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An Overview of Signal Processing Techniques for RIS/IRS-aided Wireless Systems

Cunhua Pan, Gui Zhou, Kangda Zhi, Sheng Hong, Tuo Wu, Yijin Pan, Hong Ren, Marco Di Renzo, A. Lee Swindlehurst, Rui Zhang, Angela Yingjun Zhang

arXiv:2112.05989v2eess.SP

TL;DR

RIS/IRS research addresses the limited ability of transmitter- and receiver-side schemes to control an impairing wireless environment. This paper systematically surveys signal-processing techniques for RIS/IRS-aided channel estimation, transmission design, and radio localization. The overview identifies channel-model, CSI, optimization, and implementation considerations, including estimation limitations and future research directions.

  • Problem

    Wireless propagation is treated as an uncontrollable source of signal degradation, while endpoint-only processing has limited ability to improve performance; RIS/IRS therefore requires effective signal processing.

  • Method

    The paper systematically surveys RIS/IRS signal-processing research covering channel estimation, transmission design, radio localization, optimization techniques, and different CSI-availability regimes.

  • Results

    The overview organizes channel-estimation work by unstructured or structured channels, transmission design by CSI availability and optimization, and localization by far-field or near-field models.

  • Takeaways & Limitations

    RIS/IRS signal processing can exploit tunable reflections for wireless-environment control, while practical designs must account for training overhead, channel-estimation assumptions, and CSI availability.

Abstract

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In the past as well as present wireless communication systems, the wireless propagation environment is regarded as an uncontrollable black box that impairs the received signal quality, and its negative impacts are compensated for by relying on the design of various sophisticated transmission/reception schemes. However, the improvements through applying such schemes operating at two endpoints (i.e., transmitter and receiver) only are limited even after five generations of wireless systems. Reconfigurable intelligent surface (RIS) or intelligent reflecting surface (IRS) have emerged as a new and revolutionary technology that can configure the wireless environment in a favorable manner by properly tuning the phase shifts of a large number of quasi passive and low-cost reflecting elements, thus standing out as a promising candidate technology for the next-/sixth-generation (6G) wireless system. However, to reap the performance benefits promised by RIS/IRS, efficient signal processing techniques are crucial, for a variety of purposes such as channel estimation, transmission design, radio localization, and so on. In this paper, we provide a comprehensive overview of recent advances on RIS/IRS-aided wireless systems from the signal processing perspective. We also highlight promising research directions that are worthy of investigation in the future.

I. INTRODUCTION

RIS/IRS technology aims to make wireless propagation configurable through tunable reflecting elements, addressing limits of endpoint-only signal processing. This overview organizes signal-processing advances in channel estimation, transmission design, and radio localization, while identifying practical estimation and training challenges.

  • I. INTRODUCTION: 6G targets substantially higher data rates, reliability, latency, spectrum and energy efficiency than 5G, but existing physical-layer techniques face important limitations.The cited passage gives expected 6G energy-efficiency gains of 10-100 times and spectrum-efficiency gains of 5 times over 5G.
  • I. INTRODUCTION: RIS/IRS uses many quasi-passive, low-cost reflecting elements to tune signal phase and amplitude, enabling constructive combining or destructive interference control.These operations can enhance desired-user power and mitigate multiuser interference or signal leakage.
  • I. INTRODUCTION: The paper systematically surveys RIS/IRS signal processing for channel estimation, transmission design, and radio localization across channel structures, CSI availability, and propagation regions.Its channel-estimation coverage distinguishes unstructured and structured channels; transmission design is organized by optimization method and instantaneous, two-timescale, or long-term CSI; localization distinguishes far-field and near-field models.
  • I. INTRODUCTION: For single-user unstructured channels, LMMSE-DFT provides the best reported MSE accuracy, whereas LS-on-off performs worst; LMMSE performance improves as spatial correlation increases.The LS methods generally do not exploit prior spatial-correlation knowledge, while the LMMSE-DFT method does.

B. Structured Channel Models

Structured channel models characterize RIS-aided links through sparse multipath components, steering vectors, spatial frequencies, and path gains. These models support channel estimation by representing channels with a relatively small number of geometric parameters.

