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Joint Deployment and Multiple Access Design for Intelligent Reflecting Surface Assisted Networks

Xidong Mu, Yuanwei Liu, Li Guo, Jiaru Lin, Robert Schober

arXiv:2005.11544v2eess.SPcs.IT

TL;DR

The paper addresses joint IRS deployment and multiple-access design for improving communication between an access point and multiple users. It develops optimization methods for NOMA, FDMA, and TDMA, showing near-optimal suboptimal solutions and benefits from deployment optimization, with asymmetric placement favored for NOMA and symmetric placement for FDMA/TDMA.

  • Problem

    The paper studies maximizing users’ weighted sum rate by jointly optimizing IRS deployment, reflection coefficients, and access-point power allocation.

  • Method

    It combines monotonic optimization, semidefinite relaxation, alternating optimization, and successive convex approximation to obtain upper bounds and low-complexity suboptimal solutions.

  • Results

    The proposed suboptimal algorithms achieve near-optimal performance, while optimizing IRS deployment significantly improves performance.

  • Takeaways & Limitations

    Asymmetric IRS deployment is preferable for NOMA, whereas symmetric deployment is preferable for FDMA and TDMA.

Abstract

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The fundamental intelligent reflecting surface (IRS) deployment problem is investigated for IRS-assisted networks, where one IRS is arranged to be deployed in a specific region for assisting the communication between an access point (AP) and multiple users. Specifically, three multiple access schemes are considered, namely non-orthogonal multiple access (NOMA), frequency division multiple access (FDMA), and time division multiple access (TDMA). The weighted sum rate maximization problem for joint optimization of the deployment location and the reflection coefficients of the IRS as well as the power allocation at the AP is formulated. The non-convex optimization problems obtained for NOMA and FDMA are solved by employing monotonic optimization and semidefinite relaxation to find a performance upper bound. The problem obtained for TDMA is optimally solved by leveraging the time-selective nature of the IRS. Furthermore, for all three multiple access schemes, low-complexity suboptimal algorithms are developed by exploiting alternating optimization and successive convex approximation techniques, where a local region optimization method is applied for optimizing the IRS deployment location. Numerical results are provided to show that: 1) near-optimal performance can be achieved by the proposed suboptimal algorithms; 2) asymmetric and symmetric IRS deployment strategies are preferable for NOMA and FDMA/TDMA, respectively; 3) the performance gain achieved with IRS can be significantly improved by optimizing the deployment location.

I. INTRODUCTION … B. Motivations and Contributions

The paper motivates IRS-assisted multi-user networking by its controllable, low-energy, passive operation and develops joint deployment, reflection, and power-allocation designs across multiple access schemes. It addresses deployment-sensitive double fading with upper-bound, optimal, and low-complexity algorithms, reporting near-optimal performance and scheme-dependent deployment preferences.

  • I. INTRODUCTION: IRSs passively reconfigure reflected-signal amplitudes and phases, making the wireless environment controllable while avoiding active RF chains and self-interference.Their low-energy passive full-duplex operation motivates IRSs as a technology for future 6G networks.
  • I. INTRODUCTION: IRS-assisted NOMA provides additional degrees of freedom because reflection coefficients and deployment can more freely shape users’ decoding order.In conventional NOMA, decoding order is determined by users’ channel power gains.
  • 1) Reflection Coefficient Design in IRS-assisted Networks:: Prior work optimized IRS reflection coefficients for transmit power, energy efficiency, spectral efficiency, and interference management using mathematical and learning-based methods.These studies covered single-user and multi-user IRS-assisted systems, with discrete and continuous coefficients.
  • 2) NOMA in IRS-assisted Networks:: Existing IRS-NOMA studies examined outage, transmit-power minimization, sum rate, NOMA–OMA comparisons, capacity regions, and centralized or distributed deployment.These works considered ideal and non-ideal IRS elements and different user-pairing strategies.
  • 3) Channel Estimation Schemes for IRS-assisted Networks:: Accurate CSI acquisition is challenging because passive IRSs require estimating both direct and reflected channels, prompting specialized grouping, pattern, hierarchical, and iterative training designs.Prior work addressed OFDM, discrete phase shifts, and multi-user MISO systems while minimizing estimation error.
  • B. Motivations and Contributions: Double fading makes IRS-assisted performance sensitive to deployment location, while prior deployment studies did not optimize locations for link-level multi-user design.A single-user study found deployment should be close to either the AP or the user, but those solutions are not applicable to the paper’s multi-user focus.
  • B. Motivations and Contributions: The paper formulates WSR maximization for joint IRS deployment, reflection coefficients, and AP power allocation in a downlink multi-user network with blocked direct links, covering NOMA, FDMA, and TDMA.For NOMA and FDMA, monotonic optimization and SDR provide performance upper bounds; for TDMA, time-selective IRS operation yields closed-form optimal user reflection coefficients.
  • B. Motivations and Contributions: Low-complexity AO–SCA algorithms optimize power, reflection coefficients, and deployment location alternately, using local-region deployment optimization and efficient NOMA user ordering.Numerical results show near-optimal performance with fewer iterations than MO, greater IRS gains from location optimization, and OMA/NOMA deployment preferences that respectively equalize or separate users’ channel gains.

