Array Configuration Codebook (ACC)

Updated 9 July 2026

ACC is a codebook paradigm that predefines antenna activation patterns in XL-MIMO arrays to create structured, physically viable configurations.
It reduces combinatorial complexity by limiting the search space with a finite set of codewords, enabling efficient two-stage scanning for array-level and pixel-level optimization.
ACC supports multiple architectures (CA, USA, MoA, NA, CPA) and is tailored to different tasks like multi-user communication and localization by optimizing metrics such as sum rate and RMSE.

Searching arXiv for the provided ACC-related papers and closely related codebook literature. Array Configuration Codebook (ACC) denotes a codebook-based mechanism for configuring array operation under stringent search, hardware, and propagation constraints. In the most specific formulation, ACC is defined as a set of pre-designed array configuration codewords, where each codeword specifies the positions of activated antenna pixels in an XL-MIMO array; flexible XL-MIMO is then realized through dynamic pixel activation over this finite set rather than exhaustive exploration of all antenna subsets (Lu et al., 28 Aug 2025). Related literature also uses ACC in a broader sense as a general, adaptable codebook paradigm for analog or hybrid beamforming under constraints such as array geometry, phase quantization, and beam-sweeping resources (Ganji et al., 2019). Across these formulations, ACC serves as a structural interface between array physics, hardware feasibility, and beam or configuration training.

1. Terminological scope and conceptual foundations

The term ACC has acquired two closely related meanings in the literature. In the broad beamforming-oriented sense, it refers to a general, adaptable codebook for analog or hybrid beamforming in millimeter-wave systems, especially when array geometry, quantization, and sweeping resources constrain direct channel observation and exhaustive search (Ganji et al., 2019). In the flexible XL-MIMO sense, ACC refers specifically to a codebook of array configurations, not merely beamforming vectors: each codeword determines which antenna pixels are active, and training selects the most suitable physical array realization for the current task (Lu et al., 28 Aug 2025).

This distinction is technically significant. Conventional beam codebooks quantize steering or beamforming vectors over a fixed aperture, whereas ACC in XL-MIMO elevates the design variable to the aperture itself. The channel after activation depends on the chosen pixel positions, and the codebook therefore governs both effective aperture geometry and downstream beamforming or inference quality (Lu et al., 28 Aug 2025). A plausible implication is that ACC generalizes the classical role of a codebook: it no longer only discretizes direction, but also discretizes physically realizable array topologies.

The broader literature reinforces this interpretation. Metric-driven analog beamforming codebooks have been posed as vector quantization problems optimized for average beamforming gain, outage, or average data rate over arbitrary array shapes, including uniform linear and planar arrays (Ganji et al., 2019). Hierarchical beam-training codebooks impose full-layer coverage and tree-structured refinement to reduce search complexity while preserving angular coverage (Xiao et al., 2015). Near-field and conformal-array work further extends codebook design to distance-sensitive focusing, localized subarray activation, and full-sphere or Fresnel-region coverage (Zhang et al., 2020, Chen et al., 2022).

2. ACC as a codebook of array configurations in flexible XL-MIMO

In flexible XL-MIMO, ACC is organized as a union of architecture-specific codebooks: $\mathcal{W}^{\mathrm{ACC}} = \mathcal{W}_\mathrm{CA} \cup \mathcal{W}_\mathrm{USA} \cup \mathcal{W}_\mathrm{MoA} \cup \mathcal{W}_\mathrm{NA} \cup \mathcal{W}_\mathrm{CPA},$ where the constituent families are the compact array (CA), uniform sparse array (USA), modular array (MoA), nested array (NA), and co-prime array (CPA) (Lu et al., 28 Aug 2025). Each codeword specifies activated pixel positions, and the codebook restricts the feasible reconfigurations to physically meaningful sparse or structured apertures.

