Robust RIS Codebook Index Assignment

• The topic defines robust RIS codebook index assignment as designing finite, hardware-feasible configuration sets that reliably map control signals to distinct response patterns under practical impairments.
• It emphasizes response-domain separability and low-loss adjacency to mitigate index errors caused by quantization, feedback channel errors, and near-field model mismatches.
• Robust design strategies integrate offline environment-aware codebook generation with online index assignment and beam training to enhance system performance and adaptability.

Robust RIS codebook index assignment is the design of finite, hardware-feasible reconfigurable intelligent surface (RIS) or fluid RIS (FRIS) configuration sets together with the rules that map bits, locations, channel observations, or control messages to codeword indices in a manner that remains reliable under practical impairments. In the recent literature, the problem appears in several closely related forms: FRIS-assisted index modulation, where information bits select spatial configurations; finite RIS reflection-pattern control, where the system selects one index from a predesigned codebook; near-field XL-RIS beam training, where an index corresponds to a geometry-dependent beam; and control-link-robust indexing, where binary labels themselves are optimized against feedback errors. Across these formulations, robustness is tied to response-domain distinguishability, low-loss codeword adjacency under bit flips, environment awareness, near-field model consistency, and explicit accommodation of quantization, coupling, calibration errors, and training overhead (Zhu et al., 21 May 2026, Wu et al., 24 Jul 2025, An et al., 2022).

1. Formal definition and index semantics

In codebook-based RIS control, the surface does not optimize arbitrary continuous phases online; instead it operates on a finite codebook of feasible states. One generic representation is a reflection-pattern codebook

$$\mathcal{C}=\{\boldsymbol{\Theta}_1,\boldsymbol{\Theta}_2,\ldots,\boldsymbol{\Theta}_Q\},$$

where each entry is a legitimate RIS reflection pattern extracted from a universal solution set under hardware constraints such as discrete phase shifts, limited tuning range, mutual coupling or correlation, component aging, and nonideal element behavior. The operational problem is then to select, assign, or learn the appropriate index rather than to solve a full passive beamforming problem online (An et al., 2022).

The same abstraction appears in FRIS-assisted index modulation. A controller stores a feasible configuration set $\mathcal S_{\rm cand}$ and selects a codebook

$\mathcal C = \{\mathcal S_1,\ldots,\mathcal S_K\}.$

The chosen configuration index conveys $\log_2 K$ bits per reconfiguration interval, and the received signal under configuration $\mathcal S_i$ is modeled as

$$\mathbf{y} = \mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)} x + \mathbf{n}.$$

Here the index is meaningful only insofar as the induced receiver-side response is distinguishable; the codebook is therefore a set of distinguishable response patterns, not merely a set of layouts (Zhu et al., 21 May 2026).

In near-field XL-RIS beam training, the meaning of an index becomes explicitly geometric. A codeword can correspond to a sampled pair of 3D points that parameterize the near-field cascaded steering vector, so the index is a geometry index rather than an angle-only label. In environment-aware protocols for MISO and MU-MISO systems, by contrast, each codeword index corresponds to one offline-generated RIS reflection vector or matrix, and online selection proceeds by testing candidate indices through composite-channel estimation and beamforming performance (Wei et al., 2021, Jia et al., 2023, Yu et al., 2024).

2. Why robustness is needed

A central misconception rejected by recent work is that physical layout diversity alone guarantees reliable indexing. In FRIS-assisted IM, two layouts may be visually or geometrically different, yet after propagation, mutual coupling, calibration errors, and receiver observation, their induced effective responses can become very similar. The relevant distinction is therefore between layout-domain diversity and response-domain separability. If receiver responses overlap, the detector confuses indices even though the surface states are physically distinct (Zhu et al., 21 May 2026).

A second failure mode arises on the RIS control link itself. In the imperfect-control formulation, the base station sends the selected codeword index over a binary symmetric channel with independent bit-flip probability $q$. If the intended index is $i$ but the controller decodes $j\neq i$, the RIS applies $\mathbf c_j$ instead of $\mathcal S_{\rm cand}$0, causing index mismatch and SNR degradation. The paper models the relative loss as

$\mathcal S_{\rm cand}$1

so robustness requires that likely binary confusions correspond to low-loss codeword substitutions (Wu et al., 24 Jul 2025).

