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In cellular systems, multiple users share the same radio spectrum, which leads to cochannel interference. Cochannel interference ultimately limits the quality of service offered to the users. At the moment, general capacity analysis for multiple-input-multiple-output (MIMO) correlated Rayleigh fading channels in the presence of correlated Rayleigh cochannel interference is not available in the literature, although its counterpart without cochannel interference has been thoroughly investigated. The difficulty arises from the quadratic form of the interference term. In this paper, based on the theory of matrix variate distribution, we investigate the capacity of MIMO Rayleigh fading channels with Rayleigh cochannel interference. We assume that perfect channel information is available to the receiver, but the transmitter has no channel information. We focus on the case when signals for the desired user and cochannel interferers are correlated at receiving antennas. We first derive an exact closed-form expression of the moment-generating function (MGF) of mutual information of MIMO channels with interference. Then, we further obtain an exact expression of the MIMO ergodic capacity with the MGF formula of mutual information. As a double check, these analytical results are validated by Monte Carlo simulations, and as an illustration of the mathematical formalism, numerical examples for particular cases of interest are plotted and discussed.