The main motivation is combinatorial complexity. The XL-MIMO formulation explicitly notes that selecting 32 active pixels out of 256 yields over $5.8 \times 10^{40}$ combinations, making exhaustive antenna selection impractical. ACC reduces this search space to a carefully designed finite set; the provided example states that, for $M=256$ and $N=32$ , an ACC can contain less than $10^4$ codewords, and the summary comparison further gives an exhaustive ACC example with fewer than 7000 candidates (Lu et al., 28 Aug 2025). This reduction is not merely computational. It imposes structural priors that preserve array patterns known to exhibit useful spatial properties.

The principal architecture families are parameterized as follows.

Architecture	Activated-position structure	Configuration parameters
CA	Consecutive half-wavelength pixels	Reference position $b$
USA	Uniform spacing $\eta d$ with $\eta \geq 2$	Sparsity level $\eta$ , reference position $b$
MoA	$5.8 \times 10^{40}$ 0 modules with intra-module CA and inter-module spacing $5.8 \times 10^{40}$ 1	Inter-module spacing $5.8 \times 10^{40}$ 2, reference position $5.8 \times 10^{40}$ 3
NA	Inner CA plus outer USA with spacing $5.8 \times 10^{40}$ 4	$5.8 \times 10^{40}$ 5, reference position $5.8 \times 10^{40}$ 6
CPA	Union of two USAs with coprime element numbers	$5.8 \times 10^{40}$ 7, reference position $5.8 \times 10^{40}$ 8

For CA, the activated positions are

$5.8 \times 10^{40}$ 9

and the codebook is

$M=256$ 0

For USA, the positions are

$M=256$ 1

with architecture-dependent bounds on $M=256$ 2. MoA groups pixels into modules, while NA and CPA exploit non-uniform sparsity patterns associated with larger virtual apertures or enhanced degrees of freedom (Lu et al., 28 Aug 2025).

The design rationale is therefore dual. First, ACC makes dynamic pixel activation feasible with a limited number of RF chains. Second, it transforms array selection from an unstructured combinatorial problem into a structured codebook search over canonical apertures. This suggests that ACC is most naturally viewed as a morphology codebook: it codifies a discrete set of physically interpretable aperture realizations.

3. Array-configuration training and optimization criteria

In the multi-user communication formulation, ACC is trained by selecting the codeword that maximizes the sum rate: $M=256$ 3 where $M=256$ 4 is the optimized SINR of user $M=256$ 5 under the chosen configuration (Lu et al., 28 Aug 2025). The channel after pixel activation is written as

$M=256$ 6

and the SINR can be expressed in terms of the configuration-dependent channel and interference covariance (Lu et al., 28 Aug 2025).

Exhaustive scanning over the entire ACC is already far cheaper than exhaustive antenna selection, but the work further introduces a two-stage scanning scheme to reduce training overhead. The first stage is array-level scanning: for each architecture, the XL array is partitioned into non-overlapping segments matched to the physical size of that architecture, and the best segment-level realization is identified. The second stage is pixel-level scanning: once the architecture and coarse segment are fixed, the reference point is shifted within that segment for fine optimization (Lu et al., 28 Aug 2025). The procedure is explicitly described as a two-stage scanning scheme including array- and pixel-level scanning.

This coarse-to-fine structure aligns ACC with the wider literature on hierarchical codebooks. In hierarchical beamforming training, upper layers provide coarse coverage and lower layers refine the search space; the classical criteria require full angular coverage per layer and child-codeword refinement across successive layers (Xiao et al., 2015). Near-field hierarchical codebooks apply a similar logic over the Fresnel region, with beam rotation and beam relocation used to place beam patterns at target angular and range locations (Chen et al., 2022). ACC therefore inherits a broader methodological pattern: structured search is as important as codeword construction.

