Source-linked AI summary
Reconfigurable Intelligent Surface (RIS) Assisted Wireless Coverage Extension: RIS Orientation and Location Optimization
Shuhao Zeng, Hongliang Zhang, Boya Di, Zhu Han, Lingyang Song
TL;DR
The paper addresses how to deploy an RIS to maximize coverage in a one-BS, one-UE downlink network, beyond using a fixed RIS location. It analyzes coverage, formulates placement optimization over orientation and BS–RIS distance, and proposes CMA; analysis and simulations identify a vertical orientation and moderate BS–RIS distance as preferred.
Problem
Existing RIS studies extend coverage for a given RIS location, but how deployment can further maximize cell coverage remains unstudied.
Method
The paper analyzes a one-BS, one-UE RIS-assisted downlink network and proposes CMA to optimize RIS orientation and horizontal BS–RIS distance.
Results
The optimal RIS orientation is ψ = π/2, meaning the RIS is vertical to the direction from the BS to the RIS, while the preferred BS–RIS distance is moderate.
Takeaways & Limitations
RIS placement should use the vertical orientation and a moderate distance from the BS to maximize the analyzed cell coverage.
Abstract
from arXiv · showhide
Recently, reconfigurable intelligent surfaces (RIS) have attracted a lot of attention due to their capability of extending cell coverage by reflecting signals toward the receiver. In this letter, we analyze the coverage of a downlink RIS-assisted network with one base station (BS) and one user equipment (UE). Since the RIS orientation and the horizontal distance between the RIS and the BS have a significant influence on the cell coverage, we formulate an RIS placement optimization problem to maximize the cell coverage by optimizing the RIS orientation and horizontal distance. To solve the formulated problem, a coverage maximization algorithm (CMA) is proposed, where a closed-form optimal RIS orientation is obtained. Numerical results verify our analysis.
I. INTRODUCTION
The paper studies RIS-assisted coverage extension and addresses the previously unstudied problem of optimizing RIS deployment rather than assuming a fixed location. It introduces a one-BS, one-UE model and a coverage maximization algorithm that jointly considers RIS orientation and BS–RIS horizontal distance.
- RIS elements dynamically tune their electromagnetic responses through PIN diodes to optimize received signal strength.
- Prior RIS studies considered point-to-point and multi-user networks, including coverage, SNR, delay outage, sum-rate, and energy-efficiency objectives.
- Existing works extended coverage for a given RIS location, leaving deployment optimization for maximizing cell coverage unstudied.
- The considered network contains one BS, one UE, and an RIS-assisted downlink cellular link.
- The proposed CMA derives a closed-form optimal RIS orientation and optimizes the horizontal BS–RIS distance using the interior point method.
B. Channel Model
The channel model combines MN RIS-mediated channels with a direct BS–UE link and expresses received SNR from their aggregate channel. Far-field assumptions make distances and pathloss approximately common across RIS elements.
- The BS–UE channel comprises MN RIS-based paths, each passing through one RIS element, plus a direct link.
- The RIS channel gain uses wavelength, antenna gain, element dimensions, pathloss exponent, and distances between the BS, RIS elements, and UE.
- Under far-field assumptions, BS-to-element and element-to-UE distances are approximated by center distances D and d, making RIS-element pathloss common.
- The received SNR is γ = P|h|2/σ2, where P is BS transmit power and σ2 is received AWGN variance.
- For average performance, RIS-channel small-scale fading is averaged, while fading across different RIS elements is assumed independent.
III. CELL COVERAGE ANALYSIS
The coverage analysis defines coverage through an SNR threshold and first optimizes RIS phase shifts to maximize SNR before deriving the resulting cell coverage.
- Cell coverage is the area where the UE received SNR satisfies γ ≥ γth = γsLmar.
- The threshold combines UE sensitivity γs with the penetration-loss margin Lmar.
- The analysis first selects RIS phase shifts that maximize SNR, then derives cell coverage.
- Theorem 1 states that the optimized phase shifts maximize the SNR, whose maximum value is given analytically.
- The proof identifies simultaneous maximization of the RIS coherent term and direct-link term under the selected phase shifts.
B. Cell Coverage Analysis
The paper derives directional coverage by comparing the SNR-based distance threshold with the geometric same-side constraint imposed by RIS orientation. Different angular regions therefore have different coverage limits.
- Cell Coverage in a given Direction: Directional coverage is analyzed using angle φ and the BS–UE horizontal distance dh_BU, with dth(φ) denoting the distance where γ reaches γth.
- Cell Coverage in a given Direction: When the UE is sufficiently far from the BS, SNR decreases with distance and approaches zero; the threshold-crossing distance is unique.
- Cell Coverage in a given Direction: When φ lies in [0, ψ) ∪ (ψ + π, 2π), the UE–BS distance must also satisfy the geometric bound dh_BU ≤ l(φ).
- Cell Coverage in a given Direction: The geometric distance l(φ) is Dh/(cos(φ) − sin(φ)cot(ψ)), where Dh is the BS–RIS horizontal distance.
