Bounds on the capacity of MISO channels with different types of imperfect CSI

Consider the downlink of an isolated cell with a base station (BS) equipped with M multiple antennas and a single user with a single antenna. For this multiple-input single-output (MISO) channel, the capacity with perfect channel state information (CSI) the transmitter and receiver is known. In practice, however, it is actually more realistic to assume imperfect CSI at the transmitter. For instance, in a frequency divsion duplex (FDD) system with limited feedback, the available transmit CSI is estimated, quantized, outdated and affected by erroneous feedback. The quality of the transmit CSI then depends on the downlink training length, the number of feedback bits, the feedback error probability and on the rate of variation of the downlink channel. However, the capacity of the MISO channel with imperfect CSI in general is unknown. In this work, nonetheless, we compute bounds of the MISO channel capacity employing coherent beamforming at the BS with different types of imperfect CSI at the transmitter.