The operational objective also depends on the chosen metric. In analog beamforming codebooks inspired by the generalized Lloyd algorithm, the codeword update maximizes a cluster-averaged utility $M=256$ 7, where $M=256$ 8 targets average beamforming gain, $M=256$ 9 approximates coverage or outage optimization, and $N=32$ 0 targets average data rate (Ganji et al., 2019). ACC in XL-MIMO uses sum rate and localization RMSE rather than only beam gain, but the same principle remains: the codebook is meaningful only relative to an application-specific utility.

4. Relation to antenna selection and task-dependent performance

ACC is explicitly contrasted with greedy antenna selection (AS). In the greedy AS baseline, the active set is built sequentially, and at each iteration the antenna pixel that produces the largest increase in sum rate is added. The work derives a closed-form incremental SINR expression for this sequential activation process, reducing the cost of repeated SINR updates (Lu et al., 28 Aug 2025). Even so, the ACC formulation emphasizes lower search overhead because it avoids evaluating arbitrary subsets.

The complexity comparison is direct. The summary table reports the following for an XL array with $N=32$ 1 and $N=32$ 2: exhaustive AS is impractical because it must consider all $N=32$ 3 possibilities or roughly $N=32$ 4 combinations; exhaustive ACC remains feasible; ACC with two-stage scanning has overhead on the order of $N=32$ 5; greedy AS has overhead on the order of $N=32$ 6 to $N=32$ 7 and is substantially more expensive than two-stage ACC (Lu et al., 28 Aug 2025). The paper also states that ACC-based two-stage scanning achieves nearly the same sum rate as exhaustive search, but with much lower overhead.

Task dependence is central. For multi-user communication, USA excels for moderate numbers of users ( $N=32$ 8), which the paper attributes to high angular resolution, while CA overtakes other architectures with very many users ( $N=32$ 9) because of better grating-lobe control and less inter-user interference (Lu et al., 28 Aug 2025). This directly counters the common assumption that the sparsest admissible array is always the best communication choice. The optimum architecture depends on user density, interference structure, and the utility being maximized.

This variability has a broader analog in related codebook research. In wideband phased arrays, beam squint shrinks effective beamwidth away from broadside and can require substantially denser codebooks; one cited example reports that 54% more beams are needed than in a design that ignores beam squint for a 32-element ULA at 73 GHz with 2.5 GHz bandwidth (Cai et al., 2016). In wideband true-time-delay arrays, the objective may instead be sub-band-to-angle mapping for multi-user orthogonalization, leading to structured Staircase TTD codebooks rather than fixed-phase steering codebooks (Wadaskar et al., 2023). ACC is therefore best understood as task-adaptive rather than architecture-maximal.

5. Extension to wireless localization and other propagation regimes

ACC-based training is extended from communication to wireless localization by changing the optimization target. In the localization scenario, the codeword is selected to minimize the angle-of-arrival estimation error: $10^4$ 0 The same two-stage scanning strategy can be used, but the figure of merit is localization RMSE rather than sum rate (Lu et al., 28 Aug 2025).

The task-dependent ranking of architectures changes sharply in this setting. The reported simulations state that USA performs poorly for localization because high grating lobes induce angle ambiguity, whereas non-uniform sparse arrays such as MoA, NA, and CPA outperform CA in localization RMSE, especially as SNR increases (Lu et al., 28 Aug 2025). Among these, NA provides the best RMSE, attributed to larger virtual aperture and enhanced degrees of freedom. This is one of the clearest demonstrations that ACC is not a single “best array” prescription; it is a mechanism for switching among structurally different apertures whose utility depends on the sensing or communication objective.

Related work generalizes the same idea to other propagation regimes. Near-field hierarchical codebooks explicitly cover the Fresnel region through lower-layer fine beams and upper-layer search beams, with beam rotation and beam relocation enabling coverage over angle and distance (Chen et al., 2022). Extremely large-scale array systems in the near field have been analyzed through elliptic and ellipsoidal correlation regions, yielding ULA and UPA uniform or dislocation codebooks that reduce quantization overhead while oversampling the angular domain (Zheng et al., 2023). For curvature-reconfigurable apertures, a unified distance-adaptive hierarchical codebook uses a direction-dependent effective Rayleigh distance and reciprocal-range sampling so that dense focusing inside the ERD automatically degenerates into sparse angle-only steering outside it, thereby avoiding hard mode switching between near-field and far-field operation (You et al., 28 Mar 2026).

