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Distributed multi-input multi-output (D-MIMO) system is a promising system to greatly improve the spectral efficiency and power efficiency of the cellular system. The performance analysis of the spectral efficiency of D-MIMO system is a fundamental problem for both theoretical study and technique evaluation. In this paper, the theoretical performances of spectral efficiency for D-MIMO system and traditional collocated MIMO (C-MIMO) system are studied and compared. First, a composite D-MIMO channel including path loss, shadow fading and multipath fading is given. Conditioned on the desired user position, by using the tight bounds and central limit theory, the analytical approximations of the mean and the cumulative distribution function (CDF) of the mutual information (MI) are derived for C-MIMO and D-MIMO channels at both high signal to noise ratio (SNR) and low SNR. Assuming that the users are randomly …