Optimization of Training and Feedback Overhead for Beamforming over Block Fading Channels

We examine the capacity of beamforming over a single-user, multi-antenna 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 $2^B$ {\em 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 $N_t$ both become large. The optimal $N_t$ is limited by the coherence time, and increases as $L/\log L$. 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 $1/\log N_t$. For the MIMO channel the optimal feedback overhead $B/L$ tends to zero faster (as $1/\log^2 N_t$).Comment: accepted for IEEE Trans. Info. Theory, 201

Optimized Training Design for Wireless Energy Transfer

Radio-frequency (RF) enabled wireless energy transfer (WET), as a promising solution to provide cost-effective and reliable power supplies for energy-constrained wireless networks, has drawn growing interests recently. To overcome the significant propagation loss over distance, employing multi-antennas at the energy transmitter (ET) to more efficiently direct wireless energy to desired energy receivers (ERs), termed \emph{energy beamforming}, is an essential technique for enabling WET. However, the achievable gain of energy beamforming crucially depends on the available channel state information (CSI) at the ET, which needs to be acquired practically. In this paper, we study the design of an efficient channel acquisition method for a point-to-point multiple-input multiple-output (MIMO) WET system by exploiting the channel reciprocity, i.e., the ET estimates the CSI via dedicated reverse-link training from the ER. Considering the limited energy availability at the ER, the training strategy should be carefully designed so that the channel can be estimated with sufficient accuracy, and yet without consuming excessive energy at the ER. To this end, we propose to maximize the \emph{net} harvested energy at the ER, which is the average harvested energy offset by that used for channel training. An optimization problem is formulated for the training design over MIMO Rician fading channels, including the subset of ER antennas to be trained, as well as the training time and power allocated. Closed-form solutions are obtained for some special scenarios, based on which useful insights are drawn on when training should be employed to improve the net transferred energy in MIMO WET systems.Comment: 30 pages, 9 figures, to appear in IEEE Trans. on Communication