  • B. Structured Channel Models: Saleh–Valenzuela models characterize mmWave and THz RIS channels through sparse multipath scattering and few channel parameters.The RIS-BS and user-RIS links are represented using path gains and array-response steering vectors.
  • B. Structured Channel Models: The RIS-BS channel uses a ULA at the base station and a UPA at the RIS, with steering vectors indexed by spatial frequencies.The RIS spatial-frequency vector is two-dimensional, while the BS uses an angle-of-arrival spatial-frequency vector.
  • B. Structured Channel Models: RIS steering vectors encode elevation and azimuth angles through horizontal and vertical array responses determined by antenna spacing and carrier wavelength.The spatial frequencies are functions of the departure angles, antenna spacing, and carrier wavelength.
  • B. Structured Channel Models: The user-RIS link has an analogous sparse structure, with path gains and steering vectors indexed by the paths’ spatial-frequency vectors.This provides the geometric representation needed for structured channel estimation.

1) Single-user case:

Single-user structured channel estimation reformulates cascaded-channel recovery as angle-of-arrival estimation or sparse recovery. One-stage and two-stage methods exploit geometric structure, with two-stage estimation achieving lower NMSE but remaining affected by on-grid angle mismatch.

  • 1) Single-user case:: Structured channel estimation reconstructs channels by estimating a small number of path angles and gains instead of all channel coefficients.This geometric approach is motivated by the sparse multipath structure of high-frequency channels.
  • 1) Single-user case:: One-stage estimation formulates cascaded-channel recovery as an AoA estimation problem and can use DML, MUSIC, ESPRIT, or compressed-sensing algorithms.The received pilot model is mapped to a standard AoA estimation problem before estimating channel gains.
  • 1) Single-user case:: Compressed sensing uses a sparse cascaded-gain vector and an overcomplete dictionary to recover the cascaded channel from pilot measurements.The l_1 norm enforces sparsity, while OMP and ADMM are example solvers.
  • 1) Single-user case:: The large dictionary size makes one-stage compressed sensing computationally burdensome, motivating more tractable estimation methods.With 100 grids per spatial-frequency dimension, the cited dictionary can reach 10^10 columns.
  • 1) Single-user case:: Two-stage estimation first estimates BS AoAs, then estimates cascaded spatial frequencies and gains after removing the estimated BS angles.The second stage can exploit correlations to reduce the number of AoA problems to one LRU-dimensional problem and LBR −1 one-dimensional problems.
  • 1) Single-user case:: The two-stage method outperforms the one-stage method in NMSE because grouping cascaded paths reduces power leakage among multipath components.Both methods remain separated from the CRB because OMP estimates on-grid angles while actual angles are continuous.

2) Multi-user case:

Multi-user structured channel estimation reduces training and computation by exploiting common RIS-BS channels, shared angular responses, and row- or column-block sparsity across users. Joint sparse recovery and geometric channel reuse provide alternative ways to estimate multiple users’ cascaded channels.

  • 2) Multi-user case:: All users share the RIS-BS channel, enabling common structure to reduce pilot overhead and computational complexity.The shared channel underlies both joint sparse recovery and geometric multi-user estimation methods.
  • 2) Multi-user case:: Double-sparse estimation exploits common column-block sparsity from shared BS AoAs and common row-block sparsity from the RIS scaling property.The resulting joint sparse matrix recovery problem is solved with an iterative reweighted algorithm.
  • 2) Multi-user case:: The double-sparse multi-user method requires pilot overhead T ≥ K⌈M/(LBRLRU)⌉.Its formulation jointly estimates the common cascaded structure and user-dependent quantities.
  • 2) Multi-user case:: A geometric method estimates user 1’s cascaded-channel parameters, constructs a common channel representation, and then estimates remaining users’ channels.For each remaining user, the unknown vector is estimated through a standard AoA model.
  • 2) Multi-user case:: Pilot-overhead comparisons summarize how structured multi-user algorithms relate training requirements to the number of antennas and dictionary dimensions.The overview substitutes GB = 4N and GR = 4M to give more intuitive antenna-based relationships.

III. TRANSMISSION DESIGN

RIS-aided transmission design jointly optimizes BS beamforming and RIS reflection coefficients for objectives such as spectral efficiency, energy efficiency, power consumption, error probability, and delay. These problems generally involve coupled variables, phase-shift constraints, and continuous or discrete reflection coefficients.

