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Intelligent Reflecting Surface Aided Wireless Networks: From Single-Reflection to Multi-Reflection Design and Optimization

Weidong Mei, Beixiong Zheng, Changsheng You, Rui Zhang

arXiv:2109.13641v2cs.ITeess.SPmath.IT

TL;DR

Prior IRS research has mainly focused on single-reflection links, which may be insufficient under harsh propagation conditions. This tutorial presents multi-IRS system models and reviews reflection optimization and channel acquisition; in a free-space LoS example, doubling IRS elements from 400 to 800 yields about 4 bps/Hz rate growth for a double-reflection link versus 2 bps/Hz for two single-reflection links.

  • Problem

    Prior IRS design research has mainly focused on single-IRS systems, while single-reflection links may be insufficient to boost capacity under harsh propagation conditions.

    Source: §I · p. 2

  • Method

    The paper presents a general multi-IRS system model and reviews double- and multi-IRS design challenges, focusing on reflection optimization and channel acquisition.

    Source: §I · p. 3, §V · p. 16

  • Results

    With 400 to 800 IRS elements, the double-reflection link under free-space LoS gains about 4 bps/Hz, while two single-reflection links gain about 2 bps/Hz.

    Source: 1) Double-IRS-Aided SISO System · p. 6

  • Takeaways & Limitations

    Combining single- and double-reflection links can increase path diversity and make the network more resilient to signal blockage.

    Source: 1) IRS Deployment/Placement · p. 9

Abstract

from arXiv · show

Intelligent reflecting surface (IRS) has emerged as a promising technique for wireless communication networks. By dynamically tuning the reflection amplitudes/phase shifts of a large number of passive elements, IRS enables flexible wireless channel control and configuration, and thereby enhances the wireless signal transmission rate and reliability significantly. Despite the vast literature on designing and optimizing assorted IRS-aided wireless systems, prior works have mainly focused on enhancing wireless links with single signal reflection only by one or multiple IRSs, which may be insufficient to boost the wireless link capacity under some harsh propagation conditions (e.g., indoor environment with dense blockages/obstructions). This issue can be tackled by employing two or more IRSs to assist each wireless link and jointly exploiting their single as well as multiple signal reflections over them. However, the resultant double-/multi-IRS aided wireless systems face more complex design issues as well as new practical challenges for implementation as compared to the conventional single-IRS counterpart, in terms of IRS reflection optimization, channel acquisition, as well as IRS deployment and association/selection. As such, a new paradigm for designing multi-IRS cooperative passive beamforming and joint active/passive beam routing arises which calls for innovative design approaches and optimization methods. In this paper, we give a tutorial overview of multi-IRS aided wireless networks, with an emphasis on addressing the new challenges due to multi-IRS signal reflection and routing. Moreover, we point out important directions worthy of research and investigation in the future.

I. INTRODUCTION

Single-IRS links can be limited by coverage, blockages, finite reflection gains, and channel correlation. This tutorial surveys multi-IRS designs, their added gains and challenges, and future research directions.

I. INTRODUCTION

  • Single-IRS links can have limited coverage, fail to bypass obstacles, offer limited passive beamforming gains, and suffer reduced spatial multiplexing from correlated channels.These constraints motivate considering multiple IRSs for a wireless link.Source: §I · p. 2
  • Multi-reflection links add degrees of freedom for bypassing obstacles and, under LoS conditions, can provide higher-order cooperative passive beamforming gain than single-reflection links.The increased reflection count also increases product-distance path loss.Source: §I · p. 2
  • Multi-IRS designs complicate reflection optimization, channel acquisition, and user-specific IRS selection or routing, especially in multi-user systems with diverse QoS requirements.The routing design must balance cooperative passive beamforming gain against end-to-end path loss.Source: §I · p. 3
  • The paper presents a general multi-IRS system model, reviews double- and multi-IRS reflection optimization and channel acquisition, and identifies open research directions.It first studies double-IRS design, then multi-IRS selection and beam-routing optimization.Source: §I · p. 3

II. SYSTEM MODEL

The system model represents each user’s effective channel as a direct link plus IRS-reflected paths, subject to practical reflection and path-selection constraints. It assumes frequency-flat channels in a snapshot and models the BS, users, IRSs, and their channels.

