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Cooperative Double-IRS Aided Communication: Beamforming Design and Power Scaling
Yitao Han, Shuowen Zhang, Lingjie Duan, Rui Zhang
TL;DR
The paper addresses whether cooperative double-IRS deployment can improve communication when the direct link is blocked. It characterizes the inter-IRS LoS channel and jointly designs both IRS beamformers, obtaining O(K^4) power scaling versus O(K^2) for one IRS when K is sufficiently large.
Problem
The paper studies double-IRS communication for a blocked direct BS-user link, where the inter-IRS channel is difficult to estimate because both IRSs are passive.
Method
It models the inter-IRS channel under LoS conditions using IRS geometry and jointly designs the passive beamformers of both IRSs.
Results
O(K^4) power scaling is achieved for two cooperative IRSs versus O(K^2) for one IRS, with a significant performance gain when K is sufficiently large.
Takeaways & Limitations
Two cooperative IRSs can outperform placing all K elements on one IRS near the user when the total element count is sufficiently large.
Abstract
from arXiv · showhide
Intelligent reflecting surface (IRS) is a promising technology to support high performance wireless communication. By adaptively configuring the reflection amplitude and/or phase of each passive reflecting element on it, the IRS can reshape the electromagnetic environment in favour of signal transmission. This letter advances the existing research by proposing and analyzing a double-IRS aided wireless communication system. Under the reasonable assumption that the reflection channel from IRS 1 to IRS 2 is of rank 1 (e.g., line-of-sight channel), we propose a joint passive beamforming design for the two IRSs. Based on this, we show that deploying two cooperative IRSs with in total K elements can yield a power gain of order O(K^4), which greatly outperforms the case of deploying one traditional IRS with a power gain of order O(K^2). Our simulation results validate that the performance of deploying two cooperative IRSs is significantly better than that of deploying one IRS given a sufficient total number of IRS elements. We also extend our line-of-sight channel model to show how different channel models affect the performance of the double-IRS aided wireless communication system.
I. INTRODUCTION
The letter introduces cooperative double-IRS communication for blocked direct links and proposes studying whether two IRSs can improve wireless performance.
- IRS elements adaptively configure reflection amplitude and/or phase to modify the wireless propagation environment for specific communication needs.
- The system serves the user through the double reflection link BS-IRS1-IRS2-user when other links are unavailable because of severe blockage.
II. SYSTEM MODEL
The system models a blocked downlink from a single-antenna BS to a single-antenna user through two IRSs, with configurable unit-modulus reflection coefficients and LoS component channels.
- The blocked direct BS-user link is replaced by a double reflection path, with IRS1 near the BS and IRS2 near the user.
- The total element budget is K, divided between IRS1 and IRS2 with K1 + K2 = K.
- The baseband equivalent channels are t from BS to IRS1, S from IRS1 to IRS2, and rT from IRS2 to the user.
- The channels are modeled as LoS, while severe blockage makes other channels negligible; each IRS uses a diagonal reflection-coefficient matrix with unit-modulus entries.
- The inter-IRS channel S is difficult to estimate directly because both IRSs are passive, motivating an approach based on channel characterization and joint beamformer design.
III. PASSIVE BEAMFORMING DESIGN FOR COOPERATIVE IRSS
The paper characterizes the LoS inter-IRS channel geometrically and then jointly designs the passive beamformers of the two cooperative IRSs.
- The design procedure first characterizes the LoS channel S from IRS1 to IRS2 using their geometric relationship, then jointly designs both passive beamformers.
A. Tractable Characterization of Inter-IRS Channel
The inter-IRS LoS channel is characterized using rectangular IRS geometry, large-distance approximations, and a rank-one factorization based on element positions and orientation angles.
- Both IRSs are modeled as rectangular arrays whose elements lie on two orthogonal base directions.
- The reference elements of IRS1 and IRS2 are placed at v1 = [0, 0, 0]T and v2 = [0, dS, 0]T, respectively.
- When the inter-IRS distance is sufficiently large relative to IRS sizes, the LoS channel S can be assumed to be rank one.
- Large-distance approximations neglect element-dependent distance variations and use dS for the path loss between IRS elements.
