Source-linked AI summary
Large Intelligent Surface-Assisted Wireless Communication Exploiting Statistical CSI
Yu Han, Wankai Tang, Shi Jin, Chao-Kai Wen, Xiaoli Ma
TL;DR
The paper studies LIS-assisted large-scale antenna systems as supplementary wireless links and examines how phase shifts affect ergodic capacity. It develops a capacity approximation and statistical-CSI phase-shift design, with numerical results supporting maximum ergodic capacity and low degradation using 2-bit quantization.
Problem
The paper examines how LIS-assisted supplementary links and phase shifts affect ergodic capacity in large-scale antenna systems.
Method
The paper formulates a tight ergodic-capacity approximation, designs optimal LIS phase shifts using statistical channel state information, and derives quantization-bit requirements for acceptable degradation.
Results
2-bit quantization sufficiently guarantees high capacity while limiting capacity degradation to less than 1 bit/s/Hz, and the proposed design outperforms random phase shifts.
Takeaways & Limitations
The proposed statistical-CSI phase-shift design and 2-bit quantization provide high-capacity LIS operation with limited quantization degradation.
Abstract
from arXiv · showhide
Large intelligent surface (LIS)-assisted wireless communications have drawn attention worldwide. With the use of low-cost LIS on building walls, signals can be reflected by the LIS and sent out along desired directions by controlling its phases, thereby providing supplementary links for wireless communication systems. In this study, we evaluate the performance of an LIS-assisted large-scale antenna system by formulating a tight approximation of the ergodic capacity and investigate the effect of the phase shifts on the ergodic capacity in different propagation scenarios. In particular, we propose an optimal phase shift design based on the ergodic capacity approximation and statistical channel state information. Furthermore, we derive the requirement on the quantization bits of the LIS to promise an acceptable capacity degradation. Numerical results show that using the proposed phase shift design can achieve the maximum ergodic capacity, and a 2-bit quantizer is sufficient to ensure capacity degradation of no more than 1 bit/s/Hz.
I. INTRODUCTION
The paper motivates LIS reflector arrays as economical supplementary links for blocked wireless paths and studies their capacity benefits in large-scale antenna systems. It develops an approximation, phase-shift design, and quantization requirement for LIS-assisted communication.
- Motivation: Reflector arrays provide economical supplementary links compared with amplify-and-forward relays.Their reflected signals are not amplified, but they improve the propagation environment with extremely low power consumption and avoid self-interference concerns associated with half-duplex relaying.
- LIS-assisted links: LIS reflector arrays can support communication when the direct line-of-sight path between the base station and user is absent.The LIS adjusts incident-signal phases to reflect signals toward desired spatial directions.
- Approach: The study formulates a tight approximation of ergodic capacity for the LIS-assisted system under Rician fading.The analysis also examines how phase-shift amount affects ergodic capacity across propagation conditions.
- Approach: The proposed optimal phase-shift design maximizes ergodic capacity using statistical channel state information.The design addresses the LIS phase shifts rather than requiring instantaneous channel-state information.
- Results: 2-bit quantization ensures capacity degradation of less than 1 bit/s/Hz.Numerical results also verify the approximation’s tightness and the effectiveness of the proposed design.
II. SYSTEM MODEL
The system model considers a single-cell downlink in which a large-antenna base station communicates with a single-antenna user directly or through an LIS reflector array. The direct channel is modeled as Rayleigh fading, while the two LIS-related channels use Rician fading, and long-term LIS phases are designed from statistical CSI.
- System configuration: The modeled system contains an M-element BS ULA, an N-element LIS ULA, and a single-antenna user.The LIS is positioned between the BS and user as a reflector array.
- Channel model: The direct BS-user channel is modeled as Rayleigh fading because its LoS path may be blocked by surrounding obstacles.Its channel elements are i.i.d. zero-mean, unit-variance complex Gaussian variables.
- Channel model: The BS-LIS and LIS-user channels are modeled as Rician fading because practical LoS components exist on both links.Each channel combines a fixed LoS component with an i.i.d. complex Gaussian NLoS component.