  • Transmission design: BS beamforming vectors and RIS reflection coefficients are jointly optimized for rate, energy, reliability, and latency objectives.The design can maximize sum spectral or energy efficiency and minimize energy consumption, symbol-error probability, or transmission delay.
  • System model: The transmitted signal is formed from user-specific BS beamforming vectors, while the received signal depends on direct and RIS-reflected paths.The model defines user symbols, BS beamformers, the RIS reflection matrix, and the resulting SINR.
  • System model: The cascaded RIS channel together with the direct channel is sufficient for designing BS transmission and RIS reflection.User data rate is expressed as Rk = log2(1 + SINRk).
  • Optimization formulation: Most transmission-design problems optimize an objective over beamforming and reflection variables subject to performance constraints and phase-shift feasibility sets.Phase shifts may be continuous or discrete, and the formulation can also constrain reflection amplitudes.
  • Organization: Transmission-design research is organized around optimization techniques and the level of channel-state information available.These two perspectives structure the overview of existing contributions.

A. Optimization Techniques

RIS phase-shift optimization is difficult because unit-modulus or discrete constraints make the problems non-convex or NP-hard, and phase shifts are coupled with beamforming. The surveyed algorithms trade solution quality, flexibility, and computational cost.

  • Optimization challenges: RIS transmission optimization is non-convex or NP-hard because of unit-modulus or discrete phase constraints and coupling between phase shifts and beamforming.Consequently, most works seek efficient locally optimal solutions rather than globally optimal ones.
  • Continuous phase shifts: Continuous-phase methods include relaxation and projection, semidefinite relaxation, majorization-minimization, manifold optimization, element-wise BCD, rank-one equivalents, and ADMM.These methods handle unit-modulus constraints through relaxation, iterative surrogates, manifold updates, coordinate optimization, rank-one enforcement, or variable splitting.
  • Continuous phase shifts: Majorization-minimization replaces a difficult objective with tractable surrogate subproblems solved iteratively under the phase-shift constraints.The surrogate is constructed to support convergence of the resulting solution sequence.
  • Continuous phase shifts: Manifold optimization treats unit-modulus phase vectors as points on a product of complex circles and updates them using projected Riemannian gradients and retraction.The procedure alternates gradient computation, tangent-space projection, update, and retraction until convergence.
  • Continuous phase shifts: Element-wise BCD optimizes one reflection coefficient at a time, but its complexity may become high when the number of reflecting elements is large.Each coefficient is optimized while the others remain fixed.

B. Various Levels of CSI Availability

RIS transmission designs differ by CSI availability: instantaneous, two-timescale, or fully long-term CSI. Two-timescale designs seek a balance between performance and training overhead by combining instantaneous effective-channel adaptation with long-term RIS configuration.

  • CSI availability: RIS transmission designs are classified into instantaneous-CSI, two-timescale-CSI, and fully long-term-CSI schemes.The categories differ in the channel information used to configure BS beamforming and RIS phase shifts.
  • Instantaneous CSI: Instantaneous-CSI designs require estimating cascaded and direct channels in every coherence block, with training overhead often proportional to the number of RIS elements.Large RISs can therefore leave few or no time slots for data transmission.
  • Two-timescale CSI: Two-timescale designs use instantaneous effective channels for BS active beamforming and long-term CSI for RIS phase shifts.Only the instantaneous effective channel of each user is estimated per coherence block, making training overhead equal to the number of users.
  • Two-timescale CSI: Because long-term CSI remains invariant across many coherence blocks, two-timescale designs update RIS phase shifts more slowly and reduce computational burden and feedback overhead.The RIS configuration responds to long-term channel statistics rather than every fast-fading variation.
  • Learning-based design: Deep deterministic policy gradient can provide almost the same performance as existing methods with low training overhead after offline training on generated instantaneous-CSI samples.The samples are generated from long-term CSI and the channel distribution for subsequent coherence blocks.
  • Performance tradeoffs: Accounting for pilot overhead, instantaneous-CSI average rate first increases and then decreases with RIS size, while fully long-term CSI has the lowest overhead but relatively low achievable rate.The two-timescale scheme offers good performance while maintaining low pilot overhead.