Near-field operation introduces a further source of brittleness. For XL-RIS, the Rayleigh distance

$\mathcal S_{\rm cand}$2

becomes large, and users often lie in the near-field region where the wavefront is spherical rather than planar. Far-field angle-only codebooks therefore mismatch the actual near-field channel model, and beam training based on far-field steering vectors suffers severe performance loss. The same concern appears in physics-aware near-field focusing, where the actual incident field on each cell is not only the direct transmitter field but

$\mathcal S_{\rm cand}$3

so mutual coupling and specular secondary reflections perturb the nominal index-to-response mapping (Wei et al., 2021, Papadopoulos et al., 19 Jan 2026).

Measurement-based studies reinforce this point experimentally. Reflection behavior depends strongly on azimuth angle, elevation angle, distance, polarization, and the number of RIS boards. Pattern-induced received-power differences can reach “around some tens of dB,” but wrong polarization can make the reflection distributions largely the same for all tested patterns, and adding a second board can change lobe counts, peak width, and overall gain. A plausible implication is that a codebook that is separable in one deployment geometry may be ambiguous in another (Hatka et al., 27 Mar 2025).

3. Robust design criteria

The most explicit robustness criterion in FRIS-assisted IM is response-domain separability. For two candidate configurations $\mathcal S_{\rm cand}$4 and $\mathcal S_{\rm cand}$5, the response distance is

$\mathcal S_{\rm cand}$6

The codebook is then selected by the max-min rule

$\mathcal S_{\rm cand}$7

which directly targets worst-case index confusability rather than raw layout count (Zhu et al., 21 May 2026).

In control-link-robust RIS indexing, the design criterion is different. Under the single-bit error approximation, only codeword pairs with Hamming distance $\mathcal S_{\rm cand}$8 dominate the expected loss, so the objective reduces to minimizing the aggregate degradation over index-adjacent pairs. This yields the rule that binary neighbors should also be small-loss neighbors in codeword space. The paper reformulates the resulting ordering problem as an open Hamiltonian-path TSP, then applies Gray labeling so adjacent positions in the optimized path differ by one bit. The same paper notes that the more general formulation is a quadratic assignment problem, but that the TSP simplification is justified when multi-bit errors are negligible (Wu et al., 24 Jul 2025).

Environment-aware codebooks adopt a statistical criterion rather than a direct distance or adjacency criterion. Offline codeword generation uses location-derived LoS structure, Rician factors, and random NLoS realizations so that the retained codewords are adapted to the propagation environment. The online index is then selected by maximizing an achievable-rate metric after composite-channel estimation. This suggests that robustness can be defined not only through pairwise separability but also through environment matching and reduced dependence on explicit cascaded-channel recovery (Jia et al., 2023, Yu et al., 2024).

Near-field XL-RIS work adds a geometric criterion. In the exhaustive near-field codebook, each column corresponds to one sampled pair of near-field coordinates, and duplicate codewords are removed. In variable-width near-field codebooks, each index is associated with a codeword region $\mathcal S_{\rm cand}$9, which may be rectangular, sector-like, T-shaped, L-shaped, or disconnected. A plausible interpretation is that robust assignment in the near field increasingly replaces angle-only indexing with region-based or geometry-based indexing (Wei et al., 2021, Zhang et al., 15 Aug 2025).

Criterion	Representative formulation	Robustness target
Response separability	Maximize minimum pairwise $\mathcal C = \{\mathcal S_1,\ldots,\mathcal S_K\}.$0	Index detection reliability
Low-loss adjacency	Minimize loss over Hamming-distance-1 pairs	Imperfect control links
Environment awareness	Offline codebook from statistical CSI	CSI error and overhead reduction
Geometry or physics consistency	Near-field or EM-consistent codewords	Model mismatch, coupling, reflections

4. Codebook construction and compilation methods

The response-aware FRIS workflow begins with a dense feasible candidate set, calibrates or estimates each candidate’s receiver-side response by simulation, measurement, or offline training, and then prunes layouts with overlapping or too-close signatures. The retained codebook must also satisfy movement or spacing constraints, feasible actuation energy, and acceptable latency and control overhead. The paper further recommends a design loop: specify mobility, coherence time, pilot budget, latency, and hardware response time; choose element-, group-, or block-level actuation granularity; calibrate response maps including propagation and coupling; construct the codebook from well-separated responses; and evaluate BER, overhead, latency, energy, and throughput (Zhu et al., 21 May 2026).

The imperfect-control paper replaces codebook pruning with index-order optimization. Its solver has three phases: a provision phase that classifies the pairwise-loss distribution and builds layered neighbor sets; a shotgun phase that samples many Hamiltonian paths using a stochastic next-hop probability; and a fuzzy concatenation phase that reinforces frequently occurring good edges while gradually reducing randomness. The worst-case complexity is proved as $\mathcal C = \{\mathcal S_1,\ldots,\mathcal S_K\}.$1, which the paper presents as substantially more scalable than exact TSP solvers for large $\mathcal C = \{\mathcal S_1,\ldots,\mathcal S_K\}.$2 (Wu et al., 24 Jul 2025).