II. SYSTEM MODEL

  • The model considers downlink communication from a multi-antenna BS to single-antenna users, with each IRS having M passive elements and a controller for tuning reflection coefficients.It assumes NB ≥ K active BS antennas and frequency-flat channels in one fixed-channel snapshot.Source: §II · p. 4
  • Each user’s effective channel comprises its direct BS-user channel and reflected paths using IRSs in its region, with BS-IRS, inter-IRS, and IRS-user channels represented separately.IRSs outside a user’s region are treated as environmental scatterers.Source: §II · pp. 4–5
  • Reflected paths must respect each IRS’s 180° reflection half-space, and the model retains paths that progress outward from the BS to reduce multiplicative path loss.It excludes paths with substantially higher cascaded path loss than an outward-ordered alternative.Source: §II · p. 4
  • When all constituent links are LoS-dominated, cooperative passive beamforming gain increases with the number of IRS reflections and can exceed the direct-channel gain.Multi-reflection paths also incur multiplicative path loss across their constituent links.Source: §II · p. 4

III. REFLECTION DESIGN AND OPTIMIZATION FOR DOUBLE-IRS SYSTEM

The section models a double-IRS system with fixed IRSs near the BS and user cluster, providing two single-reflection links and a double-reflection link. Its SISO analysis finds that LoS double reflection can scale faster, but its higher path loss and channel conditions affect whether it is advantageous.

III. REFLECTION DESIGN AND OPTIMIZATION FOR DOUBLE-IRS SYSTEM

  • Two fixed IRSs near the BS and user cluster give each user two single-reflection paths and one double-reflection path.The BS-side and user-side IRSs are jointly considered in the multiuser setup.Source: §III · p. 5

1) Double-IRS-Aided SISO System:

  • With only the double-reflection path considered, properly aligned IRSs achieve O(M^4) passive beamforming gain under an LoS inter-IRS channel, versus O(M^2) for a single-reflection link.The double-reflection path also incurs higher product-distance path loss, so sufficiently many elements may be needed; routing therefore trades beamforming gain against path loss.Source: 1) Double-IRS-Aided SISO System · p. 5
  • Doubling the total IRS elements from 400 to 800 raises achievable rate by about 4 bps/Hz for the LoS double-reflection link and about 2 bps/Hz for the two single-reflection links.For insufficient element counts and/or Rayleigh or NLoS inter-IRS channels, the double-reflection link can have lower achievable rate than the two single-reflection links.Source: Figure 5 · p. 6, 1) Double-IRS-Aided SISO System · p. 6

2) Double-IRS-Aided Single-User MISO System:

For a single-user MISO system with a blocked direct link, the BS beamforming and two IRSs’ cooperative passive beamforming must be designed jointly. The single- and double-reflection links generally favor different designs, so optimization balances their gains or combines them coherently.

2) Double-IRS-Aided Single-User MISO System:

  • The BS’s active beamforming and both IRSs’ passive beamforming require joint design when the direct link is blocked.The design concerns the single-user, multiple-antenna-BS case.Source: 2) Double-IRS-Aided Single-User MISO… · p. 6
  • The single- and double-reflection links generally have different optimal joint beamforming designs, requiring a balance between their channel gains.The joint optimization is generally non-convex because of the IRS unit-modulus constraints and coupling with BS beamforming.Source: 2) Double-IRS-Aided Single-User MISO… · p. 6
  • Alternating optimization can iteratively optimize BS active beamforming and the two IRSs’ passive beamforming; a common phase shift can also achieve coherent combining of single- and double-reflection links.The common phase is selected to align the phases of the single- and double-reflection components.Source: 2) Double-IRS-Aided Single-User MISO… · p. 6

3) Double-IRS-aided Multi-user MISO System:

The double-IRS multi-user system adds path diversity that can improve effective-channel rank and multi-user rate performance. The section also describes the channel-estimation challenge and a cascaded-CSI representation for double-IRS links.

3) Double-IRS-aided Multi-user MISO System:

  • Multi-user joint active/passive beamforming must accommodate diverse QoS requirements and is coupled to IRS-user association; optimizing only the dominant reflection link is generally suboptimal.Multi-user transmission over the same frequency band also generally experiences cochannel interference.Source: 3) Double-IRS-aided Multi-user MISO… · pp. 6–7
  • The double-IRS system generally has higher channel rank than the single-IRS baseline, supporting greater spatial multiplexing and improved multi-user SINR and rate.The additional double-reflection link can help bypass obstacles; the reported rank gain is no less than min(rank(G2,k), rank(Q0,2)).Source: 3) Double-IRS-aided Multi-user MISO… · p. 7
  • With ZF beamforming, the double-IRS system achieves rank(H) = K and its max-min rate keeps increasing with user transmit power, unlike the rank-deficient, saturating single-IRS baseline.For a deficient-rank system, MMSE receive beamforming generally performs better than ZF.Source: 3) Double-IRS-aided Multi-user MISO… · p. 7, Figure 7 · p. 7

