arXiv subjects

Hongyi Liao

Publications and source records attributed to Hongyi Liao.

2 recordsLinked to original sources

arXiv2025

Discrete Beamforming Optimization for RISs with a Limited Phase Range and Amplitude Attenuation

This paper addresses the problem of maximizing the received power at a user equipment via reconfigurable intelligent surface (RIS) characterized by phase-dependent amplitude (PDA) and discrete phase shifts over a limited phase range. Given complex RIS coefficients, that is, discrete phase shifts and PDAs, we derive the necessary and sufficient conditions to achieve the optimal solution. To this end, we propose an optimal search algorithm that is proven to converge in linear time within at most NK steps, significantly outperforming the exhaustive search approach that would otherwise be needed for RISs with amplitude attenuation. Furthermore, we introduce a practical quantization framework for PDA-introduced RISs termed amplitude-introduced polar quantization (APQ), and extend it to a novel algorithm named extended amplitude-introduced polar quantization (EAPQ) that works with geometric projections. We derive closed-form expressions to assess how closely the performance of the proposed RIS configuration can approximate the ideal case with continuous phases and no attenuation. Our analysis reveals that increasing the number of discrete phases beyond K = 4 yields only marginal gains, regardless of attenuation levels, provided the RIS has a sufficiently wide phase range R. Furthermore, we also show and quantify that when the phase range R is limited, the performance is sensitive to attenuation for larger R, and sensitive to R when there is less attenuation. Finally, the proposed optimal algorithm provides a generic upper bound that could serve as a benchmark for discrete beamforming in RISs with amplitude constraints.

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arXiv2024

Received Power Maximization Using Nonuniform Discrete Phase Shifts for RISs With a Limited Phase Range

To maximize the received power at a user equipment, the problem of optimizing a reconfigurable intelligent surface (RIS) with a limited phase range R < 2{\pi} and nonuniform discrete phase shifts with adjustable gains is addressed. Necessary and sufficient conditions to achieve this maximization are given. These conditions are employed in two algorithms to achieve the global optimum in linear time for R {\ge} {\pi} and R < {\pi}, where R is the limited RIS phase range. With a total number of N(2K + 1) complex vector additions, it is shown for R {\ge} {\pi} and R < {\pi} that the global optimality is achieved in NK or fewer and N(K + 1) or fewer steps, respectively, where N is the number of RIS elements and K is the number of discrete phase shifts which may be placed nonuniformly over the limited phase range R. In addition, we define two quantization algorithms that we call nonuniform polar quantization (NPQ) algorithm and extended nonuniform polar quantization (ENPQ) algorithm, where the latter is a novel quantization algorithm for RISs with a significant phase range restriction, i.e., R < {\pi}. With NPQ, we provide a closed-form solution for the approximation ratio with which an arbitrary set of nonuniform discrete phase shifts can approximate the continuous solution. We also show that with a phase range limitation, equal separation among the nonuniform discrete phase shifts maximizes the normalized performance. Furthermore, we show that the gain of using K {\ge} 3 with R < {\pi}/2 and K {\ge} 4 with R < {\pi} is only marginal. Finally, we prove that when R < 2{\pi}/3, ON/OFF selection for the RIS elements brings significant performance compared to the case when the RIS elements are strictly ON.

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