Beam Alignment Engine (BAE) Overview

• Beam Alignment Engine (BAE) is a family of algorithmic and system architectures that optimally select beam directions under sensing and overhead constraints.
• BAE research integrates methods like search-based probing, deep learning prediction, and Bayesian optimization to enhance beam selection performance.
• These engines balance trade-offs between reliability, energy efficiency, and latency in both wireless communications and beamline applications.

Beam Alignment Engine (BAE) is a generic term for algorithmic and system architectures that select, predict, or refine beam directions, beam pairs, angular uncertainty regions, or beamline actuator settings under constraints on overhead, reliability, energy, and latency. In the mmWave and THz literature, BAEs appear in cell-free uplink processing, analog and hybrid beam sweeping, coded feedback design, location-aware inference, deep-learning beam prediction, Bayesian optimization, and multi-armed bandit formulations; in beamline science, the same label is used for Gaussian-process-based autonomous alignment of optical and x-ray systems. The literature therefore uses “BAE” not for a single standardized protocol, but for a family of engines that couple sensing, inference, control, and beam deployment (Brun et al., 2022).

1. Scope and problem formulations

Across the cited works, BAEs differ mainly in their observation model, decision space, and performance criterion. In communication systems, the decision variable is usually a transmit beam, receive beam, or beam pair drawn from an analog or hybrid codebook. In beamline alignment, the decision variable is a vector of motor-controlled degrees of freedom.

BAE setting	Inputs	Outputs
mmWave MIMO beam prediction	RSSI over wide beams, feedback, or received power	best narrow beam or beam pair
Interactive/search-based BA	ACK/NACK, posterior belief, energy measurements	next probing beam and final data beam
Beamline alignment	detector readings, beam size, flux, motor state	optimized motor settings

A representative wireless formulation appears in narrowband downlink mmWave MIMO with a BS having an $N_{\mathrm{BS}}$-element ULA and a single RF chain, a UE with one antenna, and analog beamforming over a finite codebook $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$. During sweeping over beam $\mathbf w_q$, the UE receives

$$r_u[q]=\sqrt{P_{\mathrm{BS}}}\,\mathbf h_u^H\mathbf w_q\,s_w+z_u,\qquad z_u\sim\mathcal{CN}(0,\sigma_z^2),$$

and beam selection is posed as

$q_u^*=\arg\max_q |\mathbf h_u^H\mathbf w_q|^2.$

This formulation underlies digital-twin-assisted and explainable DL-based BAEs that use RSSI vectors from wide beams to predict a narrow-beam index (Khan et al., 12 Jul 2025).

A distinct formulation appears in cell-free mmWave massive MU-MIMO uplink, with $L$ APs and $K$ UEs, total transmit dimension $N_T=K\cdot n_{\mathrm{UE}}$, total receive dimension $N_R=L\cdot n_{\mathrm{AP}}$, and OFDM input–output relation

$y^v=H^vPs^v+n^v.$

Here the BAE selects one analog transmit beam per UE from a steering-vector codebook, while APs perform full-digital receive beamforming and the CPU applies centralized LMMSE equalization (Brun et al., 2022).

Other BAEs are posed as black-box optimization over angles, fixed-confidence best-arm identification, cumulative-reward bandits, or Bayesian belief updates. For example, Bayesian-optimization-based BA treats

$\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$0

as a black-box objective over AoD/AoA, whereas beamline BAEs optimize beam quality functions such as $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$1 or $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$2 over motor settings $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$3 (Yang et al., 2022, Morris et al., 2024).

2. Canonical signal models, observables, and metrics

The most common observables used by BAEs are received power, RSSI vectors, binary ACK/NACK sequences, posterior beliefs over angles, coarse channel estimates, and detector outputs from physical beamlines. The choice of observable largely determines whether the engine is formulated as estimation, classification, search, or optimization.

In cell-free mmWave uplink, one practical simplification is a frequency-flat surrogate channel for BA,

$\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$4

built from the “strongest-subcarrier” block of the full OFDM channel. UE analog beams are selected from the codebook

$\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$5

with one beam used for all subcarriers. After BA and post-pilot CHEST, the CPU applies

$\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$6

Performance is then quantified by post-equalization $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$7, per-user RMSSE, and per-user spectral efficiency $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$8 (Brun et al., 2022).

RSSI-based BAEs reduce the sensing burden by first probing a small set of wide beams. In the DT-assisted explainable formulation, the feature vector is

$\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$9

and the target is the narrow-beam index that maximizes SNR. The same paper defines effective spectral efficiency as

$\mathbf w_q$0

making overhead an explicit part of the metric rather than a separate engineering consideration (Khan et al., 12 Jul 2025).