C. Organization and Notations · II. SYSTEM MODEL AND PROBLEM FORMULATION · A. System Model

The paper models a narrow-band, quasi-static downlink IRS-assisted multi-user network with constrained IRS deployment and Rician AP–IRS/user channels. It formulates the system around IRS-reflected links and compares NOMA with TDMA and FDMA under a weighted sum-rate optimization framework.

  • C. Organization and Notations: Section II presents the system model and weighted sum-rate maximization formulation, followed by algorithm development, complexity and performance comparisons, numerical verification, and conclusions.The paper assigns these topics to Sections II–VII, respectively.
  • C. Organization and Notations: The notation defines scalars, vectors, matrices, complex-valued vector spaces, transpose and conjugate transpose, diagonal matrices, norms, Kronecker products, Hermitian matrices, rank, trace, and positive semidefiniteness.These conventions support the mathematical system model and optimization formulation.
  • A. System Model: The considered network is a narrow-band, frequency-flat downlink with one single-antenna AP, K single-antenna users, and one IRS, while direct AP–user links are blocked.The IRS serves users in a communication dead zone, and users are static or low-mobility.
  • A. System Model: The IRS location is optimized within a predefined region Ω bounded by candidate x-, y-, and z-axis ranges, whose size is limited by coverage, LoS requirements, and available infrastructure.The deployment region can nevertheless be large because deployment design is an offline optimization problem.
  • A. System Model: The IRS uses a uniform planar array with M = MvMh passive reflecting elements, unit amplitude coefficients, and frequency-flat reflection coefficients across the signal bandwidth.The model assumes independent reflection coefficients to study maximum achievable performance, while incident-angle dependence is left for future work.
  • A. System Model: The AP–IRS and IRS–user links follow narrow-band quasi-static Rician fading, with deterministic LoS and Rayleigh NLoS components and path loss determined by the AP–IRS and IRS–user distances.The IRS-assisted link exhibits a double-fading effect, and only signals reflected once by the IRS are retained.
  • A. System Model: The system considers NOMA, in which users share time and frequency resources using successive coding at the AP and successive interference cancellation at users, alongside TDMA and FDMA.For widely distributed or high-mobility users, multiple or mobile IRSs may be required, but that deployment problem is outside the paper’s scope.

B. NOMA

The NOMA design uses SIC with an IRS-dependent decoding order and jointly optimizes AP power allocation, IRS reflection coefficients, and deployment location to maximize users’ weighted sum rate.

  • NOMA: NOMA users apply successive interference cancellation, with stronger-channel users decoding weaker-channel users’ signals before their own.For users j and k, the decoding relation requires |q_kv|^2 ≥ |q_jv|^2.
  • NOMA: Because combined channel gains depend on IRS deployment and reflection coefficients, the decoding order may be any of K! possible combinations.The set of possible decoding orders is denoted by D, with |D| = K!.
  • NOMA: The optimization maximizes users’ weighted sum rate by jointly selecting AP power allocation, IRS reflection coefficients, and IRS deployment location.The rate weight for user k is non-negative, and the formulation includes IRS deployment and unit-modulus reflection constraints.
  • NOMA: The formulation enforces NOMA decoding-order constraints and power-allocation constraints, including 0 ≤ p_k ≤ p_j when μ(k) > μ(j).The constraints govern allocated powers as well as the ordering of users’ decoding operations.

