References & Further Reading
References
- Q. Wu and R. Zhang, Beamforming Optimization for Wireless Network Aided by Intelligent Reflecting Surface With Discrete Phase Shifts, 2020
The definitive reference on discrete-phase RIS. The $\text{sinc}^2(\pi/2^B)$ loss formula and both projection and BCD algorithms are from this paper.
- M. Di Renzo et al., Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces, 2020
Section III covers hardware options and bit-depth choices relevant to Section 8.1's deployment discussion.
- E. Björnson, Ö. Özdogan, and E. G. Larsson, Reconfigurable intelligent surfaces: Three myths and two critical questions, 2020
Critical reading on RIS scaling claims. Section V covers the bit-depth vs. element-count tradeoff.
- S. Zhang and Y. Huang, Complex quadratic optimization and semidefinite programming, 2006
NP-hardness proof for unit-modulus QCQP, which extends directly to the discrete case.
- B. Di, H. Zhang, L. Li, L. Song, Y. Li, and Z. Han, Practical Hybrid Beamforming With Finite-Resolution Phase Shifters for Reconfigurable Intelligent Surface Based Multi-User Communications, 2020
Discrete-phase multi-user RIS with SDR + discrete projection. Section III is the basis of the branch-and-bound algorithm in Section 8.3.
- D. P. Bertsekas, Nonlinear Programming, Athena Scientific, 2nd ed., 1999
Convergence theory for BCD (discrete variant via finite-state arguments in Sec. 2.7).
- R. M. Karp, Reducibility among combinatorial problems, 1972
Classical paper establishing NP-hardness of MAX-CUT and related problems. Relevant context for the 1-bit RIS complexity analysis.
- V. Arun and H. Balakrishnan, RFocus: Beamforming using thousands of passive antennas, 2020
1-bit RIS prototype with $N = 3200$ elements. The classical empirical demonstration of the 'more elements, fewer bits' philosophy.
- Z. Yang, M. Chen, W. Saad, W. Xu, M. Shikh-Bahaei, H. V. Poor, and S. Cui, Energy-Efficient Wireless Communications With Distributed Reconfigurable Intelligent Surfaces, 2022
Multi-RIS with discrete phases, bit-depth/energy tradeoff. Complements Chapter 12 on multi-RIS architectures.
- W. Tang et al., Wireless Communications With Reconfigurable Intelligent Surface: Path Loss Modeling and Experimental Measurements, 2021
First experimental 1-bit RIS measurement. Confirms the $3.92\text{ dB}$ coherent-SNR loss predicted by theory.
- H. Guo, Y.-C. Liang, J. Chen, and E. G. Larsson, Weighted Sum-Rate Maximization for Reconfigurable Intelligent Surface Aided Wireless Networks, 2020
Multi-user WMMSE extended to discrete phases. Section IV presents the projection-then-refine approach of Section 8.2.
- Q. Wu, S. Zhang, B. Zheng, C. You, and R. Zhang, Intelligent Reflecting Surface-Aided Wireless Communications: A Tutorial, 2021
Tutorial with discrete-phase section synthesizing algorithmic and hardware perspectives.
Further Reading
Resources for deeper study of the discrete-phase RIS design space.
Adaptive-resolution RIS architectures
Zhang et al. (2022), 'Reconfigurable Intelligent Surface With Hybrid Discrete Phase Shifters,' IEEE TWC
Explores mixing high-resolution and low-resolution elements in one panel — one possible realization of Exercise 8.15.
Integer-programming approaches to discrete RIS
Di et al. (2020), 'Practical Hybrid Beamforming With Finite-Resolution Phase Shifters' (ch08 reference)
Branch-and-bound extensions for very small $N$; useful for research benchmarks.
Distributed discrete optimization across RIS elements
Björnson et al. (2022), 'Reconfigurable Intelligent Surfaces: A Signal Processing Perspective With Wireless Applications,' IEEE SP Magazine
Decentralized discrete updates for large arrays — relevant for future multi-panel deployments (Ch. 12).
Hardware-algorithm co-design for low-bit RIS
Tang et al. (2021) (ch08 reference)
Experimental validation of the theoretical discrete-phase loss in a 1-bit RIS prototype.
Deep-learning-based discrete-phase optimization
Liu et al. (2022), 'Deep Learning for Intelligent Reflecting Surface: A Review,' IEEE Wireless Communications
Neural-network surrogates for the discrete optimization problem — faster inference than AO at the cost of training.