Statistical analysis of correlated MIMO channels with a pinhole

This paper gives statistical distributions of SNR (signal to noise ratio) in correlated double Rayleigh fading environment which is typically found in MIMO (multiple input multiple output) pinhole channels. First, MIMO pinhole channels which have correlated branches in both the transmitter and receiver sides where each of them has a covariance matrix with different nonzero eigenvalues are considered. Next, the result is extended to the general case in which the covariance matrices of the both sides might have degenerated eigenvalues (independent but nonidentical case where plural branches have a same mean SNR is included there). The effectiveness of given equations is demonstrated through computer simulations. This result could be applied to the analysis of high SNR MIMO system with single antenna relay if the thermal noise generated in the relay is negligible.