Location-aware BAEs transform geometric uncertainty into angular uncertainty. Given noisy location estimates $\mathbf w_q$1, the estimated path angles $\mathbf w_q$2 and $\mathbf w_q$3 are accompanied by uncertainty intervals $\mathbf w_q$4 and $\mathbf w_q$5. Candidate beam subsets $\mathbf w_q$6 and $\mathbf w_q$7 are then formed by retaining only codebook beams whose steering angles lie in those intervals (Igbafe et al., 2019).

A broader observation is that BAEs often optimize not raw alignment accuracy alone, but an overhead-aware utility. Search-based engines use expected slots, probing duration, or expected beamwidth; DL-based engines use top-$\mathbf w_q$8 accuracy, spectral efficiency, calibration, or credibility; beamline engines use flux density, beam size, power loss, or coupling efficiency. This suggests that “beam alignment” in the BAE literature is better interpreted as sequential decision-making under observation and actuation constraints than as mere codebook search.

3. Search, coding, and combinatorial beam-alignment engines

A major branch of BAE research treats alignment as an interactive search problem. In “Energy-Efficient Interactive Beam-Alignment for Millimeter-Wave Networks,” the optimal protocol under the sectored model has a fixed-length beam-alignment phase of $\mathbf w_q$9 slots followed by a data-communication phase. The optimal beam-alignment procedure is a decoupled fractional beam-alignment method that alternates BS-side and UE-side refinement, scanning a fraction $$r_u[q]=\sqrt{P_{\mathrm{BS}}}\,\mathbf h_u^H\mathbf w_q\,s_w+z_u,\qquad z_u\sim\mathcal{CN}(0,\sigma_z^2),$$0 of the current uncertainty region at each slot; numerical results with analog beams depict up to $$r_u[q]=\sqrt{P_{\mathrm{BS}}}\,\mathbf h_u^H\mathbf w_q\,s_w+z_u,\qquad z_u\sim\mathcal{CN}(0,\sigma_z^2),$$1, $$r_u[q]=\sqrt{P_{\mathrm{BS}}}\,\mathbf h_u^H\mathbf w_q\,s_w+z_u,\qquad z_u\sim\mathcal{CN}(0,\sigma_z^2),$$2, and $$r_u[q]=\sqrt{P_{\mathrm{BS}}}\,\mathbf h_u^H\mathbf w_q\,s_w+z_u,\qquad z_u\sim\mathcal{CN}(0,\sigma_z^2),$$3 gains over a state-of-the-art bisection method, conventional exhaustive search, and interactive exhaustive search, respectively (Hussain et al., 2018).

Coded BAEs address detection errors directly. In “Coded Energy-Efficient Beam-Alignment for Millimeter-Wave Networks,” the alignment sequence is generated from a binary codebook $$r_u[q]=\sqrt{P_{\mathrm{BS}}}\,\mathbf h_u^H\mathbf w_q\,s_w+z_u,\qquad z_u\sim\mathcal{CN}(0,\sigma_z^2),$$4 with minimum Hamming distance at least $$r_u[q]=\sqrt{P_{\mathrm{BS}}}\,\mathbf h_u^H\mathbf w_q\,s_w+z_u,\qquad z_u\sim\mathcal{CN}(0,\sigma_z^2),$$5, so that observed error-corrupted feedback $$r_u[q]=\sqrt{P_{\mathrm{BS}}}\,\mathbf h_u^H\mathbf w_q\,s_w+z_u,\qquad z_u\sim\mathcal{CN}(0,\sigma_z^2),$$6 can be decoded by minimum-distance decoding. The beam assignment problem is then optimized through a convex upper bound and a water-filling-like solution for sector areas $$r_u[q]=\sqrt{P_{\mathrm{BS}}}\,\mathbf h_u^H\mathbf w_q\,s_w+z_u,\qquad z_u\sim\mathcal{CN}(0,\sigma_z^2),$$7. Under realistic analog-beam patterns, the coded scheme shows up to approximately $$r_u[q]=\sqrt{P_{\mathrm{BS}}}\,\mathbf h_u^H\mathbf w_q\,s_w+z_u,\qquad z_u\sim\mathcal{CN}(0,\sigma_z^2),$$8 gain over exhaustive and approximately $$r_u[q]=\sqrt{P_{\mathrm{BS}}}\,\mathbf h_u^H\mathbf w_q\,s_w+z_u,\qquad z_u\sim\mathcal{CN}(0,\sigma_z^2),$$9 over uncoded schemes at fixed spectral efficiency (Hussain et al., 2018).