Conformal-array and terminal-oriented codebooks show the same expansion of design dimensions. For cylindrical conformal arrays on UAVs, the codebook jointly specifies subarray pattern and angular beam pattern, supports tracking-error-aware adaptive beamwidth control, and provides full spatial coverage with lower outage probability than conventional planar arrays (Zhang et al., 2020). For 5G mmWave terminals, data-driven codebooks are generated directly from measured or simulated electric-field response data so that practical housing effects, irregular array placement, and multi-array coordination are internalized in the design objective of spherical coverage (Mo et al., 2019). These formulations suggest that ACC is increasingly tied to deployment realism rather than idealized steering-vector geometry.

6. Learning-based design, practical constraints, and recurring misconceptions

A recurrent misconception is that ACC or codebook design is chiefly a geometric discretization problem. The literature shows that hardware and measurement constraints are equally central. Analog beamforming codebooks have been extended to low-resolution phase shifters by projecting phase updates to the nearest feasible quantized vector and retaining the new codeword only if it improves the assigned-cluster metric (Ganji et al., 2019). In phased-array calibration, the codebook itself becomes a measurement design object: a neural network-enabled method generates unit-modulus calibration codebooks for arbitrary array sizes, with efficiency measured by the minimum number of measurements $10^4$ 1 and reliability measured by the codebook condition number (Chen et al., 15 Jun 2026). Practical over-the-air calibration performance is then tied to low condition number as much as to beam quality.

Learning-based ACC-related methods span several levels of abstraction. A machine-learning-refined hierarchical codebook process for extreme MIMO, termed X-BM, learns initial-access and refinement codebooks from beamspace representations and reports an 8 dB improvement in initial access together with a 10% increase in effective sum spectral efficiency relative to traditional codebook methods (Dreifuerst et al., 2023). In FD-MIMO with multi-panel arrays, reinforcement learning is used to allocate feedback bits among beam amplitude and co-phasing coefficients after exploiting stronger vertical than horizontal correlation through line-panel grouping (Fu et al., 2022). In 3D MIMO under spatially correlated channels, Tucker decomposition reduces the dimensionality of rotated codebooks by decomposing the high-dimensional rotation matrix into horizontal and vertical statistical directions and joint directional power, preserving near-optimal performance with much smaller feedback or storage burden (Yuan, 2015).

Another misconception is that hierarchical or structured codebooks are inherently tied to power-of-two arrays or far-field settings. One strand of work indeed notes that hierarchical or subarray methods can impose powers-of-two constraints, whereas generalized Lloyd-based analog codebooks are stated to work for arbitrary antenna numbers and arbitrary array shapes (Ganji et al., 2019). Near-field hierarchical designs, ELAA near-field quantization, and unified CuRA codebooks further show that codebook hierarchy is compatible with spherical-wave propagation and distance-sensitive focusing (Chen et al., 2022, Zheng et al., 2023, You et al., 28 Mar 2026). This suggests that ACC has evolved from a narrow beam-search convenience into a general design language for discretizing feasible array states across geometry, distance, frequency, and hardware domains.

A final misconception is that larger codebooks monotonically solve coverage problems. Wideband beam squint introduces hard tradeoffs between bandwidth, array size, and codebook density, and one analysis states explicit upper bounds beyond which no finite codebook can guarantee the target minimum gain over the full angular range (Cai et al., 2016). The broader ACC literature therefore points toward a constrained optimization viewpoint: codebook design must jointly account for propagation regime, hardware quantization, measurement burden, and the downstream task, whether multi-user communication, beam tracking, calibration, or localization.