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Channel Estimation for STAR-RIS-aided Wireless Communication

Chenyu Wu, Changsheng You, Yuanwei Liu, Xuemai Gu, Yunlong Cai

arXiv:2112.01413v1cs.ITeess.SP

TL;DR

The paper addresses efficient uplink CSI acquisition for two-user STAR-RIS systems, where estimation depends on the TS or ES protocol. It designs optimized TS and ES schemes, including joint ES design under coupled phase shifts, and finds that TS generally yields smaller channel-estimation error than ES.

  • Problem

    CSI acquisition for STAR-RIS is challenging, and existing RIS estimation schemes do not directly apply because STAR-RIS estimation depends on its TS or ES protocol.

  • Method

    The paper designs separate-channel TS estimation and simultaneous-channel ES estimation, jointly optimizing ES pilots, power splitting, and training patterns under a practical coupled phase-shift model.

  • Results

    TS generally achieves smaller uplink channel-estimation error than ES; under optimal splitting, ES NMSE is approximately twice that of TS.

  • Takeaways & Limitations

    For uplink channel estimation in the studied two-user STAR-RIS system, TS is more cost-effective than ES.

Abstract

from arXiv · show

In this letter, we study efficient uplink channel estimation design for a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted two-user communication systems. We first consider the time switching (TS) protocol for STAR-RIS and propose an efficient scheme to separately estimate the channels of the two users with optimized training (transmission/reflection) pattern. Next, we consider the energy splitting (ES) protocol for STAR-RIS under the practical coupled phase-shift model and devise a customized scheme to simultaneously estimate the channels of both users. Although the problem of minimizing the resultant channel estimation error for the ES protocol is difficult to solve, we propose an efficient algorithm to obtain a high-quality solution by jointly designing the pilot sequences, power-splitting ratio, and training patterns. Numerical results show the effectiveness of the proposed channel estimation designs and reveal that the STAR-RIS under the TS protocol achieves a smaller channel estimation error than the ES case.

I. INTRODUCTION

STAR-RIS extends RIS service beyond one side of the surface, but its hardware protocols create new channel-estimation design challenges. This letter develops efficient estimation schemes for TS and ES.

  • STAR-RIS can simultaneously transmit and reflect signals, enabling service to users on both sides of the surface.
  • CSI is indispensable for passive beamforming, yet its acquisition is challenging because RISs lack signal transmission and processing capabilities.
  • Existing ON/OFF- and DFT-based RIS training schemes cannot be directly applied to STAR-RIS because estimation depends on its TS or ES protocol.
  • The paper designs optimized TS training for separate user-channel estimation and an ES scheme for simultaneous estimation under coupled phase shifts.
  • The ES design jointly considers pilot sequences, power-splitting ratio, and training patterns, while numerical results report larger estimation error for ES than TS.

II. SYSTEM MODEL

The system is a narrow-band uplink with two single-antenna users on opposite sides of a STAR-RIS and a single-antenna BS. The model groups surface elements into sub-surfaces and considers TS and ES operation.

  • A STAR-RIS assists uplink transmission from two single-antenna users located on opposite sides of the surface to a single-antenna BS.
  • The surface elements are divided into M sub-surfaces, whose adjacent elements share a common transmission/reflection coefficient to reduce estimation overhead.
  • The T user transmits through the STAR-RIS, whereas the R user reflects through it toward the BS.
  • The channel model includes direct user-to-BS channels, user-to-surface channels, and cascaded channels involving the surface-to-BS channel.
  • The STAR-RIS operates under two practical protocols: time switching and energy splitting.

III. STAR-RIS CHANNEL ESTIMATION: TIME SWITCHING

Under TS, the STAR-RIS separates transmission and reflection into distinct periods, enabling separate estimation of the two users’ concatenated channels through designed training patterns.

  • The TS scheme separately estimates the concatenated channels of the STAR-RIS-assisted users.
  • The STAR-RIS switches all elements between transmission and reflection modes during separate T and R periods.
  • The design extends to multiple users by grouping users in pairs and assigning orthogonal time or frequency resources, and to multi-antenna BSs through parallel channel estimation.
  • During the T period, the T user consecutively sends pilot symbols to the BS across τ_t time slots.
  • The pilot symbol can be set to s_t,i = 1 for simplicity, and the received signals across the T period form the estimation observations.
  • The transmission pattern uses phase-shift coefficients for the M sub-surfaces, with phases selected in [0, 2π).

A. Problem Formulation

For TS channel estimation, the section uses an LS estimator based on the training-pattern matrix and formulates pattern design as an MSE-minimization problem under phase-shift constraints.

  • When the training matrix Θ has full column rank, the concatenated channel is estimated by least squares using Θ† = (Θ^HΘ)^−1Θ^H.
  • The LS estimate is formed as x̂ = 1/p Θ†y_t from the received training signal.
  • The training-pattern design is formulated as an optimization problem that minimizes the channel-estimation MSE.
  • The optimization constrains each transmission and reflection phase to [0, 2π) for every sub-surface and training slot.

B. Proposed Solution

The TS design uses an (M + 1) × (M + 1) DFT training matrix and acquires both users’ CSI under minimum training overhead.

  • An (M + 1) × (M + 1) DFT matrix provides an optimal solution for the TS training design.Its entries are explicitly defined as the training matrix D_M+1.
  • Under minimum overhead τ_t + τ_r = 2M + 2, the TS scheme acquires the R user’s CSI after applying the same estimation procedure.The resulting sum MSE is then obtained for TS.

