Source-linked AI summary
Intelligent Reflecting Surface Enhanced Wireless Network: Joint Active and Passive Beamforming Design
Qingqing Wu, Rui Zhang
TL;DR
The paper addresses energy and hardware-cost concerns in wireless networks by studying passive IRS assistance for an AP-to-user MISO link. It jointly designs AP transmit and IRS reflect beamforming using centralized SDR and distributed alternating optimization, achieving improved SNR and coverage over operation without an IRS.
Problem
Wireless networks still face critical energy-consumption and hardware-cost issues, while IRS design and performance optimization remain limited.
Method
The paper jointly optimizes AP transmit beamforming and IRS phase shifts, proposing centralized SDR and low-complexity distributed alternating-optimization designs.
Results
The proposed designs significantly improve link SNR and extend signal coverage compared with the conventional setup without an IRS.
Takeaways & Limitations
A passive IRS can enhance wireless link quality and coverage without installing an additional AP or active relay.
Abstract
from arXiv · showhide
Intelligent reflecting surface (IRS) is envisioned to have abundant applications in future wireless networks by smartly reconfiguring the signal propagation for performance enhancement. Specifically, an IRS consists of a large number of low-cost passive elements each reflecting the incident signal with a certain phase shift to collaboratively achieve beamforming and suppress interference at one or more designated receivers. In this paper, we study an IRS-enhanced point-to-point multiple-input single-output (MISO) wireless system where one IRS is deployed to assist in the communication from a multi-antenna access point (AP) to a single-antenna user. As a result, the user simultaneously receives the signal sent directly from the AP as well as that reflected by the IRS. We aim to maximize the total received signal power at the user by jointly optimizing the (active) transmit beamforming at the AP and (passive) reflect beamforming by the phase shifters at the IRS. We first propose a centralized algorithm based on the technique of semidefinite relaxation (SDR) by assuming the global channel state information (CSI) available at the IRS. Since the centralized implementation requires excessive channel estimation and signal exchange overheads, we further propose a low-complexity distributed algorithm where the AP and IRS independently adjust the transmit beamforming and the phase shifts in an alternating manner until the convergence is reached. Simulation results show that significant performance gains can be achieved by the proposed algorithms as compared to benchmark schemes. Moreover, it is verified that the IRS is able to drastically enhance the link quality and/or coverage over the conventional setup without the IRS.
I. INTRODUCTION
IRS is presented as a reconfigurable, passive, and potentially energy-efficient way to improve wireless links by controlling reflected signals. The paper studies joint AP transmit and IRS reflect beamforming, proposing centralized and distributed designs for an IRS-assisted system.
- IRS motivation: IRS uses many independently controllable passive elements to phase-shift incident waves for coherent signal enhancement or interference suppression.Reconfigurability is enabled by smart controllers and recent RF MEMS or metamaterial advances.
- IRS motivation: Unlike AF relays, IRS reflects ambient RF signals without transmitter modules, incurring no additional power consumption.Unlike backscatter communication, IRS enhances an existing link rather than transmitting information of its own.
- System and objective: The considered system jointly optimizes AP transmit beamforming and IRS phase shifts to maximize total received signal power at a single-antenna user.The user receives superposed direct and IRS-reflected signals.
- Proposed designs: The paper proposes a centralized SDR-based algorithm and a lower-complexity distributed alternating-optimization algorithm.The centralized method requires global CSI at the IRS, while the distributed method reduces associated estimation and exchange overheads.
- Reported outcomes: The proposed designs significantly improve link SNR, with receive SNR near the IRS increasing in the order of N^2 as reflecting elements grow.These results imply potential AP power savings or user SNR gains.
A. System Model
The system consists of a multi-antenna AP, a single-antenna user, and an IRS with dynamically controlled passive elements. The received signal combines direct and reflected paths under a quasi-static flat-fading model.
- System configuration: An AP with M antennas serves a single-antenna user with assistance from an IRS containing N passive elements.The IRS is installed on a surrounding wall to assist communication or power transfer.
- IRS operation: The IRS controller senses the propagation environment and dynamically adjusts each element’s phase shift through receiving and reflecting modes.The same passive array periodically supports environment sensing such as CSI estimation.
- Model assumptions: Signals reflected by the IRS two or more times are neglected because their power is assumed negligible under significant path loss.All channels are modeled as quasi-static and flat-fading.
- Channel model: The indirect AP–IRS–user channel is modeled through the AP–IRS link, IRS phase shifts, and IRS–user link.Each IRS element combines received multipath signals and re-scatters them as from a point source.
- Signal model: The AP uses a linear beamforming vector w subject to a maximum transmit-power constraint.The received signal includes the transmitted symbol and additive white Gaussian noise.
B. Problem Formulation
The paper formulates received-signal-power maximization over AP beamforming and IRS phase shifts. Although the constraints are convex, the objective makes the joint problem non-convex.
- Optimization objective: The objective maximizes received signal power for wireless power or information transfer by jointly selecting AP beamforming w and IRS phase shifts θ.Both applications benefit from increasing received signal power.
- Constraints: The AP beamforming must satisfy a maximum transmit-power constraint, while each IRS phase shift lies between 0 and 2π.These are the stated feasibility constraints for the formulation.
- Problem structure: The joint optimization is non-convex because its objective is non-concave in w and θ, despite convex constraints.The paper therefore applies SDR and alternating optimization in subsequent algorithm designs.
