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Coverage Characterization of STAR-RIS Networks: NOMA and OMA
Chenyu Wu, Yuanwei Liu, Xidong Mu, Xuemai Gu, Octavia A. Dobre
TL;DR
The paper studies how to characterize coverage in two-user STAR-RIS networks using NOMA and OMA, addressing the coverage limitations of conventional reflecting RISs. It jointly optimizes access-point resources and STAR-RIS coefficients, using convex reformulations and search-based optimization, and reports substantially extended coverage compared with conventional RISs.
Problem
The paper examines the unstudied coverage-range superiority of STAR-RISs over reflecting-only RISs in two-user networks.
Method
The authors jointly optimize AP resource allocation and STAR-RIS transmission/reflection coefficients for NOMA and OMA, using convex reformulation and one-dimensional search.
Results
STAR-RISs significantly extend coverage compared with conventional RISs for both NOMA and OMA, with NOMA gaining substantially over OMA in STAR-RIS networks.
Takeaways & Limitations
STAR-RIS provides wider coverage for both multiple-access schemes, while combining STAR-RIS with NOMA yields a reported win-win strategy.
Abstract
from arXiv · showhide
The novel concept of simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) is investigated, where incident signals can be transmitted and reflected to users located at different sides of the surface. In particular, the fundamental coverage range of STAR-RIS aided two-user communication networks is studied. A sum coverage range maximization problem is formulated for both non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA), where the resource allocation at the access point and the transmission and reflection coefficients at the STAR-RIS are jointly optimized to satisfy the communication requirements of users. For NOMA, we transform the non-convex decoding order constraint into a linear constraint and the resulting problem is convex, which can be optimally solved. For OMA, we first show that the optimization problem for given time/frequency resource allocation is convex. Then, we employ the one dimensional search-based algorithm to obtain the optimal solution. Numerical results reveal that the coverage can be significantly extended by the STAR-RIS compared with conventional RISs.
I. INTRODUCTION
The paper addresses the limited half-space coverage of conventional reflecting RISs by characterizing STAR-RIS coverage for two-user NOMA and OMA networks. It jointly optimizes AP resource allocation and STAR-RIS transmission/reflection coefficients, with numerical results showing substantially extended coverage.
- I. INTRODUCTION: Conventional reflecting RISs serve users on the same side, limiting deployment flexibility to half-space coverage.
- I. INTRODUCTION: STAR-RISs simultaneously transmit and reflect incident signals, enabling full-space coverage and additional signal-propagation control.
- I. INTRODUCTION: The study formulates sum coverage range maximization for two-user NOMA and OMA under users' QoS requirements.
- I. INTRODUCTION: The formulation jointly optimizes AP resource allocation with STAR-RIS transmission and reflection coefficients.
- I. INTRODUCTION: For NOMA, transforming the non-convex decoding-order constraint makes the joint optimization problem convex; for OMA, a convex fixed-allocation subproblem is solved by one-dimensional search.
- I. INTRODUCTION: Numerical results show that STAR-RIS coverage is significantly enhanced compared with conventional RISs for both NOMA and OMA.
1 KAR + 1gNLoS
The STAR-RIS model lets each element operate in transmission and reflection modes while enforcing energy conservation. Common amplitude coefficients and independently optimized phase-shift vectors characterize the two user-side links.
- 1 KAR + 1gNLoS: Each STAR-RIS element can simultaneously operate in transmission and reflection modes to reconfigure propagation toward the two users.
- 1 KAR + 1gNLoS: All elements use the same amplitude coefficients to reduce information-exchange overhead between the AP and STAR-RIS.
- 1 KAR + 1gNLoS: The transmission and reflection coefficient matrices use amplitudes √βt and √βr, with phase shifts adjusted element by element.
- 1 KAR + 1gNLoS: Energy conservation requires the transmitted and reflected signal energies to sum to the incident signal energy, giving βr + βt = 1.
- 1 KAR + 1gNLoS: The effective channel power gain is formed from the AP–STAR-RIS and STAR-RIS–user channels after applying the phase-shift vectors.
1) NOMA:
The paper compares NOMA and OMA transmission schemes for two-user STAR-RIS communication, with NOMA using superposition coding and SIC-based decoding. OMA adaptively allocates orthogonal time/frequency resources between users.
- 1) NOMA:: NOMA transmits both users’ superposition-coded signals over the same time and frequency resources.
- 1) NOMA:: Each NOMA user’s decoding order is determined by a binary variable, with the stronger user decoding the other user first through SIC.
- 1) NOMA:: The achievable NOMA rate accounts for the other user’s signal through the decoding-order configuration.
- 1) NOMA:: OMA allocates orthogonal frequency/time resources adaptively, with ω_k denoting the proportion assigned to user k.