IV. RIS-AIDED RADIO LOCALIZATION

RIS-aided radio localization uses reconfigurable surfaces to support positioning in challenging environments, including blocked links and near-field settings. Existing work spans performance analysis, algorithm development, and communication-localization integration across far-field and near-field channel models.

  • Localization motivation: Radio localization estimates agent-node positions using radio signals exchanged with known anchor nodes such as base stations or access points.It provides an alternative for obtaining location information in GPS-denied environments.
  • Localization motivation: Positioning accuracy improved from tens of meters in 3G to centimeters in 5G millimeter-wave systems, alongside rising demands from smart factories, assisted driving, and augmented reality.The passage frames localization as increasingly important for emerging applications.
  • RIS-aided localization: RISs can provide low-cost, energy-efficient, high-precision positioning and can cooperate with existing anchor nodes.An RIS can establish a virtual line-of-sight link when the direct line-of-sight path is blocked.
  • Research directions: Current RIS-aided localization research mainly addresses performance analysis, algorithm development, and the interplay between communication and localization.Reported analyses use tools such as the Fisher information matrix and Cramér–Rao bound.
  • Channel conditions: The surveyed localization methods consider both far-field and near-field channel models.Near-field work includes codebook design for extremely large-scale RIS beam training and studies effects of transmitted-signal characteristics.

1) System Model:

The localization system models a BS, mobile user, and multiple RISs in 3D, combining direct and RIS-reflected channels. Pilot transmission produces received signals whose propagation, angular, and channel parameters support localization.

  • The system contains a BS ULA, a mobile-user ULA, and K−1 RISs with square UPAs of L^2 reflecting elements.
  • The overall channel combines the direct BS–MU link with the reflected channels from all RISs.The analysis considers line-of-sight paths and represents each RIS through a reflection coefficient matrix and array responses.
  • The model uses antenna and RIS array-response vectors determined by AoAs, AoDs, antenna spacing, and RIS incidence and departure angles.
  • Pilot signals with bandwidth B and duration T_o are transmitted using a beamforming matrix F, producing received vector y(t) at the MU.The number of pilots satisfies M_t ≪ N_t.
  • The received signal includes direct-path and RIS-path propagation delays, called TOAs, together with Gaussian noise of power spectral density N_0/2.

2) Two-Step Localization Scheme:

The localization procedure first estimates channel-related measurements and then jointly solves their nonlinear geometric equations for the user’s position and orientation. It combines time, angle, and optionally distance information using established localization algorithms.

  • Two-Step Localization Scheme: The first step estimates channel gains, angles, and time delays from the received signal using LS, MUSIC or ESPRIT, and pilot-signal processing.
  • Distance-Related Measurements: ToA and TDoA measurements provide path lengths or distance differences linked to the MU position through propagation delays.
  • Angle-Related Measurements: AoA and AoD measurements at the BS, MU, and RIS are related to the MU position, while some angles can be computed from known BS and RIS coordinates.
  • Channel-Gain Measurements: Channel gains are excluded from the numerical results because shadowing makes distance extraction from gains potentially inaccurate.
  • Two-Step Localization Scheme: The second step maps the estimated measurements to the MU position and rotation angle through multi-angulation, multi-lateration, or their combination.
  • Solution Algorithms: The resulting equations are nonlinear and error-affected, so Chan and Taylor-series algorithms are used to obtain the position estimate.

3) Position Error Bound (PEB) and Rotation Error Bound (REB) Analysis:

The analysis derives position and rotation error bounds by constructing a Fisher information matrix for channel parameters and transforming it to location parameters. Simulations compare practical estimators with the resulting CRB benchmark.

  • PEB and REB Analysis: The FIM is constructed from ToA, AoA, AoD, and complex channel-gain parameters to analyze position and orientation estimation.
  • PEB and REB Analysis: A transformation matrix maps the FIM from channel parameters to the MU’s position and orientation parameters.
  • PEB and REB Analysis: The CRB is obtained by inverting the transformed FIM, with PEB and REB extracted from specified diagonal and submatrix terms.
  • Simulation Results: Taylor’s and Chan’s algorithms achieve almost the same performance with negligible loss relative to the CRB in the RIS case study.The comparison uses position-estimation RMSE based on TDoA measurements.