B. Double-IRS Channel Estimation

  • For fully passive IRSs, the system can estimate cascaded CSI at an endpoint such as the BS, and cascaded single- and double-reflection CSI suffices for joint active/passive beamforming without loss of optimality.The cascaded model distinguishes the two single-reflection links from the double-reflection channel associated with each IRS 2 element.Source: B. Double-IRS Channel Estimation · p. 7

1) Double-IRS-Aided SISO System:

The section compares channel-estimation requirements for double-IRS SISO and single-user MISO systems. It describes how LoS structure and relationships between single- and double-reflection channels can reduce training overhead.

1) Double-IRS-Aided SISO System:

  • With a general inter-IRS channel, double-IRS SISO estimation requires at least M^2 pilots, while an LoS inter-IRS channel permits a 2M-pilot scheme using separately estimated signature vectors.The LoS scheme fixes one IRS reflection while tuning the other during training.Source: 1) Double-IRS-Aided SISO System · p. 8

2) Double-IRS-aided Single-user MISO System:

  • In single-user MISO, double-reflection channels have more coefficients than the two single-reflection links, making channel estimation more challenging than in SISO.The two single-reflection links contain 2MNB coefficients, while the double-reflection links contain M^2NB coefficients.Source: 2) Double-IRS-aided Single-user MISO… · p. 8
  • The estimation approach exploits the shared BS-IRS channel to express higher-dimensional double-reflection channels as scaled versions of single-reflection CSI, avoiding their direct estimation.A decoupled scheme estimates the direct CSI, cascaded CSI, and scaling vectors successively; ON/OFF training can incur residual interference and reflection-power loss, while always-ON joint estimation uses full reflection power.Source: 2) Double-IRS-aided Single-user MISO… · p. 8
  • For sufficiently large NB (say, NB ≥ M), minimum training overhead in the double-IRS single-user MISO system is comparable to the single-IRS case, with both scaling linearly in total IRS elements M.The cited minimum overhead decreases as NB grows until reaching 3M.Source: 2) Double-IRS-aided Single-user MISO… · p. 8

3) Double-IRS-aided Multi-user MISO System:

The multi-user channel-estimation scheme uses shared channel structure to limit the extra training needed for additional users. Its overhead falls as BS antenna count increases, unlike the cited benchmark, whose overhead is independent of that count.

3) Double-IRS-aided Multi-user MISO System:

  • A user-by-user successive approach would multiply the single-user training overhead by K, since the multi-user channel has K times as many coefficients.The users share several links but have different IRS-user links.Source: 3) Double-IRS-aided Multi-user MISO… · p. 8
  • Using one user’s cascaded CSI as reference, the scheme estimates low-dimensional scaling vectors for other users to recover their high-dimensional cascaded CSI.This exploits common BS-IRS and IRS-IRS links across users; the added overhead for the remaining users can be as low as max…Source: 3) Double-IRS-aided Multi-user MISO… · p. 8
  • The additional training overhead for the remaining users can decrease with NB to a lower bound of K − 1, while the proposed scheme’s overall overhead decreases with NB and the benchmark’s is independent of NB.The comparison is shown against BS antenna count in Fig. 8.Source: 3) Double-IRS-aided Multi-user MISO… · p. 9, Figure 8 · p. 9

C. Other Related Work and Future Direction

The future directions consider extending double-IRS deployments to multiple BS- and user-side IRSs serving distributed user clusters. They identify IRS placement and IRS-user association as coupled design challenges.

1) IRS Deployment/Placement:

  • Hybrid deployment places IRSs on both BS and user sides, combining complementary performance advantages with flexibility to select single- or double-reflection modes for users or clusters.The added path diversity can make the network more resilient to signal blockage.Source: 1) IRS Deployment/Placement · p. 9
  • Future work should determine how to place and allocate BS- and user-side IRSs to balance reflection-channel gains and control of the radio environment.The availability of LoS inter-IRS channels may depend on deployment, including the direction the IRSs face.Source: 1) IRS Deployment/Placement · p. 9

2) IRS-User Association:

  • IRS-user association must account for communication requirements and channel conditions, and is coupled with beamforming, CSI availability, and user mobility.Possible associations range from no IRS to BS-side, user-side, or both types of IRSs, changing transmission modes and CSI requirements.Source: 2) IRS-User Association · p. 9

3) Resource Allocation and User Scheduling:

The section identifies unresolved multi-IRS resource-allocation challenges and develops a LoS-focused framework for multi-reflection routing. It also marks FDD, broadband, and imperfect-CSI designs as open extensions.

