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Joint Active and Passive Beamforming for IRS-Aided Wireless Energy Transfer Network Exploiting One-Bit Feedback

Taotao Ji, Meng Hua, Chunguo Li, Yongming Huang, Luxi Yang

TL;DR

This work tackles IRS-aided wireless energy transfer with a hardware-constrained energy receiver by introducing two joint beamforming schemes that rely on one-bit ER feedback. The channel-estimation-based method uses IRS grouping and analytic center cutting plane method (ACCPM) to learn a scaled cascaded ET-IRS-ER channel, then optimizes the transmit covariance and IRS phases. The distributed-beamforming-based method avoids explicit CSI, performing stochastic IRS perturbations with one-bit feedback to converge to a local optimum, followed by a single ACCPM run to obtain the effective channel for final optimization. Numerical results show high-accuracy cascade channel estimation and significant energy harvesting gains, with considerable hardware savings at the ER compared with pilot-based methods. Overall, the paper contributes practical one-bit-feedback strategies for joint active and passive beamforming in IRS-enabled WET systems, suitable for low-complexity ERs.

Abstract

To reap the active and passive beamforming gain in an intelligent reflecting surface (IRS)-aided wireless network, a typical way is to first acquire the channel state information (CSI) relying on the pilot signal, and then perform the joint beamforming design. However, it is a great challenge when the receiver can neither send pilot signals nor have complex signal processing capabilities due to its hardware limitation. To tackle this problem, we study in this paper an IRS-aided wireless energy transfer (WET) network and propose two joint beamforming design methods, namely, the channel-estimationbased method and the distributed-beamforming-based method, that require only one-bit feedback from the energy receiver (ER) to the energy transmitter (ET). Specifically, for the channelestimation-based method, according to the feedback information, the ET is able to infer the cascaded ET-IRS-ER channel by continually adjusting its transmit beamformer while applying the analytic center cutting plane method (ACCPM). Then, based on the estimated cascaded CSI, the joint beamforming design can be performed by using the existing optimization techniques. While for the distributed-beamforming-based method, we first apply the distributed beamforming algorithm to optimize the IRS reflection coefficients, which is theoretically proven to converge to a local optimum almost surely. Then, the optimal ET's transmit covariance matrix is obtained based on the effective ET-ER channel learned by applying the ACCPM only once. Numerical results demonstrate the effectiveness of our proposed one-bitfeedback-based joint beamforming design schemes while greatly reducing the requirement on the hardware complexity of the ER. In particular, the high accuracy of our IRS-involved cascaded channel estimation method exploiting one-bit feedback is also validated.

Joint Active and Passive Beamforming for IRS-Aided Wireless Energy Transfer Network Exploiting One-Bit Feedback

TL;DR

This work tackles IRS-aided wireless energy transfer with a hardware-constrained energy receiver by introducing two joint beamforming schemes that rely on one-bit ER feedback. The channel-estimation-based method uses IRS grouping and analytic center cutting plane method (ACCPM) to learn a scaled cascaded ET-IRS-ER channel, then optimizes the transmit covariance and IRS phases. The distributed-beamforming-based method avoids explicit CSI, performing stochastic IRS perturbations with one-bit feedback to converge to a local optimum, followed by a single ACCPM run to obtain the effective channel for final optimization. Numerical results show high-accuracy cascade channel estimation and significant energy harvesting gains, with considerable hardware savings at the ER compared with pilot-based methods. Overall, the paper contributes practical one-bit-feedback strategies for joint active and passive beamforming in IRS-enabled WET systems, suitable for low-complexity ERs.

Abstract

To reap the active and passive beamforming gain in an intelligent reflecting surface (IRS)-aided wireless network, a typical way is to first acquire the channel state information (CSI) relying on the pilot signal, and then perform the joint beamforming design. However, it is a great challenge when the receiver can neither send pilot signals nor have complex signal processing capabilities due to its hardware limitation. To tackle this problem, we study in this paper an IRS-aided wireless energy transfer (WET) network and propose two joint beamforming design methods, namely, the channel-estimationbased method and the distributed-beamforming-based method, that require only one-bit feedback from the energy receiver (ER) to the energy transmitter (ET). Specifically, for the channelestimation-based method, according to the feedback information, the ET is able to infer the cascaded ET-IRS-ER channel by continually adjusting its transmit beamformer while applying the analytic center cutting plane method (ACCPM). Then, based on the estimated cascaded CSI, the joint beamforming design can be performed by using the existing optimization techniques. While for the distributed-beamforming-based method, we first apply the distributed beamforming algorithm to optimize the IRS reflection coefficients, which is theoretically proven to converge to a local optimum almost surely. Then, the optimal ET's transmit covariance matrix is obtained based on the effective ET-ER channel learned by applying the ACCPM only once. Numerical results demonstrate the effectiveness of our proposed one-bitfeedback-based joint beamforming design schemes while greatly reducing the requirement on the hardware complexity of the ER. In particular, the high accuracy of our IRS-involved cascaded channel estimation method exploiting one-bit feedback is also validated.
Paper Structure (18 sections, 4 theorems, 61 equations, 10 figures, 1 algorithm)

This paper contains 18 sections, 4 theorems, 61 equations, 10 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model And Problem Formulation
  3. Channel-Estimation-Based Method
  4. IRS Elements Grouping
  5. Estimation of Group Composite Channel Matrix ${{{\bf{\bar{H}}}}_c}$
  6. Scaled Channel Learning Using ACCPM
  7. Determination of Scale Factor $\left\{ {{\gamma _i}} \right\}$
  8. Amplitude Ratio Determination
  9. Phase Difference Determination
  10. Downlink Transmission Design
  11. Feedback Number Complexity Analysis
  12. Distributed-Beamforming-Based Method
  13. Numerical Results
  14. Channel-Estimation-Based Method
  15. Distributed-Beamforming-Based Method
  16. ...and 3 more sections

Key Result

Proposition 1

Let the transmit beamforming vector be Then, the value of $\angle {\gamma _i} - \angle {\gamma _j}$ can be found by where we use $\arg {\rm{ ext}}$ to denote an argument that yields the unique local maximum point within the interval of $\left[ {0,2\pi } \right)$.

Figures (10)

  • Figure 1: An indoor IRS-aided WET system where the ER feeds back one-bit of information to the ET periodically to assist the joint beamforming design for the system.
  • Figure 2: The procedure of ACCPM: the working set gradually shrinks to the target set.
  • Figure 3: Simulation setup.
  • Figure 4: NE of estimated channel matrix by applying the ACCPM versus iteration number $N_A$ for different $M_t$.
  • Figure 5: Performance of the proposed one-bit feedback channel estimation method under different IRS group sizes.
  • ...and 5 more figures

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4