On the Capacity Bounds of Beamforming over MISO Time-Selective Channels with Estimation Errors and Feedback Delay

We examine the ergodic capacity of beamforming over a multiple-input single-output (MISO) time-selective channel with channel estimation error and delayed limited feedback. At each frame, the receiver obtains the minimum mean squared error estimation of the channel, chooses a transmit beamforming vector, according to the error channel estimation, from a codebook based on random vector quantization design, and feeds back the corresponding index to the transmitter using a finite number of bits. We derive the bounds on the capacity, and show that the tightness of the lower and upper bounds, and the bounds decreasing with the increase of channel estimation error or normalized Doppler spread.