Environment-aware codebook generation for MISO and MU-MISO systems is primarily offline. One method generates multiple virtual channels from statistical CSI and location information, designs continuous element phases by aligning reflected and direct components for each virtual realization, quantizes to the discrete phase set, and keeps generating vectors until $\mathcal C = \{\mathcal S_1,\ldots,\mathcal S_K\}.$3 diverse reflection-coefficient vectors are obtained. Another method generates $\mathcal C = \{\mathcal S_1,\ldots,\mathcal S_K\}.$4 virtual channel realizations consistent with the statistical CSI, then alternates between ZF-based power allocation and successive refinement over discrete RIS phases to produce $\mathcal C = \{\mathcal S_1,\ldots,\mathcal S_K\}.$5 (Jia et al., 2023, Yu et al., 2024).

Near-field compilation methods are more explicitly physics- or geometry-driven. MATCH initializes each target by geometric optics, refines phases under a full EM model including mutual coupling and specular reflections, performs a multi-objective NSGA-II search over focus enhancement and outer-region suppression, and finishes with local refinement before storing the resulting $\mathcal C = \{\mathcal S_1,\ldots,\mathcal S_K\}.$6 as a codebook entry. In discrete-phase XL-RIS near-field MIMO, JOCC jointly optimizes BS precoding and RIS phase shifts for each hierarchical region, whereas SOCC first fixes the BS beam and then optimizes the RIS phases; both approaches explicitly enforce discrete-phase feasibility. For arbitrary-shaped near-field coverage, the AWBCD algorithm optimizes the RIS phases offline over the target region $\mathcal C = \{\mathcal S_1,\ldots,\mathcal S_K\}.$7 and stores the resulting phase profile as the codeword (Papadopoulos et al., 19 Jan 2026, Zhang et al., 26 Aug 2025, Zhang et al., 15 Aug 2025).

5. Online index assignment, beam training, and learning

A major theme in robust RIS indexing is that online operation should evaluate end-to-end behavior of candidate codewords rather than reconstruct all constituent channels. In the survey framework, each reflection pattern is tested through uplink pilots and end-to-end composite-channel estimation, and the simplest rule is rote learning: choose the codeword that gives the best objective function. The associated control signaling overhead is only $\mathcal C = \{\mathcal S_1,\ldots,\mathcal S_K\}.$8 bits. The same framework also describes fusion learning, which weights and superimposes multiple codewords with coefficients proportional to their objective values, and supervised DNN-based selection, in which labeled performance samples train a network that maps a QoS target to a codeword index (An et al., 2022).

Environment-aware MISO and MU-MISO protocols instantiate this idea concretely. In the single-user case, the system cycles through the offline codebook, estimates the composite channel corresponding to each reflection pattern using LS or MMSE, applies MRT, computes

$\mathcal C = \{\mathcal S_1,\ldots,\mathcal S_K\}.$9

and selects

$\log_2 K$0

In the MU-MISO extension, the protocol divides training into $\log_2 K$1 blocks, estimates $\log_2 K$2 under each $\log_2 K$3, computes a ZF precoder, evaluates the resulting sum rate, and selects

$\log_2 K$4

These formulations explicitly tie robust assignment to composite-channel-based scoring rather than to full BS–RIS and RIS–user estimation (Jia et al., 2023, Yu et al., 2024).

Beam training provides a second major online mechanism. In exhaustive near-field XL-RIS training, the system applies every codeword in the near-field codebook and returns

$\log_2 K$5

Hierarchical variants reduce overhead by searching sub-codebooks level by level. In discrete-phase XL-RIS near-field MIMO, the area is partitioned into regions at each level, the beam or codeword producing the maximum received gain is selected, and the next level refines the search within the winning region. The overhead becomes $\log_2 K$6 rather than $\log_2 K$7, so the chosen index simultaneously identifies a beam and localizes the user’s dominant-path region (Wei et al., 2021, Zhang et al., 26 Aug 2025).

Physics-aware compilation changes the online problem further. Once a robust $\log_2 K$8 has been compiled offline for each focal region, real-time control reduces to mapping a user or query location to the nearest precompiled focal entry. This is still index assignment, but the index now addresses a codebook of EM-consistent focal states rather than a beam codebook derived from simplified phase laws (Papadopoulos et al., 19 Jan 2026).