Group-testing BAEs exploit multi-path sparsity. In “Hybrid Beam Alignment for Multi-Path Channels: A Group Testing Viewpoint,” angular sectors are treated as “items” and path-containing sectors as “defectives.” The analog AGTBA adapts Hwang’s Generalized Binary Splitting, while HGTBA$q_u^*=\arg\max_q |\mathbf h_u^H\mathbf w_q|^2.$0–HGTBA$q_u^*=\arg\max_q |\mathbf h_u^H\mathbf w_q|^2.$1 extend the logic to $q_u^*=\arg\max_q |\mathbf h_u^H\mathbf w_q|^2.$2. In the noiseless model, the expected analog duration satisfies $q_u^*=\arg\max_q |\mathbf h_u^H\mathbf w_q|^2.$3, whereas HGTBA$q_u^*=\arg\max_q |\mathbf h_u^H\mathbf w_q|^2.$4 satisfies $q_u^*=\arg\max_q |\mathbf h_u^H\mathbf w_q|^2.$5. In 28 GHz simulations, AGTBA outperforms prior analog schemes by up to $q_u^*=\arg\max_q |\mathbf h_u^H\mathbf w_q|^2.$6–$q_u^*=\arg\max_q |\mathbf h_u^H\mathbf w_q|^2.$7 in expected slots, HGTBA$q_u^*=\arg\max_q |\mathbf h_u^H\mathbf w_q|^2.$8 cuts training time in half compared to AGTBA, and by more than $q_u^*=\arg\max_q |\mathbf h_u^H\mathbf w_q|^2.$9 compared to naive exhaustive hybrid search (Yildiz et al., 2021).

Multi-path and multi-user BAEs also induce specialized beam-design structures. In “Multi-user Beam Alignment in Presence of Multi-path,” the set of scanning beams has a Tulip Design that maximizes the number of distinguishable feedback patterns when $L$0 or $L$1. The resulting optimization minimizes the expected transmission beamwidth over feedback patterns, with BF, SD, p-BF, and p-SD policies defining different ways to cover discovered path components. Reported simulations show that BF yields significantly smaller expected beamwidth than SD, and that increasing the number of scanning beams $L$2 decreases expected beamwidth (Torkzaban et al., 2022).

A recurring implication is that exhaustive search is not the reference model for all BAEs. Several engines instead formalize alignment as structured uncertainty reduction, where code design, group testing, or posterior geometry determine the next probe.

4. Learning-based, explainable, and map-driven engines

A second major branch replaces explicit search with learned beam prediction. In “Explainable and Robust Millimeter Wave Beam Alignment for AI-Native 6G Networks,” the BAE is a CNN classifier that maps an $L$3 RSSI vector to a narrow-beam label, followed by a DkNN layer that evaluates internal representations through nearest-neighbor conformity. The reported overhead is $L$4 instead of $L$5, giving a $L$6 reduction when $L$7; DkNN$L$8 achieves approximately $L$9 of the greedy 128-beam DFT codebook across SNRs, sustains $K$0 top-3 accuracy down to $K$1 when trained with noise, and improves adversarial-example filtering by up to $K$2 (Khan et al., 23 Jan 2025).

The DT-assisted extension makes the explainability and robustness machinery more explicit. It uses a site-specific digital twin to generate synthetic channels, transfer learning to refine a pre-trained DNN with small real datasets, Deep-SHAP to rank wide-beam features, and DkNN to produce prediction, credibility, and confidence. Reported results include up to $K$3 fewer real samples than real-only training, beam training overhead reduced by $K$4 versus full-codebook DL and by $K$5 versus exhaustive search over 128 narrow beams, Top-1/2/3 accuracy of approximately $K$6 with $K$7, and up to $K$8 better outlier detection against FGSM adversarial inputs than standard softmax (Khan et al., 12 Jul 2025).

Location and map information provide another route to scan reduction. “InferBeam” formulates best-BS and sector-tuple inference as cascaded conditional random fields over a discretized 3D grid. With fewer than $K$9 sampled locations, it infers the rest dynamically and achieves best-beam selection for $N_T=K\cdot n_{\mathrm{UE}}$0 of locations in test environments such as condo and office spaces, while reducing online alignment to lookup plus a small number of directed trials (Zhang et al., 2018). “Location-aware Beam Alignment for mmWave Communications” uses noisy UE and reflector coordinates to pre-select candidate beams inside angle-error windows, then performs alternating downlink/uplink refinement within a small sliding window; at $N_T=K\cdot n_{\mathrm{UE}}$1 with $N_T=K\cdot n_{\mathrm{UE}}$2, the reported rate is within $N_T=K\cdot n_{\mathrm{UE}}$3 of the genie-optimal rate while requiring approximately $N_T=K\cdot n_{\mathrm{UE}}$4 of the alignment slots, and remains within $N_T=K\cdot n_{\mathrm{UE}}$5–$N_T=K\cdot n_{\mathrm{UE}}$6 of perfect-CSI exhaustive search while using approximately $N_T=K\cdot n_{\mathrm{UE}}$7 fewer beam measurements (Igbafe et al., 2019).

