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% this function computes the lowe triangular Matrix L with N*N dimension, % using Cholesky factorization of C^-1 % for detail see paper [1] % C= E{hh'}+sigma2*I % E{h(k+n)h*(k)}=sig_1*sig_2*J0(2*pi*fsr*n)*J0(2*pi*frd*n) % C^-1=L*Lh function Lh=computeL(P0,A2,N0,N,fsr,frd,ch_dis,sig_1,sig_2) % N is the dimention of matrix % fsr and frd normalized fading bandwidth % N0 is AWGN noise variance sigman2=(1+A2*sig_2)*N0; % Double-Rayleigh fading autocorrelation function, Jakes model k=0:ch_dis:(N-1)*ch_dis; phi=A2*P0*sig_1*sig_2*besselj(0,2*pi*fsr*k).*besselj(0,2*pi*frd*k); % Correlation matrix C=E{hh'}+sigma2*I is a Toeplitz matrix C=toeplitz(phi)+sigman2*eye(N); % inverse of correlation matrix Cinv=inv(C); % Cholesky decomposition: R'*R=A, R=chol(A) Lh=chol(Cinv); end