Source-linked AI summary
Wireless Energy and Information Transfer Tradeoff for Limited Feedback Multi-Antenna Systems with Energy Beamforming
Xiaoming Chen, Chau Yuen, Zhaoyang Zhang
TL;DR
The paper addresses joint energy harvesting and information transmission in a multi-antenna system where the receiver powers its own information transmission. It uses limited CSI feedback for adaptive energy beamforming and optimizes the energy/information duration split through two rate-bound-based schemes, while also analyzing imperfect CSI. Numerically, the proposed UA scheme nearly matches OA and exceeds EA by more than 5 dBm at R = 5 b/s/Hz.
Problem
Existing wireless energy-transfer studies often neglect using harvested energy for information transmission, motivating joint transfer analysis when harvesting and transmission occupy separate durations.
Method
The paper uses quantized CSI feedback for adaptive energy beamforming and derives duration-feedback tradeoff schemes by maximizing upper and approximate lower bounds on average information rate.
Results
UA nearly matches OA across the transmit-power region and provides more than 5 dBm gain over EA at R = 5 b/s/Hz; CSI mismatch increasingly creates a gap from perfect CSI as ρ decreases.
Takeaways & Limitations
Small feedback codebooks already improve performance over no energy beamforming, while the proposed UA offers a favorable performance-complexity balance.
Abstract
from arXiv · showhide
In this paper, we consider a multi-antenna system where the receiver should harvest energy from the transmitter by wireless energy transfer to support its wireless information transmission. In order to maximize the harvesting energy, we propose to perform adaptive energy beamforming according to the instantaneous channel state information (CSI). To help the transmitter to obtain the CSI for energy beamforming, we further propose a win-win CSI quantization feedback strategy, so as to improve the efficiencies of both power and information transmission. The focus of this paper is on the tradeoff of wireless energy and information transfer by adjusting the transfer duration with a total duration constraint. Through revealing the relationship between transmit power, transfer duration and feedback amount, we derive two wireless energy and information transfer tradeoff schemes by maximizing an upper bound and an approximate lower bound of the average information transmission rate, respectively. Moreover, the impact of imperfect CSI at the receiver is investigated and the corresponding wireless energy and information transfer tradeoff scheme is also given. Finally, numerical results validate the effectiveness of the proposed schemes.
I. INTRODUCTION
The paper studies joint wireless energy and information transfer when a receiver uses harvested energy to transmit information. It develops CSI-assisted energy beamforming and feedback-duration tradeoffs to improve the resulting information rate.
- CSI-assisted transfer: Energy beamforming coordinates the transmit direction toward the receiver, requiring channel state information at the power source.
- Motivation: Wireless energy transfer can power receivers such as implanted medical equipment, but prior work often did not consider how harvested energy is used for information transmission.
- System objective: The proposed system makes the power receiver also serve as the information transmitter, using harvested energy for its transmission.
- Time allocation: Because harvesting and information transmission cannot occur simultaneously, the time slot is divided between energy harvesting and information transmission.
- Contributions: The paper investigates how CSI feedback amount affects average information rate and derives tradeoffs between energy-transfer and information-transfer durations.
- Contributions: Two tradeoff schemes maximize an upper bound and an approximate lower bound, while a further scheme addresses receiver-side channel-estimation error.
II. SYSTEM MODEL
The system uses multi-antenna nodes for energy beamforming and receive combining, with limited CSI feedback selecting a beam before alternating energy harvesting and information transmission.
- System model: The FDD system equips the power source and information receiver with N_t antennas to enhance energy transfer and information reception.
- Channel model: The harvesting channel includes path loss α and an N_t-dimensional complex Gaussian fast-fading vector h.
- Energy beamforming: The unit-norm beamforming vector w adapts the transmit direction to instantaneous h, with full CSI yielding maximum ratio transmission w = h/∥h∥.
- CSI feedback: A vector-quantization codebook of size 2^B conveys a selected beam from the receiver to the transmitter for limited-feedback energy beamforming.
- Protocol: At each slot's beginning, the selected codeword index is fed back, followed by energy transfer for duration τ and information transfer during T − τ.
- Information transfer: During information transfer, the receiver uses harvested energy Q_harv to transmit a normalized signal, while the transmitter applies receive combining.
III. WIRELESS ENERGY AND INFORMATION TRANSFER TRADEOFF
The paper optimizes the energy-transfer duration to maximize average information rate, using tractable bound-based tradeoff designs because the exact average rate is difficult to obtain.
- Tradeoff formulation: The tradeoff problem selects energy-transfer duration τ to maximize the average information transmission rate under the total slot duration.
- Tradeoff formulation: The exact average information transmission rate is difficult to express in closed form because it depends on multiple random variables.
- Bound-based design: The analysis therefore derives tradeoffs from an upper-bound and an approximate-lower-bound perspective.
A. The Upper Bound Case
The upper-bound analysis models limited-feedback energy beamforming through the statistics of the selected beam and optimizes the energy-transfer duration. This yields a tradeoff scheme based on maximizing an upper bound of the average information transmission rate.
- A. The Upper Bound Case: The selected beam’s squared channel projection is the maximum of 2^B independent beta-distributed random variables.The beta distribution is Beta(1, N_t−1).
- A. The Upper Bound Case: The expectation of the selected beam gain is characterized using the beta-function distributional relationship.This expectation is substituted into the rate analysis to obtain the upper-bound expression.