C. OMA … A. NOMA

The paper formulates OMA designs with common frequency-flat IRS coefficients for FDMA and time-selective coefficients for TDMA, then develops optimization methods for these schemes and NOMA. It also addresses deployment under unavailable NLoS channel components by separating offline location optimization from online coefficient and power optimization.

  • 1) FDMA:: FDMA serves users in equal-size orthogonal frequency bands using one common frequency-flat IRS reflection coefficient vector.The FDMA achievable-rate expression and optimization problem are formulated under this shared reflection vector.
  • 2) TDMA:: TDMA serves users in equal-size orthogonal time slots and permits different IRS reflection coefficients in each slot through time-selectivity.Unlike NOMA and FDMA, TDMA can use user-specific coefficients because only one user is served at a given time.
  • 2) TDMA:: TDMA requires repeated IRS reconfiguration, creating higher hardware complexity and potentially time-consuming reconfiguration for large IRSs.NOMA and FDMA could theoretically exploit time-selectivity too, but jointly optimizing slotwise coefficients and power is outside this work.
  • D. Discussion: Because NLoS components are unavailable before deployment, the joint optimization problems are solved only for deterministic channel coefficients dominated by LoS components.The proposed workflow first optimizes deployment offline using LoS components, then optimizes reflection coefficients and power online using the deployed location and instantaneous CSI.
  • D. Discussion: The paper focuses mainly on the offline deployment problem, while the online deployed-IRS optimization can be solved similarly and yields similar WSR when the Rician factor is large.Instantaneous CSI can be obtained using recently proposed channel-estimation methods for IRS-assisted multi-user networks.
  • III. MONOTONIC OPTIMIZATION BASED ALGORITHMS: For NOMA and FDMA, monotonic optimization transforms the non-convex problems into canonical forms solved with polyblock outer approximation and semidefinite relaxation, while TDMA is solved in closed form.The TDMA solution exploits the IRS’s time-selective nature.
  • A. NOMA: For NOMA, auxiliary variables and lifted matrix variables yield an equivalent monotonic optimization problem whose optimum lies on the feasible set’s upper boundary.The polyblock algorithm iteratively reduces containing polyblocks while preserving the feasible set and selects vertices with maximum objective value.
  • A. NOMA: The initial NOMA polyblock vertex is constructed by allocating all transmit power Pmax to one user and maximizing that user’s combined channel power gain through IRS phase selection.This initialization supports the subsequent polyblock outer approximation iterations.

3) Finding the projection of vertex z(n):

The projection of vertex z(n) is computed by bisection search over a convex relaxation solved after applying semidefinite relaxation to the rank-one constraint. This procedure yields an upper-bound benchmark, with Gaussian randomization available when the relaxed solution is not rank-one.

  • Projection algorithm: Bisection search finds the optimal α∗ by checking problem (27) for feasibility and then solving it at α∗.The resulting variables {p_k, λ_k} and V determine the projected vertex.
  • Projection algorithm: Semidefinite relaxation removes the rank-one constraint, converting problem (27) into a convex problem solvable by standard solvers such as CVX.The original problem is non-convex because of the rank-one constraint.
  • Performance bound: The relaxed solution from Algorithm 1 generally provides an upper bound for the original problem and a benchmark for validating suboptimal solutions.Relaxing the rank constraint enlarges the feasible set, explaining the upper-bound property.
  • Rank-one recovery: When V∗ is not rank-one, Gaussian randomization constructs a rank-one solution, and Cholesky decomposition obtains the reflection coefficients v.This provides a recovery procedure for the relaxed solution.
  • Post-deployment optimization: After deploying the IRS at location s∗, Algorithm 1 can re-optimize reflection coefficients and power allocation using I-CSI.The re-optimization is used to find a performance result after deployment.

