  Feedback of quantized channel state information (CSI), called limited
feedback, enables transmit beamforming in multiple-input-multiple-output (MIMO)
wireless systems with a small amount of overhead. Due to its efficiency,
beamforming with limited feedback has been adopted in several wireless
communication standards. Prior work on limited feedback commonly adopts the
block fading channel model where temporal correlation in wireless channels is
neglected. This paper considers temporally-correlated channels and designs
single-user transmit beamforming with limited feedback. Analytical results
concerning CSI feedback are derived by modeling quantized CSI as a first-order
finite-state Markov chain. These results include the source bit rate generated
by time-varying quantized CSI, the required bit rate for a CSI feedback
channel, and the effect of feedback delay. In particular, based on the theory
of Markov chain convergence rate, feedback delay is proved to reduce the
throughput gain due to CSI feedback at least exponentially. Furthermore, an
algorithm is proposed for CSI feedback compression in time. Combining the
results in this work leads to a new method for designing limited feedback
beamforming as demonstrated by a design example.