- The approximated channel entries factor into two scalar signatures, allowing S to be decomposed as the product of signature vectors g1 and g2.
B. Design of Joint Passive Beamforming
Under a rank-one LoS inter-IRS channel, the two IRSs use coordinated passive beamformers to align reflections and maximize the end-to-end power gain. The optimal allocation splits the total elements equally, producing fourth-order scaling.
- Joint passive beamforming: Rank-one inter-IRS channels make the entries of S highly correlated, enabling beamformers that align all inter-IRS reflections.The design relies on the inter-IRS channel being LoS and rank one.
- Joint passive beamforming: IRS 1 beams BS signals toward IRS 2, while IRS 2 beams the reflected signals toward the user.The two stages jointly align the double-reflection path.
- Power-gain characterization: The resulting end-to-end power gain is (K1K2)^2 under the proposed two-IRS beamforming design.The gain combines the K1-fold contribution from IRS 1 with the K2-fold contribution from IRS 2.
- Power-gain characterization: K1 = K2 = K/2 maximizes the gain when the total number of elements is fixed at K.The equal allocation follows from optimizing the gain over K1 with K2 = K − K1.
- Power-gain characterization: O(K^4) power scaling from two cooperative IRSs exceeds the O(K^2) scaling of a single IRS with the same total number of elements.The comparison uses a single IRS placed near the user as the baseline.
- Model condition: The enhanced scaling requires a sufficiently large inter-IRS distance so that the inter-IRS channel satisfies the rank-one LoS condition.The paper leaves more complicated beamforming and deployment design for systems with more than two IRSs as future work.
IV. SIMULATION RESULTS
Simulations evaluate cooperative double-IRS beamforming against a one-IRS benchmark under LoS and Rician fading. The double-IRS configuration benefits from balanced element allocation and sufficiently large total element counts, while lower Rician factors degrade its performance.
- Simulation setup: The simulation uses a 5 GHz setup with 1 m, 100 m, and 15 m distances for the BS–IRS1, IRS1–IRS2, and IRS2–user links, respectively.The performance metric is received SNR, with transmit power P = 43 dBm and receiver noise power σ2 = −60 dBm.
- Simulation setup: The benchmark places all K elements on one IRS, using LoS channels from the BS to the IRS and from the IRS to the user.The direct BS–user link remains unavailable, and the single IRS aligns the entries of both channels.
- Element allocation: The received SNR is maximized by equal element allocation, with K1 = K2 = 400 for K = 800 and K1 = K2 = 800 for K = 1600.These results match Proposition 3.1; 800 elements per IRS corresponds to an area of 0.72 m2 under the simulation spacing.
- Comparison with one IRS: K = 800 leaves the double-IRS case inferior to one IRS, whereas K = 1600 makes cooperative double IRSs significantly better than one IRS.The double-reflection architecture must compensate for additional loss, including extra α and dt terms.
- Power scaling: Doubling K from 800 to 1600 increases received SNR by ΔI ≈ 6 dB for one IRS and ΔII ≈ 12 dB for two IRSs.These correspond to 4-times and 16-times received-power increases, consistent with O(K2) and O(K4) power scaling, respectively.
- Rician fading: With K = 1600, decreasing the Rician factor τ lowers average received SNR for two IRSs but has little effect for one IRS.Lower τ increases the rank of the IRS1–IRS2 channel, preventing the proposed beamformers from aligning all its entries.
V. CONCLUSION
The letter develops a double-IRS system with joint passive beamforming under LoS assumptions, achieving O(K^4) power gain and improved performance over one IRS for sufficiently large K.
- V. CONCLUSION: O(K^4) power gain is achieved by jointly designing passive beamformers for two cooperative IRSs with K total elements.The design assumes an LoS channel between the IRSs and characterizes it from their geometry.
- V. CONCLUSION: Simulation results validate that two cooperative IRSs outperform placing all K elements on one IRS when K is sufficiently large.
- V. CONCLUSION: The LoS channel model is extended to Rician fading to study how non-LoS propagation affects the proposed system and beamforming design.
- V. CONCLUSION: Future extensions include multi-antenna transceivers, multiple users, and more than two IRSs.