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Physics-Guided Bayesian Optimization for High-Dimensional Mixed-Variable MIMO Base Station Design

Koki Kanzaki, Koya Sato

arXiv:2610.00974v1eess.SPcs.NI

TL;DR

Site-specific MIMO base-station design requires costly ray tracing and combines discrete candidate-site selection with continuous settings that depend on those choices. The paper uses a physics-based proxy and residual Gaussian process in Bayesian optimization; after 100 evaluations, it reports higher coverage than TuRBO in both urban scenarios.

  • Problem

    High-dimensional base-station design combines discrete site selection with conditional continuous parameters, while each evaluation requires costly site-specific ray tracing.

    Source: B. Problem Setting · p. 3

  • Method

    The method uses proxy-estimated coverage as a GP prior mean and a residual GP over three-dimensional physical features to model discrepancies and guide configuration selection.

    Source: §I · p. 2, B. Physical Feature · p. 4, C. Sequential Search Using a Residual GP · p. 5

  • Results

    After 100 evaluations, Proposed (fine) improves coverage over TuRBO by 15.2 percentage points in Munich and 6.4 percentage points in Etoile.

    Source: §IV · p. 6

  • Takeaways & Limitations

    The framework improves the fraction of receiver locations meeting the spectral-efficiency requirement within a limited budget of full evaluations.

    Source: §V · p. 6

Abstract

from arXiv · show

This paper proposes a physics-guided Bayesian optimization for high-dimensional mixed-variable multiple-input and multiple-output (MIMO) base station (BS) design. The considered problem jointly selects a subset of candidate sites for BS deployment and optimizes the azimuth angles, downtilt angles, and transmit power spectral densities of the BSs, while each configuration is evaluated using computationally expensive site-specific ray tracing. To efficiently optimize the system configuration, the proposed method constructs a low-cost physics-based proxy from precomputed propagation information. The proxy-estimated communication coverage is used as the Gaussian process (GP) prior mean, and a residual GP with three-dimensional physical features learns the discrepancy between the proxy and full evaluations. Ray-tracing-based evaluations in two urban scenarios show that the proposed method achieves up to approximately 15 percentage points higher coverage than conventional and high-dimensional optimization baselines under the same evaluation budget.

I. INTRODUCTION

Site-specific ray tracing makes MIMO base-station design costly, while practical deployments combine discrete site choices with conditional continuous settings. The paper proposes physics-guided Bayesian optimization to search this mixed-variable space efficiently.

I. INTRODUCTION

  • Site-specific ray tracing over many receiver locations makes joint placement-and-configuration search computationally expensive.High-fidelity channel simulation captures environmental effects, but an efficient optimizer must work with limited ray-tracing evaluations.Source: §I · p. 1
  • Practical deployment restricts base stations to finite candidate sites, creating a high-dimensional problem with discrete site choices and conditional continuous parameters.The continuous parameters apply only to base stations at selected sites, and existing methods for high-dimensional conditional mixed-variable optimization remain insufficiently explored.Source: §I · p. 1
  • Modern MIMO performance depends on spatial channels, precoding, and inter-BS interference, so received-power metrics or static antenna patterns alone are insufficient.The design should be evaluated on communication performance over spatial MIMO channels after precoding and interference mitigation.Source: §I · pp. 1–2
  • The proposed physics-guided Bayesian optimization uses proxy-estimated coverage as a GP prior mean and a residual GP over low-dimensional physical features to guide costly evaluations.The proxy uses propagation information precomputed for candidate sites and a discrete set of antenna orientations.Source: §I · p. 2

II. SYSTEM MODEL

The system model considers multiple MIMO base stations sharing a frequency band in a three-dimensional area, with deployment and parameter choices aimed at maximizing communication area.

II. SYSTEM MODEL

  • Multiple MIMO base stations operate on a shared frequency band in area A ⊂ R^3, and the design objective is to maximize communication area.The discussion identifies cellular systems, private 5G, and public Wi-Fi as possible applications.Source: §II · p. 2

A. Signal Model

The signal model represents a configuration by selected candidate sites and each deployed base station’s azimuth, downtilt, and transmit power spectral density. It evaluates downlink MIMO links under independent operation and inter-base-station interference.

A. Signal Model

  • A configuration selects candidate-site indices and assigns each selected site a parameter vector of azimuth angle, downtilt angle, and transmit power spectral density.The downtilt angle is measured from the horizontal plane, and power spectral density is total across transmit antennas.Source: A. Signal Model · p. 2
  • The formulation focuses on a shared frequency band, with multi-channel extension described as possible through additive objective decomposition.The extension is omitted because the paper treats it as straightforward.Source: A. Signal Model · p. 2
  • The evaluation uses receiver locations as points rather than simultaneously active users; all selected base stations are active, and scheduling is not modeled.The serving base station transmits to the receiver under evaluation while other base stations generate inter-base-station interference.Source: A. Signal Model · p. 2
  • Base stations operate independently without coordinated transmission or joint precoding, and perfect instantaneous CSI is assumed for each receiver’s serving link.The serving base station uses that CSI to precode the desired signal.Source: A. Signal Model · p. 2
  • The number of spatial streams is fixed within 1 ≤ Ns ≤ min(Nt, Nr), and each base station divides its total transmit power spectral density equally among the streams.The precoder uses the Ns columns corresponding to the largest singular values.Source: A. Signal Model · p. 2

B. Problem Setting

The problem maximizes coverage over constrained base-station configurations, with each configuration requiring high-fidelity channel simulation. Coverage is the fraction of evaluation locations meeting the required spectral efficiency.

