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Adaptive Beamforming Design for mmWave RIS-Aided Joint Localization and Communication
Jiguang He, Henk Wymeersch, Tachporn Sanguanpuak, Olli Silvén, Markku Juntti
TL;DR
The paper addresses RIS phase optimization for joint positioning and high-rate communication in mmWave MIMO systems, including obstructed-LoS settings. It proposes adaptive hierarchical codebooks with MS feedback and simultaneous refinement of the MS combiner. Simulations report improved positioning and data-rate performance over random phase design, with convergence toward exhaustive search even at low SNR.
Problem
RIS-aided mmWave MIMO systems need optimized discrete RIS phase values for accurate positioning and high-data-rate transmission, while prior designs require channel information or active elements and computation.
Method
The paper adaptively selects RIS analog phase shifters and MS combiners from hierarchical codebooks using limited MS feedback and sequential beam refinement.
Results
The proposed scheme improves positioning accuracy and data rate over random phase design and converges toward exhaustive-search performance even in the low-SNR regime.
Takeaways & Limitations
The design provides feasible RIS-aided positioning and communication without active RIS elements or complicated baseband processing, while using much less training overhead than exhaustive search.
Abstract
from arXiv · showhide
The concept of reconfigurable intelligent surface (RIS) has been proposed to change the propagation of electromagnetic waves, e.g., reflection, diffraction, and refraction. To accomplish this goal, the phase values of the discrete RIS units need to be optimized. In this paper, we consider RIS-aided millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems for both accurate positioning and high data-rate transmission. We propose an adaptive phase shifter design based on hierarchical codebooks and feedback from the mobile station (MS). The benefit of the scheme lies in that the RIS does not require deployment of any active sensors and baseband processing units. During the update process of phase shifters, the combining vector at the MS is also sequentially refined. Simulation results show the performance improvement of the proposed algorithm over the random design scheme, in terms of both positioning accuracy and data rate. Moreover, the performance converges to exhaustive search scheme even in the low signal-to-noise ratio regime.
I. INTRODUCTION
The paper develops a RIS-aided mmWave MIMO system for localization, orientation estimation, and high-data-rate transmission when the line of sight is blocked. It uses limited feedback to adapt RIS phase shifters and MS combiners without requiring active RIS elements or baseband processing.
- Motivation: RISs passively control electromagnetic waves and can steer incident radio waves toward different directions than conventional reflecting surfaces.The paper motivates RISs as a way to improve energy and spectrum efficiency without sophisticated baseband units or RF chains.
- Motivation: Prior RIS positioning work achieved improved positioning and orientation error bounds under perfect channel state information, but phase-shifter design requires channel knowledge.Earlier approaches based on compressive sensing and deep learning also involve active RIS elements and non-negligible computational complexity.
- System objective: The proposed system jointly localizes and estimates the orientation of an MS while enabling high-data-rate transmission through a RIS when the LoS path is obstructed.It uses mmWave MIMO with OFDM subcarriers, a BS, an MS, and a RIS in a 2D ULA-based setting.
- Channel model: The RIS-aided channel consists of tandem BS–RIS and RIS–MS reflection links, with the RIS phase-control matrix applied independently of subcarrier index.The model uses array-response vectors, path delays, path-loss coefficients, and a constant-modulus diagonal RIS matrix.
- Channel model: Known BS–RIS geometry supports BS beam steering, whereas unknown RIS–MS parameters must be estimated for MS localization, orientation estimation, and MS combiner design.The RIS phase design is therefore the central unresolved design problem in the system model.
III. HIERARCHICAL CODEBOOK DESIGN
The hierarchical codebook design creates multi-resolution analog or hybrid codewords whose beam coverage narrows and resolution increases across levels. Codewords are obtained by least-squares fitting, normalized, and adapted to hardware constraints.
- Architecture-specific codebooks: RIS codebooks contain analog codewords, whereas MS codebooks contain hybrid analog-digital codewords because the two devices have different architectures.The resulting hierarchical codebooks support phase-shifter control at the RIS and combining at the MS.
- Codebook construction: The design uses three steps: solve A H C_s = G_s by least squares, normalize each column of C_s, and enforce the hardware constraint.These steps transform ideal codewords into implementable codebooks.
- Multi-resolution structure: Each level-s codebook contains K^s codewords whose beam patterns cover progressively narrower angular ranges with increasing resolution.The target matrix G_s is constructed through circular shifts so the beam pattern is approximately constant over each level’s angular range.
A. RIS
RIS codewords must satisfy constant-modulus hardware constraints, so the unconstrained codebook is converted through a constrained optimization procedure. Gradient projection alternates descent with projection onto the constant-modulus space.
- RIS hardware constraint: Each RIS codeword element must have constant modulus, |[C̄_RIS,s]m,n| = 1/√N_R, for every codeword entry.This constraint reflects the RIS’s purely analog phase-shifter architecture.
- Constrained design: The constrained RIS codebook is obtained by solving an optimization problem column by column.The optimization converts the least-squares codewords into codewords compatible with the RIS hardware.
- Constrained design: Gradient projection addresses the constraint through gradient descent followed by projection onto the constant-modulus space.This procedure is identified as a potential algorithm for the RIS codebook optimization.
B. MS
The MS uses a hybrid architecture in which multiple RF chains enable simultaneous observations, requiring matrix factorization to realize hierarchical combiners. The factorization is solved through alternating minimization with phase extraction.