- Cell Coverage in a given Direction: For φ ∈ [ψ, ψ + π], the UE and BS are always on the same side of the RIS, so the directional coverage follows the SNR-based condition.
- Cell Coverage in a given Direction: The curves dth(φ) and l(φ) intersect at two angles, φu and φl, and dth(φ) exceeds l(φ) only outside the interval between them.
2) Area of cell coverage:
The cell-coverage area is derived by integrating the squared coverage radius over all angular directions, using direction-dependent edge distances.
- The area of the cell coverage is derived in Theorem 2.The proof expresses coverage area as an angular integral and selects the limiting distance by direction.
- Coverage uses l(φ) outside the RIS-influenced angular interval and dth(φ) inside it.
IV. RIS PLACEMENT OPTIMIZATION
The section formulates a coverage maximization problem and proposes the CMA to solve it.
- The coverage maximization problem is formulated before designing the coverage maximization algorithm.
- The coverage maximization algorithm (CMA) is proposed to solve the formulated problem.
A. Coverage Maximization Problem Formulation
The coverage objective is to maximize the cell-coverage area by jointly optimizing the RIS–BS horizontal distance and RIS orientation.
- The optimization jointly chooses the RIS–BS horizontal distance Dh and RIS orientation ψ.
- The objective is to maximize the cell-coverage area S.
B. Coverage Maximization Algorithm Design
The algorithm first obtains a closed-form optimal RIS orientation, then transforms horizontal-distance optimization into a constrained finite-dimensional problem solved numerically.
- Closed-form orientation: The optimal RIS orientation is ψ = π/2 regardless of the horizontal distance.This places the RIS vertical to the direction from the BS to the RIS.
- Horizontal-distance optimization: With the optimal orientation fixed, the algorithm optimizes the horizontal distance Dh.
- Problem transformation: The integral objective is discretized into K equal parts to avoid introducing infinitely many optimization variables.Each part has width ∆ = (φu − φl)/K.
- Problem transformation: The discretized problem imposes g(φl + i∆, yi) = γth for i = 0, . . . , K.The constraint is derived from equation (9).
- Optimality: The transformed problem is equivalent to the horizontal-distance problem, so its solution is optimal for RIS deployment.
- Numerical solution: The constrained problem can be solved with an interior-point method using a logarithmic barrier and Newton iterations.
V. SIMULATION RESULTS
Simulations validate the theoretical coverage analysis and show that coverage depends strongly on RIS placement, transmit power, and the number of RIS elements. The proposed CMA outperforms the random algorithm and the BS side scheme.
- Simulation validation: Theoretical and simulated coverage results match for RIS orientation and horizontal distance, validating the analytical derivation.The orientation result uses 10^5 Monte Carlo simulations; the horizontal-distance results are also reported as consistent.
- RIS orientation: The optimal RIS orientation is ψ = π, consistent with Theorem 3.
- RIS placement: Coverage first increases and then decreases as the RIS moves away from the BS, so the RIS should be placed at a moderate distance.The increase is attributed to a higher reflection coefficient, while the later degradation follows the negative relationship between received SNR and BS–RIS distance.
- RIS placement: The optimal RIS deployment is close to the cell edge, benefiting cell-edge UEs.
- Transmit power: Coverage increases with transmit power because the received SNR improves.
- Algorithm comparison: The CMA achieves larger coverage than both the random algorithm and the BS side scheme, while more RIS elements further increase coverage.The BS side scheme does not account for the incidence-angle influence on the reflection coefficient.
VI. CONCLUSION
The paper analyzes a one-BS, one-UE downlink RIS-assisted network and proposes CMA to optimize RIS placement for cell coverage. The supported deployment conclusion is a vertical RIS orientation and moderate BS–RIS distance.
- VI. CONCLUSION: The considered network contains one base station and one user equipment in a downlink RIS-assisted setting.
- VI. CONCLUSION: CMA maximizes cell coverage by optimizing RIS placement.
- VI. CONCLUSION: The RIS should be deployed vertical to the direction from the BS to the RIS and placed at a moderate distance from the BS.
APPENDIX A PROOF OF REMARK 1
The appendix compares coverage regions under different RIS orientations and uses geometric and SNR arguments to establish the optimal orientation. It also characterizes how angular geometry affects coverage boundaries.
- Geometric coverage analysis: As φ approaches π, dth(φ) decreases while l(φ) increases; the larger UE–RIS distance lowers SNR and reduces dth(φ).
- Geometric coverage analysis: When φ = ψ or ψ + π, l(φ) tends to infinity while dth(φ) remains limited; when φ = 0, l(φ) = Dh < dth(φ).
- Geometric coverage analysis: The boundary equation dth(φ) = l(φ) has two solutions, and dth(φ) exceeds l(φ) only outside the interval [φl, φu].
- Orientation comparison: The coverage region under ψ* is compared with that under another orientation ψ(0) through sector areas S* and S(0).The proof reduces the comparison to the corresponding sector areas ΔS* and ΔS(0).
- Orientation comparison: Because equal-threshold-SNR points are closer to the RIS under ψ(0), r(0) < r*, yielding ΔS(0) < ΔS* and S(0) ≤ S*.