The most aggressive form of prediction is scan-free alignment. In “Intelligent Angle Map-based Beam Alignment for RIS-aided mmWave Communication Networks,” a lightweight MLP first classifies UEs as LoS or NLoS, and Transformer-based angle maps then map UE coordinates directly to direct-link and RIS-link angles. Beamforming vectors are constructed from the dominant predicted path, RIS phases are set analytically, and the workflow completes with zero scanning overhead. In the DeepMIMO O1_28 scenario, beam alignment accuracy rises to $N_T=K\cdot n_{\mathrm{UE}}$8 at 60K samples, predicted angles are within $N_T=K\cdot n_{\mathrm{UE}}$9 error when trained on 60K, and alignment delay is reduced from tens of ms to $N_R=L\cdot n_{\mathrm{AP}}$0 (Xia et al., 2024).

These works also expose a central controversy in AI-native BA: high predictive accuracy does not remove the need for calibration and distribution-shift detection. DkNN credibility, SHAP feature ranking, transfer learning, and reliability diagrams are introduced precisely because softmax confidence alone is repeatedly reported as overconfident under noise, out-of-distribution inputs, and adversarial perturbations.

5. Bayesian, bandit, and black-box optimization engines

Bayesian and bandit BAEs treat alignment as sequential optimization under uncertainty. In “Fast mmWave Beam Alignment via Correlated Bandit Learning,” the Hierarchical Beam Alignment (HBA) algorithm exploits the smoothness of neighboring beams through a tree-based zooming search with confidence bonuses. Theoretical analysis gives regret $N_R=L\cdot n_{\mathrm{AP}}$1, and reported simulations show that HBA reduces beam alignment from approximately $N_R=L\cdot n_{\mathrm{AP}}$2 to $N_R=L\cdot n_{\mathrm{AP}}$3, with $N_R=L\cdot n_{\mathrm{AP}}$4 optimal-beam probability in 1–5 path channels (Wu et al., 2019).

“Fast Beam Alignment via Pure Exploration in Multi-armed Bandits” formulates BA as fixed-confidence best-arm identification with heteroscedastic Gaussian rewards and spatially correlated beams. The Two-Phase Heteroscedastic Track-and-Stop algorithm first identifies the best super-arm among grouped beams and then the best beam within a local window. For $N_R=L\cdot n_{\mathrm{AP}}$5, correlation length $N_R=L\cdot n_{\mathrm{AP}}$6, and $N_R=L\cdot n_{\mathrm{AP}}$7, the reported sample complexity is on the order of $N_R=L\cdot n_{\mathrm{AP}}$8 steps versus approximately $N_R=L\cdot n_{\mathrm{AP}}$9–$y^v=H^vPs^v+n^v.$0 for exhaustive BA and Track-and-Stop baselines, with alignment overhead below $y^v=H^vPs^v+n^v.$1 over practical coherence times of approximately 14 000 slots (Wei et al., 2022).

A different bandit perspective appears in “Second-best Beam-Alignment via Bayesian Multi-Armed Bandits,” where the state is the posterior over angular sectors and the action is the beam pair with the second-largest current posterior weight. The resulting “second-best preference” policy is derived from lower and upper bounds on the value function and is reported to improve alignment probability by up to $y^v=H^vPs^v+n^v.$2, $y^v=H^vPs^v+n^v.$3, and $y^v=H^vPs^v+n^v.$4 relative to first-best preference, Thompson sampling, and UCB, respectively (Hussain et al., 2019).