B. OMA · IV. ALTERNATING OPTIMIZATION BASED ALGORITHMS · A. NOMA

For OMA, FDMA uses monotonic optimization for fixed IRS locations, while TDMA is globally optimal through independent per-user subproblems. The proposed low-complexity AO framework alternates NOMA power, reflection, and deployment optimization, using SROCR, local-region optimization, and weight/distance-based user ordering to guarantee convergence.

  • B. OMA: FDMA applies monotonic optimization for each fixed IRS deployment location, while exhaustive location search yields the optimal WSR.The FDMA formulation is transformed into a monotonic-optimization problem and solved with polyblock outer approximation.
  • B. OMA: TDMA globally optimizes the fixed-location WSR by decomposing the problem into K independent subproblems.The AP can use unique IRS reflection coefficients across time slots, and each subproblem has the optimal solution given by (25).
  • IV. ALTERNATING OPTIMIZATION BASED ALGORITHMS: The AO section replaces exponentially complex monotonic optimization and exhaustive NOMA-order/location searches with low-complexity suboptimal algorithms balancing complexity and performance.Polyblock complexity increases exponentially with the number of users, while exhaustive decoding-order search has prohibitive practical complexity.
  • A. NOMA: For NOMA, AO alternately optimizes power allocation, IRS reflection coefficients, and deployment location for a fixed decoding order.The method applies successive convex approximation to non-concave subproblems and solves the resulting convex formulations with standard solvers.
  • A. NOMA: SROCR successively finds a rank-one IRS solution and guarantees convergence to a locally optimal rank-one solution.It addresses the suboptimal rank-one construction and possible convergence issue associated with conventional SDR and Gaussian randomization.
  • A. NOMA: NOMA deployment optimization uses a local region method that keeps AP-IRS and IRS-user link angles approximately unchanged during each iteration.The local region is constrained by s − s(l) ≤ ∆, with relatively small ∆.
  • A. NOMA: The proposed NOMA user ordering scheme uses user rate weights and IRS-user distances instead of exhaustive decoding-order search, whose complexity can be O(K!).Higher-weight users receive higher decoding orders, while equal-weight users are ordered using their distances from the initial IRS location.
  • A. NOMA: Alternating optimization produces a non-decreasing objective value in every iteration and is guaranteed to converge because the WSR is finitely upper bounded.Power, reflection, and deployment variables are optimized successively, with each iteration using updated local points.

B. OMA

This subsection develops alternating-optimization algorithms for FDMA and TDMA. FDMA alternates convex power allocation, SROCR-based reflection optimization, and local-region deployment optimization, while TDMA uses prior reflection design and SCA for deployment.

  • FDMA: FDMA power allocation is a convex problem because its objective is concave in {p_k}.It can be solved using standard convex problem solvers such as CVX.
  • FDMA: FDMA reflection optimization is handled with SROCR because non-convexity arises from the rank-one constraint.The problem fits the SROCR framework and is solved via Algorithm 3.
  • FDMA: FDMA IRS deployment location is optimized using the proposed local-region optimization method and the same solution procedure as the corresponding NOMA problem.The deployment subproblem has a structure similar to problem (45) for NOMA.
  • TDMA: For TDMA, IRS reflection coefficients are designed using the earlier fixed-location formulation, while deployment location is optimized with the local-region method.The reflection-coefficient design for a given IRS location was addressed in problem (32).
  • TDMA: TDMA deployment optimization is efficiently solved using the SCA method described in the previous subsection.The details of the solution are omitted for brevity.

V. DISCUSSION OF COMPLEXITY AND PERFORMANCE

The section compares the computational complexity and performance of exhaustive monotonic-optimization and alternating-optimization algorithms for NOMA, FDMA, and TDMA. MO-based methods provide upper bounds, EX-TDMA finds the global optimum, and AO-based methods provide suboptimal solutions.

