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Simultaneously Transmitting And Reflecting (STAR) RIS Aided Wireless Communications

Xidong Mu, Yuanwei Liu, Li Guo, Jiaru Lin, Robert Schober

arXiv:2104.01421v2cs.IT

TL;DR

Conventional RIS research faces challenging CSI acquisition, while conventional reflecting-only operation restricts users to the same side of the surface. This paper introduces STAR-RIS signal splitting, develops ES, MS, and TS protocols with joint beamforming optimization, and finds protocol preferences that depend on transmission type and QoS.

  • Problem

    Conventional RISs have challenging CSI acquisition, and reflecting-only operation restricts transmitter and receiver placement to the same side of the surface.

  • Method

    The paper introduces STAR-RIS signal splitting, proposes ES, MS, and TS protocols, and formulates joint active and passive beamforming optimization for unicast and multicast transmission.

  • Results

    TS is preferable for unicast with low QoS requirements, while ES is best for unicast with high QoS requirements and for multicast communication.

  • Takeaways & Limitations

    STAR-RIS designs significantly reduce BS power consumption compared with conventional reflecting- or transmitting-only RISs.

Abstract

from arXiv · show

The novel concept of simultaneously transmitting and reflecting (STAR) reconfigurable intelligent surfaces (RISs) is investigated, where the incident wireless signal is divided into transmitted and reflected signals passing into both sides of the space surrounding the surface, thus facilitating a full-space manipulation of signal propagation. Based on the introduced basic signal model of `STAR', three practical operating protocols for STAR-RISs are proposed, namely energy splitting (ES), mode switching (MS), and time switching (TS). Moreover, a STAR-RIS aided downlink communication system is considered for both unicast and multicast transmission, where a multi-antenna base station (BS) sends information to two users, i.e., one on each side of the STAR-RIS. A power consumption minimization problem for the joint optimization of the active beamforming at the BS and the passive transmission and reflection beamforming at the STAR-RIS is formulated for each of the proposed operating protocols, subject to communication rate constraints of the users. For ES, the resulting highly-coupled non-convex optimization problem is solved by an iterative algorithm, which exploits the penalty method and successive convex approximation. Then, the proposed penalty-based iterative algorithm is extended to solve the mixed-integer non-convex optimization problem for MS. For TS, the optimization problem is decomposed into two subproblems, which can be consecutively solved using state-of-the-art algorithms and convex optimization techniques. Finally, our numerical results reveal that: 1) the TS and ES operating protocols are generally preferable for unicast and multicast transmission, respectively; and 2) the required power consumption for both scenarios is significantly reduced by employing the proposed STAR-RIS instead of conventional reflecting/transmiting-only RISs.

I. INTRODUCTION

STAR-RISs extend conventional RIS operation by splitting incident signals into independently reconfigurable transmitted and reflected components, enabling full-space signal manipulation. The paper proposes three protocols and optimizes their beamforming for unicast and multicast systems.

  • Motivations and Contributions: STAR-RIS elements divide incident signals into transmitted and reflected components, overcoming the same-side deployment restriction of conventional reflecting-only RISs.Transmission and reflection are controlled through generally independent coefficients, enabling full-space smart radio environments.
  • Motivations and Contributions: The paper proposes energy splitting (ES), mode switching (MS), and time switching (TS) as practical STAR-RIS operating protocols.These protocols provide alternative ways to control transmission and reflection across the surface.
  • Motivations and Contributions: A STAR-RIS downlink system serves users on opposite sides of the surface through transmission and reflection links.The study covers both unicast and multicast communication.
  • Motivations and Contributions: For each protocol, the paper jointly optimizes BS active beamforming and STAR-RIS passive transmission and reflection beamforming to minimize BS power under user QoS constraints.The formulation targets power consumption while satisfying communication requirements.
  • Numerical Results: TS is generally preferable for unicast, whereas ES is superior for multicast communication.For ES, element-based amplitude control significantly benefits unicast, but its gain is negligible for multicast.
  • Numerical Results: STAR-RISs provide increasing performance gains over conventional RISs as the number of RIS elements grows.The reported comparison concerns conventional reflecting/transmitting-only RISs.

C. Organization and Notation

The paper introduces STAR-RIS signal modeling and three operating protocols before presenting system formulations, algorithms, and numerical evaluations. Its notation defines standard vector, matrix, and probability concepts, while the signal model splits incident signals into transmission and reflection.