- B. MS: The MS uses N_RF RF chains to access up to N_RF simultaneous observations and combiners.This hardware differs from the purely analog RIS architecture.
- B. MS: The MS codebook is obtained by factorizing each group of N_RF columns into RF and baseband combiner components.The factorization minimizes the approximation error for each group of columns.
- B. MS: The MS factorization is solved by PE-AltMin, which alternates between optimizing one variable while fixing the other.Iterations continue until a specified stopping criterion is met.
- B. MS: After the three codebook-design steps, each column becomes an individual codeword for the RIS or MS level-s codebook.The construction applies for s = 1, · · ·, S.
A. Proposed Protocol
The proposed protocol adaptively selects RIS phase-shifter and MS combining codewords from multiresolution hierarchical codebooks. MS feedback identifies promising RIS beams, which are refined jointly across stages.
- A. Proposed Protocol: The RIS phase vector and MS combining matrix are selected adaptively from multiresolution hierarchical codebooks.Both codebook families have K^s codewords at level s.
- A. Proposed Protocol: At each stage, the protocol evaluates K selected MS codewords against K selected RIS codewords and forms a K^2-entry power matrix.The largest entry determines the selected row and column indices.
- A. Proposed Protocol: The MS feeds the selected RIS-codeword index back to the RIS controller, while both sides choose associated candidates for the next stage.The RIS uses the feedback to select K associated codewords, and the MS refines its combiner choices from the next-level codebook.
- A. Proposed Protocol: The number of consumed time slots depends on the hierarchical levels, MS RF-chain count, and initial codebook size.N_RF combining beams can be used simultaneously during phase-shifter design.
B. Positioning and Communication
The positioning procedure estimates channel parameters from the final selected codewords and then uses geometry to infer the MS position and orientation. The system evaluates positioning error, orientation error, and achievable data rate.
- B. Positioning and Communication: The selected final-stage RIS and MS codewords and their received signals across subcarriers provide estimates of channel parameters.The estimated parameters include θ_R,M, φ_R,M, and τ_R,M.
- B. Positioning and Communication: The MS position is estimated geometrically from the channel-parameter estimates.The formulation uses the known BS and RIS centers and the speed of light.
- B. Positioning and Communication: The analysis assumes far-field communications and imposes additional constraints on the number of RIS elements.This assumption limits the system model's operating setting.
- B. Positioning and Communication: Performance is evaluated using positioning MSE, orientation MSE, and achievable data rate.These metrics cover localization, orientation estimation, and communication performance.
C. Asymptotic Performance Analysis
At higher SNR, estimation performance saturates because the final hierarchical codebooks have finite resolution. The analysis then uses the selected codewords to estimate channel parameters and derive mean-square-error lower bounds.
- C. Asymptotic Performance Analysis: Estimation performance saturates at high SNR because the RIS and MS level-S codebooks have finite resolution.The saturation occurs after the correct analog phase-shifter and combiner codewords are likely selected.
- C. Asymptotic Performance Analysis: The asymptotic procedure selects the final-codebook pair with the highest sum power before estimating the channel parameters.The selected codewords are CRIS,S and CMS,S.
- C. Asymptotic Performance Analysis: Fig. 4 compares channel-parameter estimation for hierarchical codebooks, exhaustive search, and random phase.The figure presents the three design strategies as distinct comparison cases.
V. SIMULATION RESULTS
The simulations use a fixed RIS-aided mmWave MIMO setup and compare random-phase and exhaustive-search benchmarks against hierarchical codebooks.
- Simulation Parameters: The setup places the BS at (0, 0), RIS at (40, 60), and MS at (60, 45) meters, with N_R = 16 RIS elements.The carrier frequency is 60 GHz, bandwidth is 100 MHz, and the path-loss exponent is 2.08.
- Benchmarks: The benchmarks are random phase with a level-S MS codebook and exhaustive search using level-S codebooks at both the MS and RIS.The hierarchical codebooks use S = 6 levels and branching factor K = 2.
A. Channel Parameter Estimation
Hierarchical codebooks achieve performance close to exhaustive search while substantially reducing training overhead, whereas random phase performs worse.
- Training Overhead: The proposed scheme uses 12 time slots, compared with 2048 for exhaustive search and 32 for random phase with a level-S codebook.Exhaustive search provides the strongest benchmark but requires significantly more training slots.
- Estimation Performance: The proposed performance converges to exhaustive search even in the low-SNR regime.The theoretical lower bound aligns with exhaustive search in the reported simulations.
- Estimation Performance: The estimated parameter θ_R,M performs worse than φ_R,M because their hierarchical codebooks differ.The MS combiner has a better beam pattern than the RIS combiner because the MS uses multiple RF chains.
B. PE and OE
Hierarchical phase-shifter design supports positioning and communication in the RIS-aided mmWave MIMO system, approaching exhaustive-search performance with much lower training overhead.
- PE and OE: Exhaustive search outperforms the proposed positioning scheme but incurs significant overhead, while random phase performs worst for PE and OE.The results indicate that RIS-unit phase selection is important for positioning.
- Achievable Rate: The achievable rate of the proposed scheme is comparable to exhaustive search for SNR in [−10, ∞).Exhaustive search is close to the optimal combiner and phase-shifter scheme, while random phase performs worst.
- Conclusion: The proposed design uses no active RIS elements or complicated baseband processing and achieves comparable performance to exhaustive search in the low-SNR regime.The evaluation covers both positioning and data transmission and compares against random phase and exhaustive search.