3) Resource Allocation and User Scheduling:

  • Hybrid BS- and user-side IRS deployments require joint allocation of reflecting elements and time-frequency resources, while IRS coordination complicates user scheduling.IRS reflection is time-selective but not frequency-selective, and this resource-allocation topic remains at an initial research stage.Source: 3) Resource Allocation and User… · p. 9

4) Other Extensions:

  • The discussion focuses on TDD double-IRS systems and narrowband flat-fading channels; FDD design and broadband frequency-selective extensions remain open challenges.Broadband cascaded channels involve convolution, with higher-order convolution for double-reflection links.Source: 4) Other Extensions · pp. 9–10

IV. REFLECTION DESIGN AND OPTIMIZATION FOR MULTI-IRS SYSTEM

  • The multi-IRS design framework assumes all IRSs participate in reflection design and channel estimation, and focuses on LoS links because perfect CSI for all links incurs high overhead.NLoS links are treated as environmental scattering; dense, proper IRS deployment can enable LoS propagation across many links.Source: §IV · p. 10, A. LoS-Dominant Channel Model · p. 10

A. LoS-Dominant Channel Model

  • LoS availability is identified offline for fixed BS-IRS and inter-IRS links, but online for IRS-user links because users move.The binary indicators also enforce outward signal progression and effective reflection subject to each IRS's 180° half-space reflection.Source: A. LoS-Dominant Channel Model · p. 10

B. Multi-Reflection Beam Routing Optimization

1) Single User:

For a single user with a severely blocked direct link, the design selects a multi-IRS LoS path that balances coherent passive beamforming gain against accumulated path loss. If the direct link is retained, coherent combining changes the routing objective.

1) Single User:

  • Under LoS channels, n IRS reflections provide a CPB gain of M^(2n), but also increase multiplicative path loss, creating a trade-off in selecting the route.Other scattered paths are treated as negligible under the optimized beamforming design.Source: 1) Single User · p. 11
  • The blocked-direct-link routing problem is optimally recast as a shortest path on an LoS graph and solved with Bellman-Ford.Effective LoS links form graph edges, and cascaded paths correspond to routes from the BS vertex to the user vertex.Source: 1) Single User · p. 11
  • When the direct BS-user channel cannot be ignored, coherent combining adds direct-link, selected-path, and crosstalk terms to the effective channel gain.For NB > 1, the resulting routing problem requires traversing feasible paths and selecting the path with the largest gain.Source: 1) Single User · p. 11

2) Multiple Users:

Multi-user routing must coordinate users' paths to limit interference while balancing their channel gains. Simulations illustrate that path selection changes with element count and that path separation can trade one user's rate for a more balanced outcome.

2) Multiple Users:

  • When direct BS-user links are blocked, path separation can mitigate inter-user interference by keeping different users' selected IRS paths without direct LoS links between them.This can decouple BS and IRS beamforming across users; if direct links are significant, path separation alone may be insufficient and BS precoding must also account for them.Source: 2) Multiple Users · pp. 11–12
  • Path separation makes multi-user routing more difficult: maximizing one user's channel gain can reduce feasible paths for others, and the resulting problem is NP-complete.A recursive partial-enumeration algorithm balances performance and complexity; the objective also balances CPB gain against path loss for each user.Source: 2) Multiple Users · p. 12
  • For user 1 at κ = 20 dB, the optimal reflection path with M0 = 24 goes through one more IRS than with M0 = 20.At M0 = 20, end-to-end path loss dominates CPB gain, so the optimal path uses the least number of IRS reflections.Source: 2) Multiple Users · p. 13
  • With both users present, imposing path separation changes user 2's route and sacrifices its rate performance to balance the users' effective channel gains.Without the constraint, the routes share the BS-to-IRS 8 link and have an LoS link between them, which can cause strong interference.Source: 2) Multiple Users · pp. 13–14, Figure 10 · p. 13, Figure 11 · p. 13

C. Beam Training

The paper proposes codebook-based beam training as a practical alternative when perfect CSI is difficult to obtain. Exhaustive beam search can find the optimal codebook beamforming design without explicit channel estimation.

