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The theory of multiple-input multiple-output (MIMO) technology has been well-developed to increase fading channel capacity over single-input single-output (SISO) systems. This capacity gain can often be leveraged by utilizing channel state information at the transmitter and the receiver. Users make use of this channel state information for transmit signal adaptation. In this correspondence, we derive the capacity region for the MIMO multiple access channel (MIMO MAC) when partial channel state information is available at the transmitters, where we assume a synchronous MIMO multiuser uplink. The partial channel state information feedback has a cardinality constraint and is fed back from the basestation to the users using a limited rate feedback channel. Using this feedback information, we propose a finite codebook design method to maximize sum-rate. In this correspondence, the codebook is a set of transmit signal covariance matrices. We also derive the capacity region and codebook design methods in the case that the covariance matrix is rank-one (i.e., beamforming). This is motivated by the fact that beamforming is optimal in certain conditions. The simulation results show that when the number of feedback bits increases, the capacity also increases. Even with a small number of feedback bits, the performance of the proposed system is close to an optimal solution with the full feedback.

We consider the multiple antenna multicasting channel, in which a common message is simultaneously transmitted to multiple users in a wireless cellular network, under the assumption that channel state information (CSI) is perfectly available at the transmitter. In this paper, we develop a simple recursive algorithm to determine the covariance matrix of the transmitted signal vector. For a large number of transmit antennas or a large number of users, we show that the growth rate of the maximum achievable rate of the proposed scheme is the same as that of the optimal scheme while reducing computational complexity dramatically.Index Terms-Physical layer multicasting, multicast channel, multiple antenna, transmit covariance matrix.