Optimization and tradeoff analysis of two-way limited feedback beamforming systems
ABSTRACT In a two-way system where two users transmit data to each other, limited feedback beamforming is a simple method to supply channel state information to the transmitter (CSIT) for a multiple-input-multiple-output (MIMO) system when channel reciprocity is unavailable. For analytical tractability, most existing papers assume the existence of an ideal fixed-rate feedback channel to assist the transmitter to adapt to instantaneous channel conditions. The relationship between the feedback rate and data rate is typically analyzed in a unidirectional manner. In reality, judicious resource allocation to transmitting feedback and data leads to a tradeoff between the effective forward and reverse data rates. In this paper, we represent the achievable rate by effective SNRs, and we present a framework to analyze the tradeoff. We find that the forward and reverse rate tradeoff can be decomposed into two local tradeoffs, resulting from the resource allocation policy of each user. The local tradeoff region for each user is found in closed-form, whereas the overall tradeoff region is approximated for the special case when the two users have equal hardware configurations.
- SourceAvailable from: Kaibin Huang[show abstract] [hide abstract]
ABSTRACT: Transmit beamforming is a simple multi-antenna 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 net throughput, defined as throughput minus average feedback cost. 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 perfect 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 finite-rate 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 net throughput of the conventional periodic feedback by up to 0.5 bit/s/Hz without requiring additional bandwidth or antennas. Comment: 29 pages; submitted for publicationIEEE Transactions on Signal Processing 09/2009; · 2.81 Impact Factor
Conference Proceeding: Multi-Antenna Beamforming: Feedback or No Feedback?[show abstract] [hide abstract]
ABSTRACT: Transmit beamforming increases throughput and transmission range of a wireless communication system. However, the required feedback of channel state information (CSI) consumes radio resources that otherwise can be used for data transmission. This makes "Feedback or no feedback?" a relevant question to ask. This paper answers this question by proposing intelligent feedback control using a Markov decision process. The feedback controller turns feedback on/off according to the channel state and the criterion of maximum net throughput, namely throughput minus average feedback cost. Assuming channel isotropicity and Markovity, the state of the feedback controller reduces to two channel parameters. This allows the optimal control policy to be efficiently computed using dynamic programming. The optimal control policy is proved to be of the threshold type. Under this policy, feedback is performed whenever a channel parameter indicating the accuracy of transmit CSI is below a threshold, which varies with channel power. The above result holds regardless of whether the controller's state space is discretized or continuous. Simulation shows that feedback control increases net throughput by up to 0.5 bit/s/Hz without requiring additional bandwidth or antennas.Proceedings of IEEE International Conference on Communications, ICC 2010, Cape Town, South Africa, 23-27 May 2010; 01/2010
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ABSTRACT: We examine the capacity of beamforming over a single-user, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multi-input-single-output (MISO) and multi-input-multi-output (MIMO) channels are considered subject to block Rayleigh fading. Each coherence block contains L symbols, and is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a minimum mean squared error estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2<sup>B</sup> i.i.d. random vectors, and sends the corresponding B bits back to the transmitter. We derive bounds on the beamforming capacity for MISO and MIMO channels and characterize the optimal (rate-maximizing) training and feedback overhead (T and B) as L and the number of transmit antennas N<sub>t</sub> both become large. The optimal N<sub>t</sub> is limited by the coherence time, and increases as L/logL. For the MISO channel the optimal T/L and B/L (fractional overhead due to training and feedback) are asymptotically the same, and tend to zero at the rate 1/log N<sub>t</sub>. For the MIMO channel the optimal feedback overhead B/L tends to zero faster (as 1/log<sup>2</sup> N<sub>t</sub>).IEEE Transactions on Information Theory 01/2011; · 2.62 Impact Factor