rank deficient system

Dear Matlab users,

I am running the code below:

function GSVD_fad

no_samples=1e3;
SNR_dB=-5:5:35;
SNR_linear=10.^(SNR_dB/10);

Cs=zeros(6,length(SNR_dB));
for Icase=1:6
    if Icase==1, nt=2; nm=2; ne=2;
    elseif Icase==2, nt=3; nm=2; ne=2;
    elseif Icase==3, nt=4; nm=2; ne=5;
    elseif Icase==4, nt=4; nm=5; ne=4;
    elseif Icase==5, nt=4; nm=6; ne=7;
    else nt=12; nm=6; ne=54;
    end
    for i=1:no_samples;
        P=sym(zeros(nt,nt));
        P1=zeros(nt,nt);
        temp=0;
        Hm = (1/sqrt(2))*(randn(nm,nt)+j*randn(nm,nt));
        He = (1/sqrt(2))*(randn(ne,nt)+j*randn(ne,nt));
        r=rank(He)
        [U, V, A, C, D]=gsvd(Hm,He);
        C1=(C.')*C;
        D1=(D.')*D;
        A1=(A')*A;
        for l=1:nt
            syms x
            if (C1(l,l)>D1(l,l))
                if (D1(l,l)==0)
                    D1(l,l)=0.00000001;
                end
                P(l,l)=P(l,l)+((-1+sqrt(1-4*C1(l,l)*D1(l,l)+4*(C1(l,l)-D1(l,l))*C1(l,l)*D1(l,l)/(x*A1(l,l))))/(2*C1(l,l)*D1(l,l)));
            end
        end
        for m=1:length(SNR_dB)
        for l=1:nt
            s=l+1;
            if (s<=nt)
            if(C1(l,l)>D1(l,l)||C1(s,s)>D1(s,s))
                syms x
                f=sum(diag(A1*P))-SNR_linear(m);
                temp=vpa(solve(f==0,x));
            end
            end
        end
        for l=1:nt
            if(C1(l,l)>D1(l,l))
            y=((-1+sqrt(1-4*C1(l,l)*D1(l,l)+4*(C1(l,l)-D1(l,l))*C1(l,l)*D1(l,l)/(temp*A1(l,l))))/(2*C1(l,l)*D1(l,l)));
            if (y>0)
                P1(l,l)=(-1+sqrt(1-4*C1(l,l)*D1(l,l)+4*(C1(l,l)-D1(l,l))*C1(l,l)*D1(l,l)/(temp*A1(l,l))))/(2*C1(l,l)*D1(l,l));
            else
                P1(l,l)=0;
            end
            end
        end
        Cs(Icase,m)=Cs(Icase,m)+log2(real(det((eye(nt)+P1*C1))))-log2(real(det(eye(nt)+P1*D1)));
        end
    end
    end
Cs=Cs/no_samples;

and in some cases I get this warning: system is rank deficient. solution is not unique. How can I deal with this?

Thank you in advance,
El