- Signal processing: The LIS applies diagonal phase shifts to the reflected signal, and maximum-ratio transmission is used at the BS to enhance signal power.The phase matrix is also interpreted as beamforming weights introduced by the LIS.
- Phase-shift design: The optimal LIS phase matrix is a long-term design based on statistical CSI and remains unchanged within the channel coherence time.The BS estimates the combined direct and assistant channel using pilots from the user.
III. ERGODIC CAPACITY ANALYSIS
The paper first analyzes ergodic capacity theoretically and then evaluates how different LIS phase-shift amounts affect capacity under different propagation conditions.
- Capacity analysis: The analysis begins with a theoretical ergodic-capacity evaluation for the LIS-assisted large-scale antenna system.This analysis precedes the phase-shift design stage.
- Capacity analysis: The study compares the effects of different phase-shift amounts under different propagation conditions.These comparisons provide the basis for subsequent LIS phase-shift optimization.
A. Approximation of Ergodic Capacity
The section develops an approximation of the ergodic capacity for the LIS-assisted large-scale antenna system and identifies the channel and phase-shift quantities governing it.
- A. Approximation of Ergodic Capacity: Theorem 1 approximates the ergodic capacity of the LIS-assisted large-scale antenna system.The approximation is introduced to provide direct insight into ergodic-capacity behavior.
- A. Approximation of Ergodic Capacity: The derivation obtains γ2 = (K1 + K2 + 1)/((K1 + 1)(K2 + 1)) from the channel-statistics terms.The supplied derivation proceeds through the channel expressions and substitutions leading to the approximation.
- A. Approximation of Ergodic Capacity: The approximation uses E{log2(1 + x)} ≈ log2(1 + E{x}) and evaluates E{∥h2ΦH1 + g∥2}.The derivation decomposes the squared channel norm and uses zero-mean, mutually independent components for several terms.
- A. Approximation of Ergodic Capacity: The resulting capacity is determined by γ1, γ2, and ∥¯h2Φ ¯H1∥2 when transmit power and LoS components remain unchanged.γ1 and γ2 are further determined by the Rician-K factors, while the norm also depends on LIS phase shifts.
B. Effects of Rician-K Factors and Phase Shifts
The effects of Rician-K factors and LIS phase shifts depend on propagation conditions. Phase shifts matter strongly when LoS components are present, but not when either assisted link is Rayleigh faded.
- Case 1: When either H1 or h2 is under Rayleigh fading, capacity is proportional to the antenna and LIS element counts but independent of LIS phase shifts.The phase-shift independence is attributed to spatial isotropy in the assistant channel; even 0-bit phase shifting is sufficient.
- Effects of Rician-K Factors and Phase Shifts: In spatially directional propagation, capacity increases in proportion to ∥¯h2Φ ¯H1∥2 and is sensitive to beamforming weights.Proper phase shifts can beamform the signal along the assistant channel’s main lobe.
- Effects of Rician-K Factors and Phase Shifts: When phase shifts produce ∥¯h2Φ ¯H1∥2 ≫ N, extreme Rician fading yields considerably higher capacity than Rayleigh fading.The comparison reverses when ∥¯h2Φ ¯H1∥2 < N.
- Effects of Rician-K Factors and Phase Shifts: In Rician fading, phase shifts should be carefully designed to exploit the assistant channel’s LoS components.The section states that the LoS contribution can otherwise make Rician capacity inferior to Rayleigh capacity.
IV. PHASE SHIFT DESIGN OF REFLECTOR ARRAY
The paper proposes designing the LIS phase-shift matrix from statistical CSI to maximize ergodic capacity and specifies a quantization-bit criterion for acceptable degradation.
- IV. PHASE SHIFT DESIGN OF REFLECTOR ARRAY: The proposed design maximizes ergodic capacity by exploiting statistical CSI.The phase-shift matrix is designed for the LIS-assisted large-scale antenna system.
