Imperfect Channel Knowledge Based Ergodic Channel Capacity of Transmit Beamforming

In this treatise, we have derived the lower ergodic channel capacity bound of a closed-loop transmit beamforming system scheme, when considering the effects of channel estimation errors, transmit beamforming vector quantization errors, the effective capacity loss caused by pilot symbols and that imposed by the channel information feedback bits. We intend to answer the question "whether the potential capacity improvement achieved by using a closed-loop design and an increased number of transmit antennas will be completely eroded by the imperfections of the channel information acquisition and signalling?". Based on our investigations, we found that the capacity improvements predicted are indeed achievable for slowly fading channels, but erode for realtively rapidly fading channels. An improved closed-loop transmit beamforming scheme is proposed for rapidly fading channels.