  • Organization: The paper is organized around a STAR-RIS signal model, three operating protocols, system formulations, solution algorithms, numerical results, and conclusions.The system formulations cover both unicast and multicast transmission.
  • Notation: The notation section defines conventions for scalars, vectors, matrices, complex Gaussian variables, matrix operators, and positive semidefinite matrices.It also specifies standard norms, rank, trace, diagonal extraction, and all-one or all-zero matrices.
  • Basic Signal Model of STAR-RISs: A STAR-RIS divides an incident wireless signal into transmitted and reflected signals.The model indexes the incident signal by each STAR-RIS element.
  • Basic Signal Model of STAR-RISs: Transmission and reflection phase shifts can be selected independently, while their amplitude adjustments are coupled by energy conservation.For each element, transmitted and reflected signal energies sum to the incident-signal energy.

B. Three Practical Protocols for Operating STAR-RISs

STAR-RISs support full-space signal manipulation through transmission and reflection, with three operating protocols—ES, MS, and TS—offering different flexibility and implementation trade-offs.

  • Basic STAR-RIS operation: STAR-RIS elements can operate in full transmission, full reflection, or simultaneous transmission-and-reflection modes.The transmission and reflection amplitude and phase coefficients determine the operating mode.
  • Operating protocols: The paper proposes energy splitting (ES), mode switching (MS), and time switching (TS) as practical STAR-RIS protocols.These protocols are illustrated in Fig. 2.
  • Energy Splitting (ES): ES splits each incident signal’s energy between transmitted and reflected signals while optimizing both coefficient matrices.This provides a high degree of flexibility for communication-system design.
  • Mode Switching (MS): MS divides elements into transmission and reflection groups, restricting amplitude coefficients to binary values.MS is easier to implement but generally cannot achieve ES’s full-dimension beamforming gain.
  • Time Switching (TS): TS periodically switches all elements between transmission and reflection modes in orthogonal time periods with λ_t + λ_r = 1.Its transmission and reflection coefficients are not coupled, but switching imposes stringent synchronization requirements and higher hardware complexity.
  • System model: The considered downlink system uses a STAR-RIS to serve one transmission-space user and one reflection-space user when direct BS-user links are blocked.The paper formulates joint active and passive beamforming optimization for unicast and multicast transmission under all three protocols.

B. Unicast Communication and Problem Formulation

The paper formulates unicast downlink design for a two-user STAR-RIS system, jointly optimizing BS and STAR-RIS beamforming under user QoS constraints.

  • Unicast Communication and Problem Formulation: Unicast transmission uses separate BS beamforming vectors and information-bearing symbols for the transmission-space and reflection-space users.The users are indexed by k ∈ {t, r}.
  • 1) ES and MS:: Channel estimation remains challenging for RIS-assisted systems, and more efficient simultaneous CSI acquisition for ES and MS is left for future work.Existing methods can consecutively estimate transmission- and reflection-space channels under TS.
  • Unicast Communication and Problem Formulation: The objective is to minimize BS power by jointly optimizing active BS beamforming and passive STAR-RIS transmission and reflection beamforming.The optimization is subject to both users’ QoS requirements.
  • Unicast Communication and Problem Formulation: The formulation covers ES, MS, and TS through protocol-specific feasible sets for transmission and reflection coefficient matrices.TS additionally includes time-allocation variables and related constraints.
  • 1) ES and MS:: For TS, users are served in different periods, eliminating inter-user interference during the respective transmission and reflection periods.The resulting problem is always feasible for any user rate requirements.
  • 1) ES and MS:: Compared with reflecting-only RISs, STAR-RISs require optimizing both transmission and reflection beamforming.Reflecting-only RIS optimization is a special case in which transmission is disabled and only the reflection-space user is served.
  • 1) ES and MS:: ES and MS further couple transmission and reflection beamforming, making their resource-allocation problem more difficult than conventional reflecting-only RIS design.The problem is non-convex and generally difficult to solve globally.

C. Multicast Communication and Problem Formulation

The multicast formulation sends a common symbol to both STAR-RIS users and optimizes protocol-specific beamforming under a system multicast-rate constraint.

