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Coverage Characterization of STAR-RIS Networks: NOMA and OMA

Chenyu Wu, Yuanwei Liu, Xidong Mu, Xuemai Gu, Octavia A. Dobre

arXiv:2104.10006v1eess.SP

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.

    Source: §I · p. 1

  • 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.

    Source: §I · p. 1, A. NOMA Case · p. 3, B. OMA Case · p. 4

  • 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.

    Source: §IV · pp. 4–5, §V · p. 5

  • Takeaways & Limitations

    STAR-RIS provides wider coverage for both multiple-access schemes, while combining STAR-RIS with NOMA yields a reported win-win strategy.

    Source: §IV · p. 5, §V · p. 5

Abstract

from arXiv · show

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.Source: §I · p. 1
  • STAR-RISs simultaneously transmit and reflect incident signals, enabling full-space coverage and additional signal-propagation control.Source: §I · p. 1
  • The study formulates sum coverage range maximization for two-user NOMA and OMA under users' QoS requirements.Source: §I · p. 1
  • The formulation jointly optimizes AP resource allocation with STAR-RIS transmission and reflection coefficients.Source: §I · p. 1
  • 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.Source: §I · p. 1
  • Numerical results show that STAR-RIS coverage is significantly enhanced compared with conventional RISs for both NOMA and OMA.Source: §I · p. 1

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.Source: B. STAR-RIS Model · p. 2
  • All elements use the same amplitude coefficients to reduce information-exchange overhead between the AP and STAR-RIS.Source: B. STAR-RIS Model · p. 2
  • The transmission and reflection coefficient matrices use amplitudes √βt and √βr, with phase shifts adjusted element by element.Source: B. STAR-RIS Model · p. 2
  • Energy conservation requires the transmitted and reflected signal energies to sum to the incident signal energy, giving βr + βt = 1.Source: B. STAR-RIS Model · p. 2
  • The effective channel power gain is formed from the AP–STAR-RIS and STAR-RIS–user channels after applying the phase-shift vectors.Source: B. STAR-RIS Model · p. 2

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.Source: 1) NOMA · p. 2
  • Each NOMA user’s decoding order is determined by a binary variable, with the stronger user decoding the other user first through SIC.Source: 1) NOMA · p. 2
  • The achievable NOMA rate accounts for the other user’s signal through the decoding-order configuration.Source: 1) NOMA · p. 2
  • OMA allocates orthogonal frequency/time resources adaptively, with ω_k denoting the proportion assigned to user k.Source: 2) OMA · p. 2
  • The OMA achievable rate is expressed using the user’s allocated resource proportion and its corresponding transmission rate.Source: 2) OMA · pp. 2–3

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.Source: D. Problem Formulation · p. 3
  • 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.Source: D. Problem Formulation · p. 3
  • Separate sum-coverage-range maximization problems are formulated for NOMA and OMA under predefined user QoS requirements.Source: D. Problem Formulation · p. 3
  • The formulation includes far-field, QoS, total-power, phase-shift, energy-conservation, and SIC decoding-order constraints.Source: D. Problem Formulation · p. 3
  • The optimization jointly handles access-point resource allocation and STAR-RIS transmission and reflection coefficients.Source: D. Problem Formulation · p. 3
  • For two users, each coverage-related gain can be maximized independently by coherently combining signals from different paths.Source: D. Problem Formulation · p. 3

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.Source: A. NOMA Case · p. 3
  • The SIC constraint is transformed into a linear constraint involving the reflection coefficient and the users’ rate requirements.Source: A. NOMA Case · p. 3
  • For decoding order λ(r)=1, the channel-gain ordering constraint becomes a linear relation between β_t and β_r.Source: A. NOMA Case · p. 3
  • The relaxed NOMA problem for a fixed decoding order is convex.Source: A. NOMA Case · p. 3
  • The optimal NOMA coverage is obtained by exhaustively evaluating the two possible decoding orders.Source: A. NOMA Case · p. 4
  • The stated computational complexity for solving the NOMA problem is O(2N^3.5).Here, N1=7 is the number of variables.Source: A. NOMA Case · p. 4

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.Source: B. OMA Case · p. 4
  • With fixed time/bandwidth allocation ω_k=ω_0, the OMA subproblem is convex.Source: B. OMA Case · p. 4
  • 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.Source: Figure 2 · p. 4
  • The fixed-allocation OMA problem can be solved efficiently using convex optimization solvers such as CVX.Source: B. OMA Case · p. 4
  • The optimal OMA solution is obtained through one-dimensional search over 0≤ω_k≤1.Source: B. OMA Case · p. 4
  • The stated OMA computational complexity is O(N^3.5 log2(1/ε)), where N2=5 and ε is the search accuracy.Source: B. OMA Case · p. 4

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.Source: §IV · p. 4
  • The STAR-RIS nearly doubles coverage for both NOMA and OMA compared with conventional RISs.Source: §IV · p. 4
  • 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.Source: §IV · p. 5
  • Coverage range increases linearly with the total number of STAR-RIS elements, while its gain over conventional RISs becomes more pronounced as elements increase.Source: §IV · p. 5
  • NOMA enhances performance for STAR-RISs and conventional RISs in asymmetric channels, with a larger NOMA gain for STAR-RISs.Source: §IV · p. 5

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.Source: §V · p. 5
  • For NOMA, transforming the non-convex constraints makes the optimization problem convex.Source: §V · p. 5
  • For OMA, a one-dimensional search-based algorithm finds the optimal solution.Source: §V · p. 5
  • Simulation results show that STAR-RIS provides wider coverage in the studied two-user communication networks.Source: §V · p. 5

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