Transmit beamforming is a simple multiantenna technique for increasing throughput and the transmission range of a wireless communication system. The required feedback of channel state information (CSI) can potentially result in excessive overhead especially for high mobility or many antennas. This work concerns efficient feedback for transmit beamforming and establishes a new approach of controlling feedback for maximizing throughput under a constraint on the average feedback rate. The feedback controller using a stationary policy turns CSI feedback on/off according to the system state that comprises the channel state and transmit beamformer. Assuming channel isotropy and Markovity, the controller's state reduces to two scalars. This allows the optimal control policy to be efficiently computed using dynamic programming. Consider the unquantized feedback channel free of error, where each feedback instant pays a fixed price. The corresponding optimal feedback control policy is proved to be of the threshold type. This result holds regardless of whether the controller's state space is discretized or continuous. Under the threshold-type policy, feedback is performed whenever a state variable indicating the accuracy of transmit CSI is below a threshold, which varies with channel power. The practical quantized feedback channel is also considered. The optimal policy for quantized feedback is proved to be also of the threshold type. The effect of CSI quantization is shown to be equivalent to an increment on the feedback price. Moreover, the increment is upper bounded by the expected logarithm of one minus the quantization error. Finally, simulation shows that feedback control increases throughput of the conventional periodic feedback by up to 0.5 bit/s/Hz without requiring additional bandwidth or antennas.
Bibliographical noteFunding Information:
Manuscript received September 23, 2009; accepted February 15, 2010. Date of publication March 22, 2010; date of current version May 14, 2010. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Huaiyu Dai. This work was supported by Yonsei University by Grants 2009-1-0057, 2009-1-0041, and 2009-1-0131, by the Hong Kong Research Grants Council by Grant 615407, and by the Korean Science and Engineering Foundation by Grant R01-2008-000-10687-0.
All Science Journal Classification (ASJC) codes
- Signal Processing
- Electrical and Electronic Engineering