6. Performance tradeoffs, empirical findings, and open problems

The literature evaluates robust RIS codebook assignment with several recurring metrics: BER or index detection error probability, pairwise response distance, effective codebook size, average relative SNR loss, achievable rate or sum rate, normalized net throughput, overhead ratio, spectral efficiency over a target region, and outage probability. These metrics formalize the underlying tradeoff: a larger raw codebook or finer actuation granularity does not automatically yield better performance if the resulting indices become harder to train, control, or separate (Zhu et al., 21 May 2026, Yu et al., 2024, Zhang et al., 15 Aug 2025).

In FRIS-assisted IM, response-aware codebook selection is reported to achieve lower BER than random FRIS-IM, layout-based FRIS-IM, and a fixed-geometry RIS-IM benchmark under equal codebook size and equal activated-element cardinality, with the gain attributed to enlarging the minimum response-domain distance. The same paper defines the normalized net spatial-index throughput

$\log_2 K$9

and shows qualitatively that element-level control offers the largest raw index space but high overhead, block-level control yields the lowest overhead but too few distinguishable states, and group-level control gives the best overhead-aware tradeoff in the example (Zhu et al., 21 May 2026).

For imperfect control links, the TSP-based assignment consistently gives the lowest average SNR loss relative to natural and random indexing, and the gap grows as feedback SNR decreases. At uniform $\mathcal S_i$0, the proposed method attains SNR loss $\mathcal S_i$1 in $\mathcal S_i$2 s, matching LKH3’s $\mathcal S_i$3 but at a much lower runtime than $\mathcal S_i$4 s, while Concorde is reported as not feasible at that scale. The paper explicitly limits this result to the single-bit error regime and identifies multi-bit confusion as future work requiring a more general QAP formulation (Wu et al., 24 Jul 2025).

Environment-aware codebooks are reported to outperform environment-agnostic or random baselines while reducing dependence on cascaded-channel estimation. In MU-MISO simulations with $\mathcal S_i$5, $\mathcal S_i$6, and $\mathcal S_i$7, the environment-aware protocol yields a sum-rate gain of about $\mathcal S_i$8 bps/Hz over the random codebook at $\mathcal S_i$9 dBm and $$\mathbf{y} = \mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)} x + \mathbf{n}.$$0 dB under perfect CSI, while effective sum rate

$$\mathbf{y} = \mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)} x + \mathbf{n}.$$1

shows that small $$\mathbf{y} = \mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)} x + \mathbf{n}.$$2 is preferable for short coherence time and larger $$\mathbf{y} = \mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)} x + \mathbf{n}.$$3 is beneficial when coherence time is longer. In the single-user environment-aware MISO setting, the scheme can outperform AO under channel estimation errors, precisely because it estimates only the composite channel and uses an offline environment-aware codebook (Yu et al., 2024, Jia et al., 2023).

Near-field and physics-aware studies show that robustness is often inseparable from model fidelity. Hierarchical near-field beam training attains about $$\mathbf{y} = \mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)} x + \mathbf{n}.$$4 of the achievable rate of exhaustive near-field training with overhead about $$\mathbf{y} = \mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)} x + \mathbf{n}.$$5 of exhaustive overhead. MATCH increases focal energy concentration from $$\mathbf{y} = \mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)} x + \mathbf{n}.$$6 at geometric-optics initialization to $$\mathbf{y} = \mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)} x + \mathbf{n}.$$7 after final refinement while reducing unexploited energy from $$\mathbf{y} = \mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)} x + \mathbf{n}.$$8 to $$\mathbf{y} = \mathbf{h}_{\mathrm{eff}(\mathcal{S}_i)} x + \mathbf{n}.$$9. Variable-width near-field codebooks for XL-RIS are reported to support arbitrary-shaped codeword regions and to be more robust to codeword-region location and area variations; the same work states that $q$0 bits approaches continuous-phase performance (Wei et al., 2021, Papadopoulos et al., 19 Jan 2026, Zhang et al., 15 Aug 2025).

Open problems remain substantial. The survey literature states that generating an appropriate codebook for diverse application scenarios and objectives remains open, and further highlights unresolved questions in learning mechanisms, performance under limited overhead, CSI-aware versus CSI-agnostic design, and hardware or channel model realism. The imperfect-control literature adds online adaptive mapping and multi-bit error handling as explicit future directions. A plausible overall conclusion is that robust RIS codebook index assignment is converging toward a common principle: indices should represent response-distinct, hardware-valid, and environment-consistent surface states, while the mapping from system state to index should be optimized with respect to the dominant impairment model rather than to geometric or combinatorial diversity alone (An et al., 2022, Wu et al., 24 Jul 2025).