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This paper is concerned with the capacity of multiple-input multiple-output (MIMO) cellular systems. We assume an equal rate constraint for all users and adopt a realistic channel model that incorporates path loss, lognormal fading and Rayleigh fading. Several bounds are derived for the minimum transmission power of such rate-constrained MIMO cellular systems with various base station (BS) cooperation strategies. In particular, the upper power bound is based on the maximum eigenmode beamforming (MEB) scheme. These power bounds are then used to obtain the corresponding cellular capacity bounds when partial BS cooperation strategies are adopted. Our results show that, allowing more users to transmit simultaneously, introducing cooperation among BSs and increasing the number of antennas (especially at each BS) are efficient ways to improve system performance.