=1:ss-1
                    if Index(mm)==pp
                        set=1;
                    end
                end
                if set==0
                    Proj=(abs(transpose(conj(A(:,pp)))*yp)^2)/norm(A(:,pp))^2;
                    if Proj>max
                       max=Proj;
                       maxIndex=pp;
                    end 
                end
            else
                Proj=(abs(transpose(conj(A(:,pp)))*yp)^2)/norm(A(:,pp))^2;
                if Proj>max
                   max=Proj;
                   maxIndex=pp;
                end
            end                   
        end
        hHatMP(ss)=transpose(conj(A(:,maxIndex)))*yp/norm(A(:,maxIndex))^2;
        Index(ss)=maxIndex;
        yp=yp-((transpose(conj(A(:,maxIndex)))*yp*A(:,maxIndex))/norm(A(:,maxIndex))^2);
    end 
    
     
    cHatMP(Index)=hHatMP;

but I get unexpected results when using these values. So, I do not know if I am doing it wrongly in MATLAB. Any suggestion, please?

Note: Assume A is given.

Thanks

 

[mmwave]

for your post and for sharing your code. It looks like you are on the right track with your code, but there could be a few issues that are causing unexpected results. Here are some suggestions to help troubleshoot and improve your code:

1. Check your input values: Make sure that all of your input values, such as Np, L, TapsL, SNR, and Nd, are correct and consistent with the values used in the paper. Double check that you are using the correct units and that your arrays are the correct dimensions.

2. Check your equations: Make sure that you are implementing equations 4, 5, and the equation after 5 correctly in your code. Double check the order of operations and make sure you are using the correct operators for complex numbers.

3. Use built-in functions: Instead of writing your own code for the least squares channel estimation and maximum projection algorithm, consider using built-in functions in MATLAB such as "inv" and "norm". This can help ensure that the calculations are done correctly and can save you time and effort in writing and debugging your own code.

4. Debug your code: Use the built-in debugging tools in MATLAB to step through your code and check the values of your variables at each step. This can help you identify where the unexpected results are coming from and make adjustments to your code.

5. Compare your results to the paper: Finally, double check your results against the results presented in the paper. It is possible that there may be small differences due to rounding or other factors, but your results should be close to the results in the paper.

I hope these suggestions help you improve your code and get the expected results. Good luck!