- IV. PHASE SHIFT DESIGN OF REFLECTOR ARRAY: The paper provides a quantization-bit criterion to ensure acceptable ergodic-capacity degradation.The criterion is explicitly formulated for the LIS-assisted large-scale antenna system.
A. Optimal Phase Shift Design
The optimal phase-shift design maximizes the LoS-assisted term |z|2, aligning reflected signals with the assistant channel. Proper alignment makes LoS beneficial and increases capacity with the number of reflectors.
- A. Optimal Phase Shift Design: Maximizing ergodic capacity can be translated into maximizing |z|2 because the relevant array-norm factor is constant.The optimal phase-shift matrix therefore maximizes the magnitude of the reflected LoS combination.
- A. Optimal Phase Shift Design: The ergodic capacity depends on θAoA,1 and θAoD,2 but is independent of θAoD,1, so phase shifts affect only links directly connected by the LIS.The reflected LoS component can be completely blocked when phase shifts are inadequately set and |z| = 0.
- A. Optimal Phase Shift Design: If |z| = 0, additional reflectors contribute only limited capacity through the NLoS component because LoS power is wasted.This result reinforces the significance of proper phase-shift design.
- A. Optimal Phase Shift Design: Proper phase shifts reflect the signal along the assistant channel’s LoS component, making LoS beneficial and increasing capacity proportionally to N.Increasing the number of reflectors enhances receiving power at the user and further improves ergodic capacity.
B. Influence of Bit Quantization
The paper models phase-shift quantization, derives a bit requirement for bounded ergodic-capacity degradation, and shows that larger system resources reduce sensitivity to quantization.
- The LIS phase shift amount is constrained by quantization bits, with each theoretical phase shift quantized to its nearest available value.
- Theorem 2 specifies the quantization-bit requirement for limiting degradation to ξ bits/s/Hz relative to full-resolution phase shifts.
- The paper notes that acquiring θAoA,1 and θAoD,2 at the LIS remains future work.
- Quantization causes capacity degradation because the quantized-phase capacity satisfies CBQ ≤ Cmax.
- Under Rayleigh fading, the bit requirement holds for any B, whereas with fixed α > 0 and zero allowable degradation, B must be infinite.
- The minimum required B decreases as transmit power P, antenna-array size M, or LIS size N increases.
- 2-bit quantization limits degradation to less than 1 bit/s/Hz in the stated examples, including M = N = 64 at P = 0 dB with ξ = 1.
V. NUMERICAL RESULTS
Numerical experiments validate the ergodic-capacity approximation and show that optimized phase shifts outperform random shifts. They also confirm that 2-bit quantization keeps degradation below 1 bit/s/Hz.
- 10,000 Monte Carlo simulations show that the ergodic-capacity approximations closely match the simulated results.
- The approximation gap diminishes as the Rician K-factor increases, and capacity approaches a constant as the K-factor tends to infinity.
- The results support designing phase shifts from the ergodic-capacity approximation.
- Optimal phase shifts achieve higher ergodic capacity than random phase shifts, with the advantage increasing as the number of reflectors grows.
- Under Rician fading, random phase shifts can yield lower ergodic capacity than Rayleigh fading because inadequate shifts may damage the assistant channel.
- 1-bit quantization decreases ergodic capacity by more than 1 bit/s/Hz.
- 2-bit quantization keeps performance degradation below 1 bit/s/Hz, consistent with Theorem 2.
VI. CONCLUSION
The study develops an approximation-based analysis of LIS-assisted ergodic capacity, designs optimal phase shifts, and derives quantization requirements. Simulations validate the approximation and show substantial benefits from designed shifts and 2-bit quantization.
- The study evaluates LIS-assisted large-scale antenna capacity by formulating an ergodic-capacity approximation.
- The proposed optimal phase-shift design maximizes ergodic capacity using the derived approximation.
- The paper derives a quantization-bit requirement for acceptable capacity degradation.
- Monte Carlo simulations verify approximation tightness, while designed phase shifts considerably outperform random phase shifts.
- 2-bit quantization sufficiently guarantees high capacity in accordance with the analytical results.