  • Algorithm definitions: MO-EX-NOMA exhaustively searches user decoding orders and IRS deployment locations, while MO-EX-FDMA and EX-TDMA use corresponding exhaustive-search designs.EX-TDMA designs optimal IRS reflection coefficients using the proposed closed-form solution.
  • Complexity analysis: The overall complexities of MO-EX-NOMA, MO-EX-FDMA, EX-TDMA, AO-NOMA, AO-FDMA, and AO-TDMA are summarized or analyzed through their component procedures and convergence iterations.The MO-based complexities are reported in Table I, while AO-FDMA and AO-TDMA can be analyzed similarly to AO-NOMA.
  • Performance comparison: MO-based solutions serve as upper bounds because semidefinite relaxation enlarges the feasible set of IRS reflection coefficients.The bound tightness is evaluated against the other proposed solutions.
  • Performance comparison: EX-TDMA finds the global optimal solution, whereas the AO-based algorithms provide suboptimal solutions for the original problems.The closed-form IRS reflection-coefficient solutions enable the global-optimality result for EX-TDMA.

VI. NUMERICAL RESULTS

Numerical results evaluate the proposed IRS deployment and multiple-access designs in a simulated four-user IRS-assisted communication scenario. The evaluation uses two rate-weight settings and averages weighted sum rates over 100 independent channel realizations.

  • Simulation setup: The simulation considers K = 4 users with a specified AP location, user placement, IRS deployment region, and UPA orientation.The AP is at b = (0, 0, 5)T meters, while user k is at uk = (25 + 5k, 0, 1.5)T meters; the scenario is illustrated in Fig. 3.
  • Simulation setup: The IRS uses Mh = 5 elements horizontally, increases Mv linearly with M, and has element spacing dI = λ.The AP-IRS and IRS-user path loss exponents are αAI = αIU = 2.2, with Rician factors βAI = βIU = 3 dB.
  • Simulation setup: Two user-rate weight vectors are evaluated: w1 = [0.1, 0.2, 0.3, 0.4] and w2 = [0.25, 0.25, 0.25, 0.25].Other parameters include ρ0 = −30 dB and noise power σ2 = −90 dBm.
  • Evaluation procedure: 100 independent channel realizations are used to obtain the average WSR after determining the IRS deployment location from LoS components.The proposed algorithms are run once for deployment-location determination and then again for each channel realization.
  • Evaluation procedure: Fig. 4 shows convergence of the proposed upper-bound and suboptimal algorithms for NOMA and FDMA.The numerical results are intended to evaluate the effectiveness of the proposed designs.

A. Selection of the Value of ∆for Local Region Optimization

The local region optimization step selects ∆ to keep AoAs/AoDs approximately constant while balancing approximation accuracy against convergence complexity. For the considered setup, the paper uses εmax = 0.01 and ∆= 0.05 meter.

  • A. Selection of the Value of ∆for Local Region Optimization: ∆ is selected so the local region optimization keeps the AoAs/AoDs approximately constant for the considered simulation setup.The method imposes a condition relating the maximum horizontal location change to the horizontal IRS distance.
  • A. Selection of the Value of ∆for Local Region Optimization: The condition requires the ratio of the maximum horizontal location change ∆ along the x-axis to the horizontal IRS distance to remain below εmax.This yields the bound ∆≤εmaxys.
  • A. Selection of the Value of ∆for Local Region Optimization: εmax = 0.01 and ∆= 0.05 meter are selected to balance approximation accuracy and convergence complexity.Smaller εmax values improve approximation accuracy but increase the iterations needed for convergence.

B. Convergence of Proposed Algorithms · C. WSR versus M and Pmax

The proposed upper-bound and suboptimal algorithms converge, with the suboptimal method reaching a similar value much faster and negligible performance loss. Across reflecting elements and transmit power, optimized deployment and AO solutions achieve near-optimal WSR, while NOMA generally outperforms OMA.