C. Beam Training

  • Finite active and passive beamforming codebooks enable exhaustive beam search for optimal beamforming without explicit CSI or channel estimation.The codebooks contain beam patterns or directions for the BS and each IRS.Source: C. Beam Training · p. 14
  • The BS can first train with IRSs switched off, identify users with strong direct channels, and schedule them in different slots from users needing IRS assistance.Users with insufficient direct channels proceed to IRS-based passive beam training.Source: C. Beam Training · p. 14

1) Exhaustive and Sequential Beam Search:

Exhaustive and sequential beam search can impose prohibitive training overhead, motivating distributed training that uses local beam training tables to select beam patterns and reflection routes. Its approximation improves as LoS propagation becomes dominant, while the approach trades some beamforming performance for lower real-time complexity and overhead.

1) Exhaustive and Sequential Beam Search:

  • Exhaustive beam search requires D_BD_I^J pattern combinations, while sequential search has complexity of order D_B + JD_I.Both incur high complexity, and neither explicitly assigns IRSs to users through beam routing.Source: 1) Exhaustive and Sequential Beam Search · p. 14
  • Searching reflection-path sets together with active and passive beam patterns can also incur exorbitant real-time training overhead.The search may use exhaustive or sequential beam search for each path set.Source: 1) Exhaustive and Sequential Beam Search · p. 14

2) Distributed Beam Training:

  • Distributed training maintains local beam training tables at the BS and IRSs, then combines them at the BS to estimate gains and select beam patterns and reflection paths.The tables record received signal strength for candidate active or passive beam patterns and neighboring nodes.Source: 2) Distributed Beam Training · pp. 14–15
  • The distributed approach uses partial CSI and can yield suboptimal beamforming and routing, but reduces real-time training complexity and overhead.Passive training that does not involve users can be conducted offline.Source: 2) Distributed Beam Training · p. 15
  • The performance gap between distributed beam training and sequential beam search becomes negligible for κ ≥15 dB as LoS dominance improves the distributed approximation.Both schemes’ channel gains increase with κ.Source: 2) Distributed Beam Training · p. 15, Figure 13 · p. 15

D. Other Related Work and Future Direction

The paper identifies deployment, broadband beamforming, hybrid active/passive IRSs, and multi-reflection channel estimation as open design challenges. It concludes that multi-IRS systems can offer promising gains under certain conditions while outlining research directions and other potential applications.

D. Other Related Work and Future Direction

1) IRS Deployment/Placement:

  • IRS placement should shorten inter-node and BS/user distances, provide path diversity, and orient surfaces to increase effective LoS links.With low- or moderate-resolution codebooks, achievable CPB gain also depends on nearby IRS arrival and departure angles; placement can be designed offline from historical performance data.Source: 1) IRS Deployment/Placement · p. 15

2) Broadband System with Frequency-Selective Channels:

  • Broadband channels require each IRS to use common passive beamforming across a user's frequency bands, complicating beamforming and routing.Splitting elements into sub-surfaces for separate bands is a practical approach, but may require more BTTs per controller and further design work.Source: 2) Broadband System with… · pp. 15–16

3) Hybrid Active/Passive IRSs for Multi-Reflection:

  • Multi-reflection links require sufficiently many elements at each IRS to compensate for multiplicative path loss, increasing hardware and energy costs.Active IRSs reflect and amplify signals, and may better suit multiple reflections when element counts are not large; combining active and passive IRSs is also proposed for study.Source: 3) Hybrid Active/Passive IRSs for… · p. 16

4) Cascaded Channel Estimation for Multi-Reflection Links:

  • Accurate CSI is harder to acquire for multi-reflection links because separate channel acquisition is infeasible with fully passive IRSs and cascaded coefficients grow exponentially with reflections.Decomposing the cascaded channel into lower-dimensional subchannels is proposed as a possible strategy for future estimation designs.Source: 4) Cascaded Channel Estimation for… · p. 16

V. CONCLUSIONS

  • Multi-IRS systems offer promising performance gains over single-IRS systems under certain conditions, while their design and channel-acquisition challenges remain important research topics.The tutorial presents a general system model and reviews double- and multi-IRS systems alongside open issues and future directions.Source: §V · p. 16

D. Other Related Work and Future Direction

  • Multi-IRS reflection may also benefit wireless power transfer, RF sensing/localization, and spatial modulation, which remain subjects for further investigation.The paper notes that multi-reflection CPB gain could enhance the range and efficiency of RF-based wireless power transfer.Source: §V · p. 16

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