III. CENTRALIZED ALGORITHM
The centralized design transforms the IRS phase-shift problem into an SDR-based semidefinite program under global CSI, then extracts an approximate feasible solution. It provides an upper bound and high-quality solution but requires substantial CSI estimation and exchange overhead.
- Centralized optimization: For fixed IRS phase shifts, maximum-ratio transmission is the optimal AP transmit beamforming solution.
- Centralized optimization: The remaining phase-shift optimization is formulated as a unit-modulus non-convex QCQP and then homogenized with an auxiliary variable.
- Semidefinite relaxation: SDR relaxes the rank-one constraint, converting the NP-hard formulation into a convex SDP solvable by standard optimization solvers.
- Solution recovery: Because the relaxed SDP may produce a higher-rank solution, Gaussian randomization constructs a rank-one approximate solution from its eigenvalue decomposition.
- Solution quality: A sufficiently large number of randomizations guarantees a π/4-approximation of the optimal objective value of problem (P3).
- Implementation: The centralized implementation makes all link CSI available at the IRS, but channel estimation and AP–IRS signal exchange can become prohibitive for large arrays.
IV. DISTRIBUTED ALGORITHM
The distributed algorithm alternates between AP transmit-beamforming and IRS phase-shift updates, using local channel information and closed-form updates. It avoids AP–IRS CSI feedback and SDP computation while iterating to convergence.
- Algorithm design: Alternating optimization updates the AP beamforming and IRS phase shifts iteratively, keeping one fixed while optimizing the other until convergence or an iteration limit.
- IRS phase optimization: For fixed transmit beamforming, the phase-shift subproblem is expressed using an equivalent channel for each reflecting element and solved through phase alignment.
- IRS phase optimization: The phase of each IRS element is selected to align the reflected signal with the direct AP–user signal for coherent signal construction.
- Implementation: The practical algorithm alternates IRS phase estimation and AP composite-channel estimation using pilot signals, stopping when the fractional objective increase falls below a threshold or iterations are exhausted.
- Distributed implementation: A common phase rotation of the AP beamforming vector removes the need to feed back the direct-link phase from the AP to the IRS.
- Advantages: Compared with the centralized design, the distributed method needs no AP–IRS channel feedback, estimates only elementwise phases, and avoids SDP solving through closed-form updates.
V. SIMULATION RESULTS
The simulations use a ULA at the AP and a URA at the IRS, with the IRS size varied by increasing its horizontal dimension. The setup assumes a LoS-dominated AP–IRS channel and is used to study users positioned between the AP and IRS.
- Simulation setup: The AP uses a uniform linear array, while the IRS uses a uniform rectangular array with N = N_xN_y reflecting elements.
- Simulation setup: For exposition, the number of vertical IRS elements is fixed at N_y = 10 while N_x increases linearly with N.
- Channel assumptions: The AP–IRS channel is assumed to be LoS-dominated, making its channel matrix rank one with linearly dependent row and column vectors.
A. SNR versus AP-User Distance
The proposed joint beamforming designs maintain near-optimal receive SNR across AP-user distances and improve coverage by exploiting reflected signals from the IRS.
- A. SNR versus AP-User Distance: The centralized and distributed joint AP-IRS beamforming algorithms achieve near-optimal SNR and outperform the benchmark schemes across AP-user distances.The comparison uses receive SNR versus the horizontal AP-user distance d.
- A. SNR versus AP-User Distance: For a target SNR of 8 dB, IRS deployment increases network coverage from about 33 m without the IRS to about 50 m with joint beamforming.
- A. SNR versus AP-User Distance: Users near either the AP or IRS can achieve better SNR than users far from both, because users farther from the AP receive stronger reflected signals near the IRS.
- A. SNR versus AP-User Distance: AP-user MRT is near-optimal close to the AP but loses considerable SNR near the IRS, while AP-IRS MRT exhibits the opposite behavior.
- A. SNR versus AP-User Distance: The proposed designs dynamically balance AP beamforming toward the user and IRS across changing user locations.
B. SNR versus Number of Reflecting Elements
Receive SNR improves strongly with the number of IRS reflecting elements, reflecting combined aperture and passive beamforming gains.
- B. SNR versus Number of Reflecting Elements: The proposed schemes’ receive SNR scales with the number of reflecting elements N in the order of N^2.The scaling combines an array gain of N with a passive reflect beamforming gain of N.
- B. SNR versus Number of Reflecting Elements: When N increases from 30 to 60, SNR rises from 18 dB to 24 dB, yielding a 6 dB gain by doubling the reflecting elements.
- B. SNR versus Number of Reflecting Elements: When the user is near the IRS at d = 50 m, AP-IRS MRT achieves near-optimal SNR because the reflected signal is much stronger than the direct AP signal.
- B. SNR versus Number of Reflecting Elements: The reflecting-element count can be selected according to the IRS location and the target user SNR or AP coverage.
VI. CONCLUSION
The paper jointly optimizes active AP and passive IRS beamforming and develops centralized and distributed designs for IRS-enhanced MISO communication.
- VI. CONCLUSION: The proposed designs jointly optimize AP transmit beamforming and IRS phase-shifter reflect beamforming to maximize received signal power.
- VI. CONCLUSION: SDR and alternating optimization yield centralized and distributed beamforming designs, respectively.
- VI. CONCLUSION: The low-complexity distributed design achieves near-optimal performance and is appealing for practical implementation.
- VI. CONCLUSION: Simulations demonstrate SNR improvement and signal coverage extension with an IRS compared with the conventional setup without an IRS.
- VI. CONCLUSION: Joint AP and IRS beamforming is effective and crucial for optimal performance under different setups.