  • B. Convergence of Proposed Algorithms: The proposed upper-bound and suboptimal algorithms converge as the number of iterations increases for fixed deployment and decoding order.The evaluation uses Pmax = 30 dBm and M = 50.
  • B. Convergence of Proposed Algorithms: The proposed upper bound algorithm converges in less than 100 iterations, whereas the proposed suboptimal algorithm reaches a similar value in less than 15 iterations.The suboptimal algorithm converges significantly faster than the upper-bound algorithm.
  • B. Convergence of Proposed Algorithms: The performance gap between the upper bound and suboptimal solution is negligible, demonstrating the effectiveness of the proposed AO algorithms.This comparison concerns the proposed algorithms evaluated under the same deployment location and decoding order.
  • C. WSR versus M and Pmax: All schemes achieve higher WSR as M increases because more IRS reflecting elements provide higher passive array gains.The comparison uses Pmax = 30 dBm and user rate weight vector w1.
  • C. WSR versus M and Pmax: NOMA achieves the best performance, while TDMA outperforms FDMA because IRS time selectivity enables users to receive their best channel power gains.NOMA serves all users simultaneously in every time-frequency resource block.
  • C. WSR versus M and Pmax: The proposed suboptimal AO algorithms achieve near-optimal performance by closely approaching the proposed upper bound.The random-location benchmark incurs considerable performance loss for all three multiple access schemes, underscoring deployment optimization.
  • C. WSR versus M and Pmax: All schemes achieve higher WSR as Pmax increases, and NOMA’s gain over OMA becomes more pronounced at larger transmit powers.For M = 20, the proposed suboptimal solutions incur negligible loss relative to the upper bound, while random deployment performs worse.

D. Optimal IRS Deployment Locations of Different Transmission Schemes · E. Impact of Decoding Order Design · VII. CONCLUSIONS

The study shows that IRS deployment should be tailored to the multiple access scheme and that careful decoding-order design is important for NOMA. Joint optimization achieves near-optimal performance, while deployment-location optimization can provide significant gains, although one static IRS is limited for widely distributed or highly mobile users.

  • D. Optimal IRS Deployment Locations of Different Transmission Schemes: For w1 = [0.1, 0.2, 0.3, 0.4], NOMA places the IRS at (44.2, 5) meter, while TDMA and FDMA place it almost identically at (39.3, 5) meter.The deployment enhances users 3 and 4, which have larger rate weights.
  • D. Optimal IRS Deployment Locations of Different Transmission Schemes: NOMA favors asymmetric IRS deployment to create distinctive channel conditions, whereas OMA favors a more symmetric strategy across users.For OMA, the IRS strengthens users 3 and 4 while keeping users 1 and 2 moderately strong; for NOMA, it strengthens user 4 and weakens the others.
  • D. Optimal IRS Deployment Locations of Different Transmission Schemes: With w2 = [0.25, 0.25, 0.25, 0.25], the optimal NOMA, FDMA, and TDMA locations are (30, 5) meter, (34.3, 5) meter, and (34.7, 5) meter, respectively.The IRS is deployed closer to users 1 and 2, who are closer to the AP.
  • E. Impact of Decoding Order Design: The proposed user-ordering scheme achieves almost the same performance as exhaustive-search ordering, while random ordering suffers substantial performance loss.The comparison uses optimal exhaustive-search ordering and randomly selected ordering as benchmarks with the other variables optimized by the proposed AO algorithm.
  • E. Impact of Decoding Order Design: Careful user decoding-order design is important for IRS-assisted NOMA transmission.The WSR achieved with w1 is higher than that with w2 because the strongest user's communication rate contributes most to NOMA WSR.
  • VII. CONCLUSIONS: The paper jointly optimizes IRS deployment location, reflection coefficients, and AP power allocation to maximize WSR for NOMA, FDMA, and TDMA.MO and AO-based algorithms provide a performance upper bound and high-quality suboptimal solutions for the resulting non-convex problems.
  • VII. CONCLUSIONS: The proposed suboptimal algorithms achieve near-optimal performance, and optimizing IRS deployment location yields a significant performance gain.The results further support asymmetric deployment for NOMA and symmetric deployment for OMA.
  • VII. CONCLUSIONS: A single IRS in a quasi-static scenario may be ineffective for widely distributed or highly mobile users, motivating multiple or mobile IRSs as future research directions.The paper specifically suggests IRSs mounted on intelligent unmanned vehicles for such scenarios.
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