Source-linked AI summary
Passive Beamforming and Information Transfer via Large Intelligent Surface
Wenjing Yan, Xiaoyan Kuai, Xiaojun Yuan
TL;DR
The paper addresses how an LIS can enhance primary wireless communication while also transmitting its own information. It proposes PBIT with spatially modulated LIS states, optimized passive beamforming, and two-step receiver processing; experiments show improved performance and a beamforming–information-rate tradeoff.
Problem
Existing LIS beamforming enhances user communication, but the paper addresses the added challenge of having the LIS simultaneously transmit information to the receiver.
Method
PBIT encodes LIS information in reflecting-element on/off states, optimizes phase shifts for average receive SNR, and uses two-step recovery for transmitter and LIS signals.
Results
The optimized PBIT system substantially improves performance, including about 5 dB to 9 dB improvement at BER = 10^-5 with LIS enhancement and about 2 dB from phase optimization at ρ = 0.5.
Takeaways & Limitations
PBIT provides simultaneous communication enhancement and LIS information transfer, with a demonstrated tradeoff between recovery performance and LIS information rate.
Abstract
from arXiv · showhide
Large intelligent surface (LIS) has emerged as a promising new solution to improve the energy and spectrum efficiency of wireless networks. A LIS, composed of a large number of low-cost and energy-efficient reconfigurable passive reflecting elements, enhances wireless communications by reflecting impinging electro-magnetic waves. In this paper, we propose a novel passive beamforming and information transfer (PBIT) technique, in which the LIS simultaneously enhances the primary communication and sends information to the receiver. We develop a passive beamforming method to improve the average receive signal-to-noise ratio (SNR).We also establish a two-step approach at the receiver to retrieve the information from both the transmitter and the LIS. Numerical results show that the proposed PBIT system, especially with the optimized passive beamforming, significantly outperforms the system without LIS enhancement. Furthermore, a tradeoff between the passive-beamforming gain and the information rate of the LIS has been demonstrated.
I. INTRODUCTION
The paper introduces PBIT, in which an LIS both enhances user–BS communication through passive beamforming and transmits information to the receiver. It combines spatial modulation for LIS data with phase-shift optimization and develops a two-step recovery method.
- Motivation: LIS is motivated as a low-cost, energy-efficient hardware solution for improving wireless-network energy efficiency.It uses reconfigurable passive reflecting elements to enhance wireless communications.
- PBIT system: PBIT requires the LIS to transmit data while simultaneously enhancing user–BS communication through passive beamforming.Potential LIS data sources include sensors collecting environmental measurements.
- PBIT design: LIS information is carried by reflecting-element on/off states, while phase shifts of activated elements provide passive beamforming.The off state includes structure-mode reflection, whereas the on state adds antenna-mode reflection.
- Contributions: The beamforming design maximizes average receive SNR and uses semidefinite relaxation to obtain a suboptimal solution.The receiver uses a two-step algorithm combining compressed sensing and matrix factorization to recover transmitter and LIS information.
- Results: Numerical results report substantial gains for optimized PBIT and a tradeoff between passive-beamforming gain and LIS information rate.Increasing beamforming enhancement can improve communication performance while reducing the LIS information rate.
A. System Model
The system combines a single-antenna user, an M-antenna BS, and an LIS whose reflecting elements encode sensor information through on/off states. The receiver observes block transmissions affected by direct and LIS-reflected channels plus Gaussian noise.
- System components: The PBIT module contains an N-element LIS, a controller for element states and phase shifts, and sensors that provide environmental data.The user communicates with a multi-antenna BS through the LIS.
- LIS signaling: Each reflecting element is assigned an on/off state, and the state vector s carries sensor information.Each state is independently on with probability ρ and off with probability 1−ρ.
- LIS signaling: Each LIS element carries H(ρ) = −ρ log ρ−(1−ρ) log(1−ρ) bits of information.The information rate depends on the activity probability ρ.
- Transmission model: Transmission uses L time slots per block, with the LIS state matrix fixed throughout each block.The receiver collects the signal vectors y_l into an observed matrix Y.
- Transmission model: The received signal combines direct and LIS-reflected channels, user symbols, and additive white Gaussian noise.The model uses x_l for the transmitted symbol and w_l for the noise vector.
- Channel assumptions: The BS assumes perfect CSI and uses it to determine phase shifts that are sent to the LIS through a control link.The phase-shift design uses the user–BS, user–LIS, and LIS–BS channel matrices.
B. Problem Description
The paper seeks to design LIS phase shifts so the receiver can reliably recover both user and sensor information under a transmission-power constraint. It decomposes the design into passive beamforming and transceiver subproblems, then uses expected received-signal power as a tractable beamforming criterion.
- Design objective: The design objective is to recover both user information x and sensor information s while minimizing the required transmission power.The phase-shift matrix Θ must support reliable recovery at specified information rates.
- Problem decomposition: The PBIT sum capacity is represented by I(x, s; Y), and the overall design separates beamforming optimization from transceiver design.The beamforming subproblem maximizes mutual information over Θ, while the transceiver subproblem designs signaling and reception.