B. Near-Field Localization Techniques

Large RIS apertures and high-frequency operation can invalidate the far-field planar-wave approximation by increasing the Fraunhofer distance. Near-field localization therefore requires models that account for spherical wavefront curvature.

  • Near-Field Localization Techniques: An XL-RIS can become large enough that spherical wavefront curvature cannot be ignored at nearby observation points.
  • Far-Field Boundary: The RIS far field consists of observation distances greater than the Fraunhofer distance, which depends on the RIS aperture L and wavelength λ.
  • Far-Field Boundary: The conventional far-field definition corresponds to a maximum phase error of π/8 across the RIS aperture.
  • Numerical Example: For a 100×100 UPA at 200 GHz with 0.75 mm half-wavelength spacing, the aperture is approximately 10.6 cm and the Fraunhofer distance is 7.5 m.
  • Implications: Because users may lie within this near-field region indoors, spherical-wave effects cannot be ignored, and simulations indicate the issue may also arise outdoors.

1) Near-Field Channel Model:

The near-field channel model represents propagation using spherical wavefronts and three-dimensional source or scatterer locations, rather than only angular responses. It incorporates path distances, steering vectors, and cascaded channel coefficients into localization-oriented signal models.

  • Near-field steering responses are parameterized by the 3D locations of signal sources instead of only AoDs and AoAs.
  • The uplink model considers a single-antenna MU, an Mx × Mz RIS UPA, and an N-element BS ULA.
  • The channel model represents multiple propagation paths through scatterer-associated steering vectors and complex path gains, with the MU as the LoS path location r0.
  • Each RIS steering response depends on the distance from a scatterer to the corresponding RIS element.
  • For the BS–RIS LoS channel, spherical propagation makes each antenna-to-RIS-element path length determine the received-signal phase, under equal path loss α.
  • The localization formulation collects source locations and cascaded channel fading coefficients in η and uses a received-signal likelihood based on squared residual error.

2) Near-Field Localization Scheme:

The proposed near-field localization scheme estimates the MU and scatterer positions in two stages. It first obtains coarse locations and then iteratively refines them using finer searches, with performance evaluated through localization MSE.

  • The two-stage scheme first derives coarse MU and scatterer positions, then refines them through iterative methods such as two-dimensional search.
  • Stage 1 estimates the MU location from the strongest received LoS path because scatterer-reflected paths are much weaker.
  • Without prior source-location information, the objective is evaluated over grid locations, using denser sampling near the array to reduce complexity.
  • After estimating locations, the method obtains corresponding channel gains by projection and estimates scatterer locations.
  • Stage 2 refines MU and scatterer positions with a finer grid while holding other location estimates fixed, requiring several iterations for high-resolution estimates.
  • Increasing SNR improves localization accuracy, whereas more scatterers degrade MSE because of scattered energy and feedback estimation-error propagation.

V. FUTURE DIRECTIONS

The paper identifies future signal-processing challenges involving mobility, near-field propagation, active RIS architectures, and multiple RISs. Its conclusion emphasizes broad coverage of estimation, transmission design, localization, and optimization methods, including CSI-timescale choices.

  • A. Mobility: Mobility creates rapidly time-varying channels that require faster channel tracking and more frequent RIS phase-shift configuration while avoiding prohibitive overhead.
  • B. Near-Field Channel: Near-field RIS models require accurate channel characterization because spherical wavefronts alter scaling laws and may invalidate far-field angle-domain sparsity assumptions.
  • C. Active RIS: Active RISs can amplify reflected-signal magnitudes but require additional power and noise-aware channel estimation, leaving beamforming, deployment, and energy trade-offs open.
  • D. Double/multi-RIS: Double- or multi-RIS systems may route signals around blockages and obtain inter-RIS gains, but their coupled links demand highly accurate CSI and more channel coefficients.
  • VI. CONCLUSIONS: The survey reviews channel estimation, transmission design, radio localization, optimization techniques, and fully instantaneous, two-timescale, and fully long-term CSI settings.
  • VI. CONCLUSIONS: Simulation results identify two-timescale CSI as promising when pilot overhead is taken into account.
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