IV. STAR-RIS CHANNEL ESTIMATION: ENERGY SPLITTING

The ES protocol simultaneously estimates both users’ channels using energy splitting, coupled phase shifts, pilot transmission, and a full-rank linear estimation model.

  • The ES scheme estimates both users’ channels simultaneously during the channel-estimation stage.Both users transmit pilots while the STAR-RIS training patterns are designed for estimation.
  • Each ES sub-surface splits impinging signals into transmitted and reflected components using an energy-splitting ratio.The transmission and reflection coefficients are represented by corresponding vectors and training patterns.
  • The design adopts a practical coupled phase-shift model in which transmission and reflection phase shifts are coupled by hardware constraints.The model is described as practically accurate for a fully-passive STAR-RIS.
  • With full-rank V, the least-squares estimate recovers the composite channel vector x under minimum overhead τ ≥ 2M + 2.The composite vector contains the channel coefficients for both users and their associated components.

A. Problem Formulation

The ES problem minimizes channel-estimation MSE by jointly designing pilots, energy-splitting ratios, and transmission/reflection training patterns under practical phase and system constraints.

  • The practical model is extended to discrete phase shifts by proper quantization, although the paper assumes continuous phase shifts.The stated assumption concerns the phase-shift implementation used in the analysis.
  • The ES objective is to minimize channel-estimation MSE jointly over user pilot sequences, energy-splitting ratios, and training-pattern matrices.The optimization includes the pilot sequences s_k, ratios β_k^m, and matrices Θ̄ and Φ̄.
  • The training design constrains transmission and reflection phase shifts to lie in [0, 2π).This constraint applies to every sub-surface and training time slot.

B. Proposed Solutions

The proposed ES solution relaxes the coupled-phase constraint for insight, then constructs a nearly orthogonal full-rank design that approaches the ideal-model MSE under practical phase shifts.

  • B. Proposed Solutions: Relaxing the coupled-phase constraint yields an idealized problem in which transmission and reflection phase shifts can be adjusted independently.This relaxed problem is used to derive design insights.
  • B. Proposed Solutions: The ideal solution requires an orthogonal V, non-zero pilot symbols, and identical energy-splitting ratio β_m^t = 0.5.Orthogonality attains the lower MSE bound, while non-zero unit-modulus pilots support the equality conditions.
  • B. Proposed Solutions: An orthogonal matrix D_2M+2, such as a DFT or Hadamard matrix, supplies the pilot sequences and training patterns for the ideal design.The pilots are selected from the first and (M + 2)-th columns of D_2M+2.
  • B. Proposed Solutions: Substituting τ = 2M + 2 and β_m^k = 0.5 gives the ES channel-estimation MSE used as an ideal-model performance upper bound.The bound is used to evaluate the impact of practical phase shifts.
  • B. Proposed Solutions: Because coupled phase shifts make the exact ES optimization difficult, the practical design targets a high-quality suboptimal solution with nearly orthogonal V.The construction preserves orthogonality in the relevant pilot-pattern matrix while satisfying the coupled-phase constraint.
  • B. Proposed Solutions: The proposed practical design makes all V columns orthogonal except one, so its MSE is expected to approach the ideal phase-shift performance.For a DFT-based D_2M+2, the phase construction satisfies the coupled-phase condition.

C. Discussion

TS and ES require the same minimum channel-estimation overhead, but ES produces approximately twice the channel-estimation error because energy splitting reduces effective uplink signal strength.

  • 2M + 2 is the minimum channel-estimation overhead for both TS and ES.
  • ES has approximately twice the channel-estimation error of TS.Energy splitting sends part of the uplink signal away from the BS, reducing effective signal strength during estimation.

V. NUMERICAL RESULTS

Numerical results compare the proposed TS and ES estimators with ON/OFF and two-phase benchmarks across energy-splitting ratios, transmit power, and sub-surface counts. TS achieves the smallest NMSE, while ES performance reflects trade-offs from energy splitting, error propagation, and training overhead.

  • Energy splitting ratio: At βt = 0.5, the minimum NMSE of the T and R users is achieved, while ES NMSE is approximately twice TS NMSE.Varying βt creates a trade-off between the channel-estimation accuracy of the T and R users; the ES gap is attributed to uplink power leakage.
  • Transmit power: NMSE decreases as total transmit power increases for all schemes, with TS yielding the smallest NMSE.
  • Benchmark comparison: The ON/OFF scheme has much larger channel-estimation error because the surface aperture is not fully utilized during estimation.
  • Benchmark comparison: The ES two-phase benchmark performs worse than the proposed ES scheme because first-phase direct-link errors propagate into second-phase cascaded-channel estimation.
  • Phase-shift model: The proposed practical-phase-shift ES scheme achieves close NMSE performance to its ideal-phase-shift counterpart.This supports the effectiveness of the proposed near-orthogonal training pattern design.
  • Sub-surface count: ON/OFF NMSE increases with the number of sub-surfaces M, whereas other schemes remain constant.Larger M also increases training overhead and shortens data-transmission time, creating an achievable-rate versus estimation-overhead trade-off.

VI. CONCLUSION

The paper develops efficient TS and ES channel-estimation schemes for STAR-RIS-assisted two-user communication. TS uses optimal separate-user training, while ES jointly optimizes pilots, energy splitting, and training patterns; numerically, TS is more cost-effective for uplink estimation.

  • The proposed TS scheme uses optimal training patterns to separately estimate the channels of the two users.
  • The proposed ES scheme jointly optimizes pilot sequences, energy splitting ratio, and training patterns under the coupled phase-shift model.It achieves near-optimal MSE performance.
  • Numerical results show that TS is more cost-effective than ES for uplink channel estimation.
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