References & Further Reading
References
- W. Xu and G. Caire, Visibility Region Detection for XL-MIMO via Markov Random Field Priors, 2023
The CommIT contribution that is the statistical backbone of this chapter. Formulates the VR detection problem as MAP inference on a 2D Ising / Markov random field, derives the loopy-BP inference routine, and wraps it in an EM outer loop for joint VR + channel estimation. Sections III, IV, and V of the paper map directly onto Sections 18.2 and 18.5 of this chapter.
- E. de Carvalho, A. Ali, A. Amiri, M. Angjelichinoski, and R. W. Heath Jr., Non-Stationarities in Extra-Large Scale Massive MIMO, 2020
The canonical reference defining the visibility region concept and surveying its physical causes. Figure 2 of the paper illustrates aperture-range, blockage, and clustering VRs, matching the three mechanisms of Section 18.1.
- A. Amiri, M. Angjelichinoski, E. de Carvalho, and R. W. Heath Jr., Extremely Large Aperture Massive MIMO: Low Complexity Receiver Architectures, 2022
Introduces the subarray-based receiver architecture and the complexity argument of Theorem 18.3. Provides numerical comparisons of full- aperture vs subarray vs VR-pruned estimators. Section IV is the primary source for Section 18.3.
- E. Bjornson and L. Sanguinetti, Spatial Channel Models for Holographic and Extremely Large Aperture MIMO, 2024
Reviews the spatial non-stationarity phenomenon across frequency bands and aperture scales, with emphasis on 6G-era deployments. The Fraunhofer distance discussion and the near-field transition in Section 18.4 follow this reference.
- E. Bjornson and L. Sanguinetti, Massive MIMO is a Reality — What is Next? Five Promising Research Directions for Antenna Arrays, 2019
Influential survey that positioned holographic and XL-MIMO arrays as the most disruptive research direction beyond 5G. The motivating arguments in the historical note of Section 18.1 follow this paper.
- M. Cui and L. Dai, Channel Estimation for Extremely Large-Scale MIMO: Far-Field or Near-Field?, 2022
Introduces the polar-domain dictionary for near-field sparse channel estimation and proves the sparsity theorem of Section 18.4 (Theorem <a href="#thm-polar-sparsity" class="ferkans-ref" title="Theorem: Polar-Domain Sparsity of Near-Field Channels" data-ref-type="theorem"><span class="ferkans-ref-badge">T</span>Polar-Domain Sparsity of Near-Field Channels</a>). Algorithm 1 of the paper is the polar-OMP of Algorithm <a href="#alg-polar-omp" class="ferkans-ref" title="Algorithm: Polar-OMP for Near-Field Channel Estimation" data-ref-type="algorithm"><span class="ferkans-ref-badge">A</span>Polar-OMP for Near-Field Channel Estimation</a>.
- Y. Han, S. Jin, C.-K. Wen, and X. Ma, Channel Estimation for Extremely Large-Scale Massive MIMO Systems, 2020
Early short paper on XL-MIMO channel estimation with subarray partitioning. Section V contributes to the subarray discussion of Section 18.3.
- J. Besag, Spatial Interaction and the Statistical Analysis of Lattice Systems, 1974
Foundational paper introducing the Markov random field framework for spatial data, including the 2D Ising-type conditional distributions used in Section 18.2. Theorem <a href="#thm-local-conditional" class="ferkans-ref" title="Theorem: Local Conditional of the 2D Ising Prior" data-ref-type="theorem"><span class="ferkans-ref-badge">T</span>Local Conditional of the 2D Ising Prior</a> is essentially Besag's local conditional specification.
- A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum Likelihood from Incomplete Data via the EM Algorithm, 1977
The foundational EM algorithm paper. The monotone ascent property of Theorem <a href="#thm-em-convergence" class="ferkans-ref" title="Theorem: Monotone Ascent of EM for the Joint Problem" data-ref-type="theorem"><span class="ferkans-ref-badge">T</span>Monotone Ascent of EM for the Joint Problem</a> is the basic EM theorem applied to the joint VR + channel problem.
- K. T. Selvan and R. Janaswamy, Fraunhofer and Fresnel Distances: Unified Derivation for Aperture Antennas, 2017
Unified derivation of near- and far-field boundaries, including the Fraunhofer distance formula used in Section 18.4.
- T. L. Marzetta, Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas, 2010
The massive MIMO origin paper. Sets the stationary channel baseline that Chapter 18 departs from, and defines pilot contamination which reappears in the XL-MIMO regime as the motivation for Section 18.5's joint estimator.
Further Reading
For readers who want to go deeper into XL-MIMO, visibility regions, and near-field estimation.
The visibility-region framework
de Carvalho, Ali, Amiri, Angjelichinoski, and Heath, 'Non-Stationarities in Extra-Large Scale Massive MIMO,' IEEE Wireless Communications, 2020
The definitive tutorial on visibility regions and spatial non-stationarity. Read first for intuition before diving into the algorithmic papers.
2D Markov priors and belief propagation
Xu and Caire, 'Visibility Region Detection for XL-MIMO via Markov Random Field Priors,' CommIT preprint, 2023
The CommIT contribution that drives Sections 18.2 and 18.5. Contains the full EM derivation, convergence proofs, and numerical benchmarks reproduced in the interactive plots of this chapter.
Polar dictionary and near-field sparse recovery
Cui and Dai, 'Channel Estimation for Extremely Large-Scale MIMO: Far-Field or Near-Field?,' IEEE Trans. Commun., 2022
The polar-domain paper. Section 18.4 follows its dictionary construction closely; the paper provides the analytical range-resolution formulas and OMP algorithm.
Subarray architectures and complexity analysis
Amiri, Angjelichinoski, de Carvalho, and Heath, 'Extremely Large Aperture Massive MIMO: Low Complexity Receiver Architectures,' IEEE TWC, 2022
The primary reference for Section 18.3. Contains real-complexity breakdowns and comparisons across multiple partitioning strategies.
Markov random field inference beyond Ising
Wainwright and Jordan, 'Graphical Models, Exponential Families, and Variational Inference,' Foundations and Trends in Machine Learning, 2008
The authoritative reference on variational inference in graphical models. Read when you want to understand why loopy BP converges (or does not) and what happens beyond the Ising case.
Physical channel models for XL-MIMO
Bjornson and Sanguinetti, 'Spatial Channel Models for Holographic and Extremely Large Aperture MIMO,' IEEE OJCOM, 2024
The modern reference on spatial channel models in the XL-MIMO and holographic regime. Use for understanding the statistical properties that drive the VR structure.