Bayesian optimization BAEs replace codebook-wide search by a surrogate model over angular coordinates. In “Bayesian Optimization-Based Beam Alignment for MmWave MIMO Communication Systems,” GP and GBRT surrogates are coupled with Expected Improvement to optimize received power over $y^v=H^vPs^v+n^v.$5. With a $y^v=H^vPs^v+n^v.$6 beam-pair codebook, $y^v=H^vPs^v+n^v.$7 initial samples and $y^v=H^vPs^v+n^v.$8 BO iterations require 160 measurements, approximately $y^v=H^vPs^v+n^v.$9 of exhaustive search; GBRT-BO reaches approximately $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$00–$\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$01 of exhaustive-search spectral efficiency after 160 sweeps and outperforms OMP and TS-MAB by up to $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$02–$\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$03 in low-SNR regimes (Yang et al., 2022). The indoor refinement of this line, R-BO, combines a Matérn-kernel GP, online hyperparameter re-optimization, and a local refinement scan, and reports $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$04 beam-alignment accuracy within $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$05 degrees, less than $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$06 average loss, and an $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$07 reduction in probing overhead over exhaustive search across 43 receiver positions (Shiroya et al., 12 Nov 2025).

The same Bayesian-optimization logic extends beyond wireless links. “A General Bayesian Algorithm for the Autonomous Alignment of Beamlines” implements GP-based single- and multi-objective optimization in the Blop Python library using BoTorch, PyTorch, GPyTorch, and Bluesky/EPICS. It is validated on x-ray and electron beamlines, including convergence to within $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$08 of a global optimum in approximately 30 iterations on TES, doubling count rate on ISS in approximately 25 iterations, and reaching within $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$09 of optimum in median 40 iterations on an 8D simulated digital twin (Morris et al., 2024). The Raspberry Pi auto-aligner uses the M-LOOP GP optimizer on a four-parameter mirror-control problem and reports a typical total optimization time of approximately 20 min for 200 runs, with approximately $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$10 improvement in fiber-coupled power and sub-percent repeatability in the second build (Mathew et al., 2020).

6. System architecture, implementation constraints, and recurring limitations

Despite methodological diversity, many BAEs decompose into a small number of recurring modules: a probing or sensing stage, a feature-extraction or statistics-update stage, a decision engine, a control/feedback plane, and a final beam or actuator deployment stage. In the 2PHTS implementation recipe, these appear explicitly as a beam-forming controller, scheduler, RF chain and phase-shifter network, pilot TX/RX chain, feedback processor, and statistics update block (Wei et al., 2022). In mmWave user-centric cell-free massive MIMO, the architecture consists of Channel Probing, Direction Estimator, Codebook Manager, Control Exchange Unit, and a central orchestration layer, with all decisions executed within a single BA round of less than $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$11 (Buzzi et al., 2021).

Practical BAEs often depend on side channels or environmental regularity. Interference-aware cell-free BA assumes a sub-6 GHz control channel to convey beam indices, relies on channel coherence across pre-BA subcarriers and timely feedback, and notes that for extremely dense networks $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$12 residual interference may require further iterative refinement or decentralized processing (Brun et al., 2022). The one-shot cell-free BA protocol of user-centric CF-mMIMO likewise assumes a reliable control channel at sub-6 GHz frequency and prior knowledge of orthogonal channels and the transmit beamforming codebook (Buzzi et al., 2021). Map-based and angle-map BAEs require either location information or large ray-tracing datasets; the Transformer angle-map scheme explicitly lists susceptibility to localization errors, a static scene assumption, and the need for retraining or online fine-tuning under rapid environmental changes (Xia et al., 2024).

Another recurring limitation concerns the relation between analog and digital beamforming. A common assumption is that analog codebooks are intrinsically inferior to interference-unaware digital selection. The interference-aware cell-free uplink results contradict that simplification: “analog IA” reduces RMSSE by more than $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$13 for the worst UEs versus IU methods, improves 10%-tile spectral efficiency by approximately $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$14, and is approximately equal to digital IU, showing that the analog codebook is expressive enough when interference is handled (Brun et al., 2022).

Explainability claims are similarly nuanced. DkNN and SHAP provide credibility metrics, nearest-neighbor evidence, and ranked sensing-beam importance, but they do not remove the need for careful calibration. In the DT-assisted BAE, DkNN credibility is reported as well-calibrated via reliability diagrams, whereas softmax is overconfident and even on adversarial samples $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$15 are given $\mathcal W=\{\mathbf w_1,\dots,\mathbf w_Q\}$16 confidence (Khan et al., 12 Jul 2025). This suggests that explainable BAEs in the current literature are primarily post-hoc or representation-level trust mechanisms, not substitutes for robustness analysis.

Taken together, the BAE literature describes a broad systems category rather than a single algorithmic lineage. Search-theoretic, coded, Bayesian, map-driven, and deep-learning engines all address the same operational bottleneck—fast, reliable beam selection under sparse, noisy, or expensive observations—but they do so with markedly different assumptions about priors, control channels, hardware, and environmental stability.