  • C. Multicast Communication and Problem Formulation: For multicast transmission, the BS uses one beamforming vector to send the same symbol to the transmission-space and reflection-space users.The received signal includes the STAR-RIS-assisted channel and additive noise.
  • C. Multicast Communication and Problem Formulation: For TS, the two users receive the common symbol in different orthogonal periods and may use distinct active beamforming vectors.The TS multicast rate is identical to the corresponding unicast communication rate.
  • C. Multicast Communication and Problem Formulation: The multicast rate is limited by the user achieving the smaller communication rate.This defines the effective system multicasting rate for ES, MS, and TS.
  • C. Multicast Communication and Problem Formulation: The multicast optimization jointly designs active and passive beamforming for ES, MS, and TS subject to a minimum system multicast-rate constraint.The TS-specific time-allocation constraint applies only to TS.
  • D. Discussion: Because multicast has no inter-user interference, the multicast problem is feasible for each operating protocol.The ES and MS formulation can be obtained from the unicast formulation by removing the interference term.
  • D. Discussion: The paper focuses mainly on unicast optimization because multicast problems can be solved in a similar manner.For TS, the multicast problem can be directly obtained from the unicast formulation.
  • D. Discussion: The joint beamforming problem is non-convex because its rate constraint is not concave, variables are highly coupled, and feasible sets are generally non-convex.These properties make globally optimal solutions difficult to obtain.
  • D. Discussion: The paper develops efficient algorithms to obtain high-quality suboptimal solutions for all three operating protocols.The solution section introduces penalty-based methods for ES and MS and decomposition for TS.

1) Penalty-based Algorithm for ES:

The ES algorithm converts the coupled non-convex design into iterative convex semidefinite programs using penalty terms, successive convex approximation, and relaxation.

  • A. Proposed Solution for ES and MS: The ES formulation contains highly coupled non-convex constraints and non-convex rank-one constraints.The method first transforms the problem into a tractable matrix-based form.
  • Penalty formulation: The penalty method relaxes the rank-one equality into an objective penalty controlled by η.Increasing η progressively emphasizes rank-one feasibility.
  • Penalty formulation: The penalty factor is initialized small and gradually increased to avoid overwhelming the desired power-minimization objective.A large initial η would make the penalty term dominate the optimization.
  • Successive convex approximation: Successive convex approximation replaces non-convex terms with convex upper bounds and solves the resulting problem iteratively.The remaining rank-one constraint is then handled using semidefinite relaxation.
  • Semidefinite relaxation: Dropping the rank-one constraint in the relaxed problem does not sacrifice optimality because the resulting W_k matrices always have rank one.This is established by Theorem 1 for k ∈ {t, r}.
  • Algorithm structure: The inner loop repeatedly solves the relaxed convex SDP, while the outer loop increases η until the rank-one equality violation is below a predefined threshold.The objective value is non-increasing in the inner loop and bounded below.
  • Convergence: As η approaches infinity, the penalty-based iterative algorithm is guaranteed to converge to a stationary point of the original ES problem.This convergence follows from the non-increasing bounded objective sequence and the penalty construction.
  • Complexity: The algorithm has overall complexity O(I_out I_in(KN^3.5 + 2M^3.5)) and is polynomial in the number of STAR-RIS elements M.The main computational cost comes from solving the relaxed SDP in the inner loop.

2) Extended Penalty-based Algorithm for MS:

The MS formulation extends the ES penalty-based approach by adding binary-mode constraints and a second penalty term, then uses SCA and SDR to obtain a convex subproblem. The resulting algorithm can also handle multiple transmission- and reflection-side users.

  • MS adds non-convex binary constraints to the ES optimization problem, creating a mixed-integer non-convex formulation.
  • The extended method introduces equality constraint (20) as an additional penalty term with penalty factor χ.
  • As η, χ → +∞, the solution satisfies equality constraints (14) and (20).
  • Successive convex approximation upper-bounds the new penalty term, while semidefinite relaxation removes the remaining rank-one constraint and yields a convex problem solvable by CVX.
  • A two-loop penalty-based iterative algorithm is developed for MS because the method contains two penalty terms.
  • The proposed Algorithms 1 and 2 can be extended to ES/MS systems with multiple transmission- and reflection-side users.

B. Proposed Solution for TS

For TS, transmission and reflection are decoupled by serving only one user at each time instant. The problem is consequently split into effective-channel design and convex resource allocation subproblems.

  • TS assigns time fractions λ_t and λ_r satisfying 0 ≤ λ_t ≤ 1, 0 ≤ λ_r ≤ 1, and λ_t + λ_r = 1.
  • Because only one user is served at a time, the optimal BS active beamformer is maximum-ratio transmission.
  • The transmission/reflection coefficients are selected to maximize each user’s effective channel gain.
  • The coefficient-design subproblem can use either a low-complexity SDR algorithm or a globally optimal branch-and-bound algorithm.
  • After coefficient design, the remaining resource-allocation problem is convex because its rate constraint is jointly concave in p_k and λ_k.
  • Algorithm 3 alternates these subproblems, and has lower complexity than the ES/MS algorithms because TS decouples transmission and reflection.