- 1) NOMA:: The OMA achievable rate is expressed using the user’s allocated resource proportion and its corresponding transmission rate.
D. Problem Formulation
The paper formulates STAR-RIS coverage characterization as a joint optimization of access-point resources and STAR-RIS transmission/reflection coefficients for NOMA and OMA. The formulation incorporates coverage allocation, QoS, physical constraints, and decoding-order requirements.
- D. Problem Formulation: The maximum STAR-RIS coverage range D0 is defined as the sum of transmission coverage Dt and reflection coverage Dr.
- D. Problem Formulation: Coverage allocation factor μ_k specifies the maximum normalized distance μ_kD0 at which user k can be served, with μ_t + μ_r = 1.
- D. Problem Formulation: Separate sum-coverage-range maximization problems are formulated for NOMA and OMA under predefined user QoS requirements.
- D. Problem Formulation: The formulation includes far-field, QoS, total-power, phase-shift, energy-conservation, and SIC decoding-order constraints.
- D. Problem Formulation: The optimization jointly handles access-point resource allocation and STAR-RIS transmission and reflection coefficients.
- D. Problem Formulation: For two users, each coverage-related gain can be maximized independently by coherently combining signals from different paths.
A. NOMA Case
The NOMA coverage problem is difficult because of binary decoding order and a non-convex SIC constraint. The paper linearizes that constraint, obtains a convex problem for each decoding order, and searches over both orders.
- A. NOMA Case: NOMA introduces binary decoding order and a non-convex SIC constraint, making the original coverage problem challenging.
- A. NOMA Case: The SIC constraint is transformed into a linear constraint involving the reflection coefficient and the users’ rate requirements.
- A. NOMA Case: For decoding order λ(r)=1, the channel-gain ordering constraint becomes a linear relation between β_t and β_r.
- A. NOMA Case: The relaxed NOMA problem for a fixed decoding order is convex.
- A. NOMA Case: The optimal NOMA coverage is obtained by exhaustively evaluating the two possible decoding orders.
- A. NOMA Case: The stated computational complexity for solving the NOMA problem is O(2N^3.5).Here, N1=7 is the number of variables.
B. OMA Case
For OMA, the paper reduces the problem using the relation between optimal amplitude coefficients and power allocation. With fixed resource allocation, the resulting subproblem is convex, and a one-dimensional search yields the optimum.
- B. OMA Case: A preliminary lemma establishes the relation between optimal STAR-RIS amplitude coefficients and power allocation.
- B. OMA Case: With fixed time/bandwidth allocation ω_k=ω_0, the OMA subproblem is convex.
- B. OMA Case: Figure 2 evaluates coverage pairs (D_t,D_r) under QoS requirements γ_k=5 bps/Hz and compares STAR-RIS results with conventional RISs.
- B. OMA Case: The fixed-allocation OMA problem can be solved efficiently using convex optimization solvers such as CVX.
- B. OMA Case: The optimal OMA solution is obtained through one-dimensional search over 0≤ω_k≤1.
- B. OMA Case: The stated OMA computational complexity is O(N^3.5 log2(1/ε)), where N2=5 and ε is the search accuracy.
IV. SIMULATION RESULTS
Simulations show that STAR-RIS substantially extends coverage for both NOMA and OMA, with gains depending on QoS requirements, allocation balance, and the number of elements.
- The comparison uses one reflecting-only RIS and one transmitting-only RIS, each with M/2 elements, as the conventional-RIS benchmark.This benchmark provides full-space coverage for comparison with the STAR-RIS.
- The STAR-RIS nearly doubles coverage for both NOMA and OMA compared with conventional RISs.
- For STAR-RIS, NOMA provides a significant coverage gain over OMA as the T user’s QoS requirement varies, unlike conventional RISs.The gain is attributed to increased channel disparity between the two users under simultaneous transmission and reflection.
- Coverage range increases linearly with the total number of STAR-RIS elements, while its gain over conventional RISs becomes more pronounced as elements increase.
- NOMA enhances performance for STAR-RISs and conventional RISs in asymmetric channels, with a larger NOMA gain for STAR-RISs.
V. CONCLUSIONS
The paper characterizes coverage in two-user STAR-RIS networks by jointly optimizing STAR-RIS coefficients and access-point resource allocation for NOMA and OMA. It derives convex formulations or search procedures and finds wider coverage with STAR-RIS.
- The study formulates sum coverage range maximization for NOMA and OMA with joint optimization of STAR-RIS coefficients and access-point resource allocation.
- For NOMA, transforming the non-convex constraints makes the optimization problem convex.
- For OMA, a one-dimensional search-based algorithm finds the optimal solution.
- Simulation results show that STAR-RIS provides wider coverage in the studied two-user communication networks.