- A. The Upper Bound Case: J1 optimizes the upper-bound average information transmission rate over the single continuous variable τ.The rate bound is obtained using Jensen’s inequality for the concave function log2(1+x).
- A. The Upper Bound Case: The candidate durations are τ1=0, τ2=T, and τ3 from the stationary-point equation, after which the optimal τ is selected by the stated criterion.The derivative of the objective with respect to τ supplies the stationary-point condition.
- A. The Upper Bound Case: The resulting duration allocation achieves the wireless energy-and-information transfer tradeoff by maximizing the average-rate upper bound.The upper-bound rate expression is the objective underlying this scheme.
B. The Lower Bound Case
The lower-bound analysis approximates the average information transmission rate and uses Jensen’s inequality and channel statistics to formulate a duration-optimization problem. The resulting scheme maximizes an approximate lower bound and uses a criterion analogous to the upper-bound case.
- B. The Lower Bound Case: The average information transmission rate is first approximated to support a lower-bound tradeoff analysis.The approximation leads to an optimization objective in the energy-transfer duration τ.
- B. The Lower Bound Case: Jensen’s inequality for the convex function log2(1+exp(x)) produces an approximate lower bound on the average information transmission rate.The approximation used in the derivation is described as numerically quite accurate.
- B. The Lower Bound Case: The expectation required by the lower-bound derivation uses the chi-squared distribution of ∥h∥^2 with 2N_t degrees of freedom.The resulting expectation is evaluated using the digamma function and the Euler constant.
- B. The Lower Bound Case: The lower-bound rate expression yields an optimization problem whose solution selects the energy-transfer duration from candidate points including τ4.τ4 is defined as the solution of the corresponding stationary equation.
- B. The Lower Bound Case: The lower-bound scheme replaces the coefficient used in J1 with a different constant coefficient in the analogous optimization J2.The optimal duration is therefore derived using the corresponding J2 criterion.
IV. THE IMPACT OF IMPERFECT CSI
The imperfect-CSI analysis models channel estimation error through a correlation coefficient and incorporates CSI mismatch into the harvesting and information-rate calculations. It shows that imperfect CSI causes performance loss and modifies the duration-optimization coefficient.
- IV. THE IMPACT OF IMPERFECT CSI: The CSI error model represents the actual channel as a correlated estimated channel plus independent estimation-error noise.The correlation coefficient ρ measures estimation precision, with larger ρ indicating higher precision.
- IV. THE IMPACT OF IMPERFECT CSI: Because the energy beamforming vector is selected from estimated CSI, CSI mismatch can produce SNR loss.The analysis assumes that T1 has perfect CSI of g while the receiver-side channel estimate is imperfect.
- IV. THE IMPACT OF IMPERFECT CSI: The imperfect-CSI harvesting power and average information-rate expressions lead to a corresponding upper bound on the average information transmission rate.The real-part operator is used in the resulting rate expression.
- IV. THE IMPACT OF IMPERFECT CSI: Imperfect CSI replaces the perfect-CSI coefficient in the upper-bound expression with a coefficient involving ρ, the transmit parameter, and N_t.This replacement carries the estimation-error dependence into the tradeoff optimization.
- IV. THE IMPACT OF IMPERFECT CSI: Imperfect CSI inevitably causes performance loss because the relevant feedback-related quantity cannot be smaller than zero.The corresponding optimal energy-and-information transfer tradeoff is obtained after replacing the coefficient in J1.
V. NUMERICAL RESULTS
The numerical results compare tradeoff algorithms, codebook sizes, and CSI precision, showing benefits from adaptive allocation, energy beamforming, and accurate CSI.
- Simulation setup: The simulations evaluate UA and LA against equal-duration allocation and numerical optimization under Nt = 4, η = 0.8, σ2 = −125dBm, and T = 5ms.EA uses τ = T/2 = 2.5ms, while OA numerically searches for the optimal τ.
- Algorithm comparison: UA nearly matches OA across the transmit-power range, while UA and LA outperform equal allocation in moderate and high-power regions.At R = 5 b/s/Hz, UA provides more than 5dBm gain over EA, with larger gains as transmit power increases.
- Codebook size: With B = 2, energy beamforming yields more than 1 b/s/Hz gain over no beamforming at P1 = 1dB.The gain from B = 0 to B = 2 exceeds the gains from B = 2 to 4 and from B = 4 to full CSI.
- Codebook size: Increasing CSI feedback improves energy-transfer efficiency and average information transmission rate, while codebook size controls the feedback-performance tradeoff.The experiments use UA for the codebook-size comparison because of its performance in Fig. 3.
- Imperfect CSI: When CSI estimation is relatively accurate at ρ = 0.9, performance loss is very small; lower ρ creates a gap from perfect CSI.Smaller ρ denotes more severe CSI mismatch.
VI. CONCLUSION
The paper introduces wireless energy-and-information transfer tradeoffs for multi-antenna systems using CSI-feedback energy beamforming. It derives two bound-based algorithms and examines imperfect CSI effects.
- The paper introduces wireless energy-and-information transfer tradeoff optimization to maximize the average information transmission rate.
- Energy beamforming uses CSI feedback through a quantization codebook to improve wireless energy-transfer efficiency in a multi-antenna system.
- For a fixed codebook size, maximizing an upper bound and an approximate lower bound produces two tradeoff algorithms.
- The paper also analyzes imperfect CSI and presents corresponding performance results and a tradeoff scheme.