B. Problem Setting

  • Coverage is the fraction of receiver locations whose spectral efficiency meets the required threshold Rreq > 0.The optimization objective uses an indicator for whether each receiver location satisfies that condition.Source: B. Problem Setting · p. 3
  • The configuration constraints bound the number of deployed base stations, downtilt angles, and transmit power spectral densities.The resulting feasible set defines the design space for the optimization problem.Source: B. Problem Setting · p. 3
  • Evaluating a configuration requires high-fidelity channel simulation because propagation is strongly affected by surrounding buildings.The optimization combines discrete site selection with continuous parameters defined only for base stations deployed at selected sites.Source: B. Problem Setting · p. 3

III. PHYSICS-GUIDED BAYESIAN OPTIMIZATION

Ray tracing makes full evaluations costly, while a GP over raw design variables is problematic in this high-dimensional setting. The method instead uses a physics-based proxy and low-dimensional physical features for Bayesian optimization.

  • Each configuration requires costly, site-specific ray tracing to evaluate its objective.Source: §III · p. 3
  • A GP defined directly over design variables is problematic because its dimension grows with the number of candidate sites.Source: §III · p. 3
  • The approach constructs a low-cost physics-based proxy and uses its low-dimensional physical features as GP inputs.Source: §III · p. 3

A. Construction of the Physics-Based Proxy

The physics-based proxy uses precomputed propagation information and interpolated channel representations to estimate coverage without ray tracing each configuration. Its discrepancy from the full objective is modeled by a residual function.

A. Construction of the Physics-Based Proxy

B. Physical Feature

The residual GP uses three physical features derived from proxy outputs to represent communication conditions rather than raw design variables. These features summarize local variation and representative spectral efficiency, then are standardized before fitting.

B. Physical Feature

  • Raw configuration variables may poorly represent propagation similarity, so the residual model uses proxy-derived physical features.Source: B. Physical Feature · p. 4
  • The proxy features capture local variation in spectral-efficiency satisfaction and serving-base-station dominance, plus representative spectral efficiency relative to the requirement.Local variation is measured over a graph connecting horizontally or vertically adjacent proxy receiver points.Source: B. Physical Feature · p. 4
  • The three feature components are standardized before use as GPR inputs, and input dimension remains three regardless of candidate-site or deployment count.Source: B. Physical Feature · pp. 4–5

C. Sequential Search Using a Residual GP

A residual GP models the difference between full evaluations and the physics-based proxy, whose value serves as the prior mean. Expected improvement guides sequential selection, balancing proxy-predicted coverage with residual corrections and uncertainty.

C. Sequential Search Using a Residual GP

  • The proxy value serves as the physics-based prior mean, while the residual GP models the discrepancy using physical features.Observed residuals are centered and scaled before GP fitting, with target statistics updated at each refit.Source: C. Sequential Search Using a Residual GP · p. 5
  • Expected improvement uses the predictive distribution to compare proxy-predicted coverage with residual-corrected promise and uncertainty on the same objective scale.Source: C. Sequential Search Using a Residual GP · p. 5
  • Candidates include random configurations and modifications of high-performing configurations through site replacement or continuous-parameter changes.Source: C. Sequential Search Using a Residual GP · p. 5
  • The figure plots best observed coverage in Munich and Etoile against elapsed time and the number of ray-tracing evaluations.Source: Figure 3 · p. 5
  • The evaluation budget counts full configuration evaluations, including initial samples, but excludes proxy and acquisition evaluations and database precomputation.Source: C. Sequential Search Using a Residual GP · p. 5

IV. PERFORMANCE EVALUATION

The evaluation compares proxy discretizations and optimization baselines in Munich and Etoile under a limited full-evaluation budget. The fine proxy leads on fixed-budget coverage, while medium offers a favorable balance with precomputation cost.

IV. PERFORMANCE EVALUATION

  • The evaluation uses Munich and Etoile scenes, five selected sites from 100 candidates, and a 100-evaluation budget including five initial samples.Full evaluations use a 100 × 100 receiver grid over a 500 × 500 m² area, with 5 m spacing and a 1 bps/Hz spectral-efficiency requirement.Source: §IV · pp. 5–6
  • The proxy database is evaluated at fine, medium, and coarse angular and receiver-grid resolutions, with the same ray-tracing settings and full-evaluation grid.The fine setting uses 45°/5° angle steps and 25 m receiver spacing; medium uses 90°/10° and 50 m; coarse uses 180°/20° and 100 m.Source: §IV · p. 6
  • Baselines include Random, GA, 400-dimensional GP BO, TuRBO, and REMBO; Physics BO isolates the effect of the physical prior mean against Proposed (medium).Fig. 4 also presents Munich optimization examples for Proposed (fine) and the five named baselines.Source: §IV · p. 6, Figure 4 · p. 6
  • 15.2 and 6.4 percentage points: Proposed (fine) improves over TuRBO in Munich and Etoile, respectively, after 100 evaluations.Proposed (fine/medium/coarse) reaches 87.6/86.2/83.0% coverage in Munich and 96.0/95.2/93.2% in Etoile; Physics BO reaches 85.5% and 93.9%.Source: §IV · p. 6
  • At 300 s, medium reaches 78.4% coverage in Munich and 93.1% in Etoile; fine performs best at fixed evaluation budget but costs more to precompute.The paper describes medium as a favorable balance between performance and precomputation cost.Source: §IV · p. 6

V. CONCLUSION

The conclusion presents a physics-based proxy and residual GP as an efficient BO framework for MIMO base-station design, improving coverage within a limited full-evaluation budget.

V. CONCLUSION

  • The framework uses a physics-based proxy to provide both the prior mean and a three-dimensional feature representation.Source: §V · p. 6
  • A residual GP corrects the propagation-based approximation to improve coverage under a limited budget of full evaluations.Source: §V · p. 6
  • The target is the fraction of receiver locations meeting the spectral-efficiency requirement.Source: §V · p. 6
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