V. NUMERICAL RESULTS

The numerical evaluation uses a three-dimensional STAR-RIS setup with Rician fading, two users, and channel averaging over 100 realizations. STAR-RIS protocols are compared with conventional RIS and uniform energy splitting baselines.

  • Simulation Setup: The simulation considers a three-dimensional BS–STAR-RIS–user geometry with two users located on opposite sides of the surface.
  • Simulation Setup: The STAR-RIS uses a uniform planar array with M = M_hM_v elements, where M_h = 5 and M_v increases linearly with M.
  • Simulation Setup: The BS-to-surface and surface-to-user channels are modeled as narrow-band quasi-static Rician fading channels.
  • Simulation Setup: Results are averaged over 100 channel realizations generated from 100 random user distributions.
  • Baselines: The comparison includes conventional reflecting-only and transmitting-only RISs, each with M/2 elements, and uniform energy splitting with shared amplitude coefficients.
  • Baselines: Uniform energy splitting is treated as a special case of ES using group-wise or surface-wise amplitude design.

C. Convergence of Algorithms 1 and 2

The proposed penalty-based algorithms converge quickly and reach the prescribed constraint accuracy. Across power-consumption comparisons, TS is preferable for unicast, whereas ES is preferable for multicast, with STAR-RIS generally outperforming conventional RISs.

  • Convergence: The penalty-based algorithms converge in 6 iterations for unicast and 4 iterations for multicast communication.
  • Convergence: Constraint violation decreases quickly and reaches ε_1 = ε_2 = 10^-7 after 8 outer-loop iterations.
  • Power Consumption: TS achieves the best performance for unicast, whereas ES is preferable for multicast communication.
  • Power Consumption: TS benefits unicast by serving one user per time instant and preventing inter-user interference from degrading communication rates.
  • Power Consumption: ES benefits multicast because the same symbol creates no inter-user interference, allowing users to be served throughout the available communication time.
  • Baseline Comparison: STAR-RISs outperform conventional RISs for unicast across operating protocols, while conventional RISs can outperform TS for multicast when M is small.
  • Baseline Comparison: As M increases, conventional RISs become the worst multicast option because fixed transmission/reflection assignments lose degrees of freedom.
  • Baseline Comparison: Element-wise amplitude control gives ES a unicast advantage over UES by improving desired-signal enhancement and interference mitigation, but its multicast gain is negligible.

E. Required Power Consumption Versus Number of BS Antennas

Required power consumption decreases as the number of BS antennas increases, while the preferred STAR-RIS protocol depends on transmission type and QoS requirements. STAR-RIS schemes generally exploit additional transmission and reflection degrees of freedom, but TS can lose efficiency when communication time is split.

  • Power versus BS antennas: Required power consumption decreases for all schemes as the number of BS antennas N increases.The reduction is attributed to higher active beamforming gain.
  • Power versus BS antennas: STAR-RISs outperform conventional RISs for unicast communication by exploiting more transmission and reflection design degrees of freedom.For multicast communication with small M, the conventional-RIS loss in degrees of freedom is not significant.
  • Power versus BS antennas: Conventional RISs outperform TS STAR-RIS for multicast communication because they exploit communication time more efficiently.The comparison is reported for the considered small-M setting.
  • Power versus required SINR: TS achieves the best unicast performance at small minimum required SINR, whereas ES, MS, and baseline schemes perform better at larger SINR.TS avoids inter-user interference but inefficiently uses communication time; the other schemes serve both users throughout communication.
  • Power versus required SINR: For multicast communication, the performance gap between TS and the other schemes increases with the minimum required SINR γc because TS inefficiently uses communication time.The results motivate selecting different operating protocols for different communication objectives and scenarios.
  • Conclusions: Overall, TS is preferable for unicast with low QoS requirements, while ES is preferable for unicast with high QoS requirements and for multicast communication.The paper presents these protocol choices as design guidelines for STAR-RIS aided systems.

APPENDIX A: PROOF OF THEOREM 1

The appendix establishes structural properties of the optimal solution using convex relaxation, strong duality, and KKT conditions. It characterizes the optimal beamforming structure through the Lagrangian formulation.

  • Proof strategy: The relaxed problem without the rank-one constraint is jointly concave with respect to the relevant optimization variables.This relaxation supports the subsequent optimality analysis.
  • Proof strategy: Slater’s constraint qualification holds, so strong duality applies to the relaxed optimization problem.The Lagrangian is formed using multipliers associated with the QoS and related constraints.
  • Optimal solution structure: KKT conditions characterize the structure of the optimal BS beamforming solution through the gradient of the Lagrangian.The proof further establishes rank properties for the auxiliary optimal variables.
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