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

Joint Wireless Information and Energy Transfer with Reduced Feedback in MIMO Interference Channels

To determine the transmission strategy for joint wireless information and energy transfer (JWIET) in the MIMO interference channel (IFC), the information access point (IAP) and energy access point (EAP) require the channel state information (CSI) of their associated links to both the information-decoding (ID) mobile stations (MSs) and energy-harvesting (EH) MSs (so-called local CSI). In this paper, to reduce th e feedback overhead of MSs for the JWIET in two-user MIMO IFC, we propose a Geodesic energy beamforming scheme that requires partial CSI at the EAP. Furthermore, in the two-user MIMO IFC, it is proved that the Geodesic energy beamforming is the optimal strategy. By adding a rank-one constraint on the transmit signal covariance of IAP, we can further reduce the feedback overhead to IAP by exploiting Geodesic information beamforming. Under the rank-one constraint of IAP's transmit signal, we prove that Geodesic information/energy beamforming approach is the optimal strategy for JWIET in the two-user MIMO IFC. We also discuss the extension of the proposed rank-one Geodesic information/energy beamforming strategies to general K-user MIMO IFC. Finally, by analyzing the achievable rate-energy performance statistically under imperfect partial CSIT, we propose an adaptive bit allocation strategy for both EH MS and ID MS.Comment: accepted to IEEE Journal of Selected Areas in Communications (IEEE JSAC), Special Issue on Wireless Communications Powered by Energy Harvesting and Wireless Energy Transfe

Energy Beamforming with One-Bit Feedback

Wireless energy transfer (WET) has attracted significant attention recently for providing energy supplies wirelessly to electrical devices without the need of wires or cables. Among different types of WET techniques, the radio frequency (RF) signal enabled far-field WET is most practically appealing to power energy constrained wireless networks in a broadcast manner. To overcome the significant path loss over wireless channels, multi-antenna or multiple-input multiple-output (MIMO) techniques have been proposed to enhance the transmission efficiency and distance for RF-based WET. However, in order to reap the large energy beamforming gain in MIMO WET, acquiring the channel state information (CSI) at the energy transmitter (ET) is an essential task. This task is particularly challenging for WET systems, since existing channel training and feedback methods used for communication receivers may not be implementable at the energy receiver (ER) due to its hardware limitation. To tackle this problem, in this paper we consider a multiuser MIMO system for WET, where a multiple-antenna ET broadcasts wireless energy to a group of multiple-antenna ERs concurrently via transmit energy beamforming. By taking into account the practical energy harvesting circuits at the ER, we propose a new channel learning method that requires only one feedback bit from each ER to the ET per feedback interval. The feedback bit indicates the increase or decrease of the harvested energy by each ER between the present and previous intervals, which can be measured without changing the existing hardware at the ER. Based on such feedback information, the ET adjusts transmit beamforming in different training intervals and at the same time obtains improved estimates of the MIMO channels to ERs by applying a new approach termed analytic center cutting plane method (ACCPM).Comment: This is the longer version of a paper to appear in IEEE Transactions on Signal Processin

Opportunistic Scheduling and Beamforming for MIMO-OFDMA Downlink Systems with Reduced Feedback

Opportunistic scheduling and beamforming schemes with reduced feedback are proposed for MIMO-OFDMA downlink systems. Unlike the conventional beamforming schemes in which beamforming is implemented solely by the base station (BS) in a per-subcarrier fashion, the proposed schemes take advantages of a novel channel decomposition technique to perform beamforming jointly by the BS and the mobile terminal (MT). The resulting beamforming schemes allow the BS to employ only {\em one} beamforming matrix (BFM) to form beams for {\em all} subcarriers while each MT completes the beamforming task for each subcarrier locally. Consequently, for a MIMO-OFDMA system with $Q$ subcarriers, the proposed opportunistic scheduling and beamforming schemes require only one BFM index and $Q$ supportable throughputs to be returned from each MT to the BS, in contrast to $Q$ BFM indices and $Q$ supportable throughputs required by the conventional schemes. The advantage of the proposed schemes becomes more evident when a further feedback reduction is achieved by grouping adjacent subcarriers into exclusive clusters and returning only cluster information from each MT. Theoretical analysis and computer simulation confirm the effectiveness of the proposed reduced-feedback schemes.Comment: Proceedings of the 2008 IEEE International Conference on Communications, Beijing, May 19-23, 200

Open-Loop Beamforming Technique for MIMO System and Its Practical Realization

The concept of close-loop beamforming for MIMO system was well known proposed the singular value decomposition on channel matrix. This technique can improve the capacity performance, but the cost of feedback channel and the complexity processing discard the interest of implementation. Therefore, this paper aims to investigate the benefit of using an open-loop beamforming for MIMO system in practical approaches. The low-profile concept of open-loop beamforming which is convenient for implementation is proposed by just inserting Butler matrices at both transmitter and receiver. The simulation and measurement results indicate that the open-loop beamforming with Butler matrix outperforms the conventional MIMO system. Although, the close-loop beamforming offers a better performance than open-loop beamforming technique, the proposed system is attractive because it is low cost, uncomplicated, and easy to implement