- Passive beamforming: Because the user-information rate is typically higher than the LIS-information rate, the paper adopts a heuristic metric for passive beamforming.The metric avoids directly evaluating the complicated mutual-information model.
- Passive beamforming: The heuristic beamforming objective is to maximize the expected squared norm of the effective received channel, corresponding to average SNR improvement.The effective channel includes the LIS-reflected path and the direct link.
- Transceiver design: Receiver design focuses on recovering s and x from Y for a given Θ, while signal shaping and channel coding are outside the paper’s scope.Those additional designs are identified as necessary for approaching channel capacity but are not addressed.
III. BEAMFORMING DESIGN
The phase-shift design is formulated as a non-convex QCQP and approximated by an SDP relaxation. Eigenvalue decomposition of the relaxed solution produces a suboptimal phase-shift vector.
- The LIS phase-shift optimization is a non-convex quadratically constrained quadratic program with unit-modulus constraints |θ_n| = 1.
- Introducing an auxiliary variable reformulates the design as a homogeneous QCQP before semidefinite relaxation.
- The relaxed formulation replaces the rank-one constraint on Q with a positive-semidefinite matrix constraint and diagonal constraints Q_n,n = 1.
- The resulting SDP can be solved by convex optimization software, but its optimal Q is not generally rank-one.
- An eigenvalue decomposition of Q and a random CSCG vector yield a suboptimal solution for the phase-shift vector.
A. Problem Description
The receiver must jointly recover the user information x and LIS information s from the received signal matrix. The signal model factors the observation into a rank-one product plus noise, enabling a two-step recovery procedure.
- The receiver aims to recover both the user signal x and the LIS signal s from the received observation.
- The observation matrix is modeled as Y = (As + h_d)x^T + W = zx^T + W.
- A = βGΘD_h is a known coefficient matrix, while z is formed from the rows of A.
- The proposed receiver first recovers x and z from Y, then recovers s from the estimated z.
B. Recovery of x and z
Recovery of x and z is treated as rank-one matrix decomposition. The paper considers SVD and BiG-AMP methods, with a reference symbol correcting the scalar ambiguity in the latter estimates.
- The recovery of z and x from Y is formulated as a rank-one matrix decomposition problem using SVD and BiG-AMP methods.
- The SVD method estimates x from the first right singular vector and z from the leading singular value multiplied by the first left singular vector.
- BiG-AMP factorizes x and z from Y using prior distributions for both variables.
- The two-step approach is not necessarily optimal, although numerical results indicate that its performance loss is usually marginal.
- A reference symbol in the first position of x removes the scalar offset between the estimated factors, after which the corrected x is mapped to its constellation.
C. Recovery of s from z
After estimating z, the receiver removes the direct channel contribution and recovers the structured binary LIS signal s. GAMP is used to exploit s’s prior structure.
- An estimate of z is obtained from the recovered x before recovering the LIS signal s.
- The intermediate estimate contains a distortion term w; when x is correctly recovered, w is modeled as AWGN with variance σ_w^2/P.
- The direct channel h_d can be precancelled from the z estimate before recovering s.
- Errors in the recovered x can make the actual distortion power slightly higher than σ_w^2/P.
- Because s is a structured signal containing only 0s and 1s, the paper uses GAMP to exploit its prior knowledge for recovery.
V. NUMERICAL RESULTS
The simulations evaluate recovery of the user signal x and LIS signal s under different detection methods, phase-shift designs, and LIS activity rates. Optimized passive beamforming improves SNR, while increasing activity improves BER at the cost of LIS information rate.
- 5000 random realizations were used, with maximum BiG-AMP and GAMP iterations of 200 and 50, respectively.
- Recovery of x: Optimized phase shifts provide about 2 dB SNR improvement at ρ = 0.5, while LIS enhancement improves performance by about 5 dB to 9 dB at BER = 10^-5.These comparisons use M = 32, N = 32, and L = 100.
- Recovery of x: At BER = 10^-5, BiG-AMP approaches the lower bound within 0.5 dB, while SVD remains about 2 dB away from BiG-AMP.
- Recovery of s: The GAMP approach reaches the lower bound for s at SNR = −14 dB and outperforms OMP and CoSaMP by exploiting prior information.
- Activity-rate tradeoff: Increasing ρ decreases both BERs by increasing receive SNR, but reduces the information rate per entry of s from 1.0000 at ρ = 0.5 to 0 at ρ = 1.
- Activity-rate tradeoff: Reducing ρ from 1 to 0.9 raises the rate of s from 0 to 0.4690 at a cost of about 0.5 dB SNR loss for x at BER = 10^-5.
VI. CONCLUSIONS
The paper proposes a PBIT system in which the LIS simultaneously enhances user–BS communication and transmits information. It combines optimized phase shifts, an approximate SNR-maximization algorithm, and two-step recovery of the LIS and user signals, with substantial performance gains demonstrated.
- The LIS enhances user–BS communication through phase adjustments on activated elements while transmitting information through reflecting-element on/off states.
- The proposed design optimizes the phase-shift vector to maximize average receiver SNR and approximately solves the resulting problem.
- A two-step receiver approach retrieves both the LIS signal s and the user signal x.