x + n describe the input-output relationship of the MIMO channel where y is the output vector with NRX components, X is the input vector with NTX components, n is the additive noise vector with NRX components, and H is the NRX NTX channel matrix. Using the SVD theorem, we can show H = UEVH Let x = VHx,y=UHy, and n = UHn denote the unitary transformation of the channel input and output and noise vectors, it can be shown that G=EX+n Since U and V are unitary matrices and =diag(A1,A2, ^min(NRx,NTX), 0,0,...,0), it is clear that the capacity of this model is the same as the capacity of the model Hx n. However, is a diagonal matrix with K non-zero elements on the main diagonal, YK + , +1 . The latter equations are conceptually equivalent to K parallel SISO eigenchannels, each with signal power of X},i=1,2, min(NTx,NRX). As a result, the MIMO channel capacity can be rewritten in terms of the eigenvalues of the input signal covariance matrix E. When the channel knowledge is available at the transmitter and receiver then H is known, and we can optimize the capacity over E subject to the power constraint tr(E) VI Y. It is shown in the literature that the optimal E in this case exists and is known as water-filling solution. The channel capacity in this case is given by where <0 and n is a nonlinear function of eigenvalues of the channel input covariance matrix. The effect of various channel conditions on the channel capacity has been extensively studied in the literature. For example, increasing the LoS sig- nal strength at fixed SNR reduces capacity in Rician channels [22,24]. This can be explained in terms of the channel matrix rank or through various eigenvalue properties. The issue of correlated fading is of considerable importance for implementations where the The concept of decomposition of an NXN Hermitian matrix in terms of quadratic product of NXN unitary matrix composed of eigenvectors and NXN diagonal matrix of eigenvalues can be generalized to MXN complex-valued matrices of rank K. If A is a M X Nwhere(M > N) c