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Optimal Joint Power and Subcarrier Allocation for Full-Duplex Multicarrier Non-Orthogonal Multiple Access Systems

Yan Sun, Derrick Wing Kwan Ng, Zhiguo Ding, Robert Schober

arXiv:1607.02668v1cs.IT

TL;DR

The paper addresses resource allocation for FD MC-NOMA systems serving multiple HD DL and UL users simultaneously. It formulates weighted-sum-throughput maximization, develops an optimal monotonic-optimization policy and a lower-complexity iterative alternative, and reports close-to-optimal performance with throughput and fairness gains over baseline systems.

  • Problem

    The achievable spectral-efficiency improvement and optimal resource allocation design for FD MC-NOMA systems had not been established.

  • Method

    The paper solves a non-convex weighted-sum-throughput problem using monotonic optimization and proposes successive convex approximation for a lower-complexity iterative scheme.

  • Results

    The proposed suboptimal algorithm achieves close-to-optimal performance in a small number of iterations, while FD MC-NOMA substantially improves throughput over FD MC-OMA, HD MC-NOMA, and HD MC-OMA.

  • Takeaways & Limitations

    The proposed FD MC-NOMA scheme balances improved system throughput with fairness among users.

Abstract

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In this paper, we investigate resource allocation algorithm design for multicarrier non-orthogonal multiple access (MC-NOMA) systems employing a full-duplex (FD) base station (BS) for serving multiple half-duplex (HD) downlink (DL) and uplink (UL) users simultaneously. The proposed algorithm is obtained from the solution of a non-convex optimization problem for the maximization of the weighted sum system throughput. We apply monotonic optimization to develop an optimal joint power and subcarrier allocation policy. The optimal resource allocation policy serves as a system performance benchmark due to its high computational complexity. Furthermore, a suboptimal iterative scheme based on successive convex approximation is proposed to strike a balance between computational complexity and optimality. Our simulation results reveal that the proposed suboptimal algorithm achieves a close-to-optimal performance. Besides, FD MC-NOMA systems employing the proposed resource allocation algorithms provide a substantial system throughput improvement compared to conventional HD multicarrier orthogonal multiple access (MC-OMA) systems and other baseline schemes. Also, our results unveil that the proposed FD MC-NOMA systems achieve a fairer resource allocation compared to traditional HD MC-OMA systems.

I. INTRODUCTION

The paper motivates FD MC-NOMA as a way to address underused spectral resources and unresolved optimality questions in multicarrier systems. It formulates optimal and low-complexity resource-allocation approaches while accounting for interference and evaluates their throughput and fairness benefits.

  • Conventional multicarrier schemes can underutilize spectral resources when fairness assigns subcarriers exclusively to users with poor channels.
  • MC-NOMA multiplexes multiple users on shared frequency resources, using SIC to remove undesired multiuser interference.
  • Applying NOMA in multicarrier systems exploits multiuser diversity and power-domain degrees of freedom to improve spectral efficiency.
  • Prior MC-NOMA resource-allocation schemes were strictly suboptimal, leaving the maximum spectral-efficiency improvement over MC-OMA unknown.
  • FD transmission enables simultaneous DL and UL operation on the same frequency band, but SI and CCI make power allocation and scheduling important.
  • The paper formulates weighted-sum-throughput maximization for FD MC-NOMA, derives an optimal policy via monotonic optimization, and proposes a successive-convex-approximation alternative.
  • The suboptimal algorithm achieves close-to-optimal performance, while simulations show improved spectral efficiency over HD MC-OMA and the need for careful SI suppression.

II. SYSTEM MODEL

The paper models an FD MC-NOMA system with an FD BS serving HD downlink and uplink users over orthogonal subcarriers. Each subcarrier multiplexes at most two DL and two UL users, while residual interference, SIC, and global CSI assumptions shape the system model.

  • The considered network comprises an FD BS, K DL users, and J UL users, with single-antenna users and BS operation supporting simultaneous DL transmission and UL reception.
  • DL user n performs SIC on DL user m’s signal, while DL users treat UL signals as noise; the FD BS uses SIC for uplink reception.The model assumes DL users can remove other DL signals but generally cannot demodulate and decode UL signals.
  • The total bandwidth W is partitioned into NF orthogonal subcarriers, each allocated to at most two DL users and two UL users.This limit is imposed to control MUI and UL-to-DL CCI while maintaining low hardware complexity and processing delay.
  • The model includes BS-to-DL, UL-to-BS, and UL-to-DL channel coefficients, path-loss and shadowing effects, self-interference, and AWGN.
  • Increasing the number of multiplexed DL and UL users increases MUI and UL-to-DL CCI, which can degrade individual-user performance.
  • The optimal-resource-allocation analysis assumes global CSI for all network links is available at the BS to expose an FD MC-NOMA performance upper bound.

III. RESOURCE ALLOCATION PROBLEM FORMULATION

The formulation defines weighted throughput for FD MC-NOMA under specified multiplexing and SIC orders, incorporating interference, user priorities, and residual self-interference. It also shows that FD MC-OMA is a special case of the generalized throughput expression.

  • A. Weighted System Throughput: Each subcarrier can multiplex up to two DL users and two UL users, with DL user n decoding DL user m and the BS decoding UL user r before UL user t.
  • A. Weighted System Throughput: DL users generally treat UL transmissions as noise because they cannot demodulate and decode UL signals under the considered receiver assumptions.
  • A. Weighted System Throughput: The weighted sum throughput combines DL and UL rates under the selected subcarrier allocation and SIC decoding order.The binary indicator s_i^{m,n,r,t} specifies whether the corresponding DL/UL user tuple is allocated to subcarrier i.
  • A. Weighted System Throughput: The non-negative weights w_m and μ_r represent DL and UL user priorities in resource allocation and can support a notion of fairness.
  • A. Weighted System Throughput: The throughput model accounts for imperfect self-interference cancellation by representing residual SI as Gaussian distortion noise with variance proportional to received power.The cancellation quality is modeled by a small parameter ρ.
  • A. Weighted System Throughput: The SIC condition requires DL user n’s SINR for decoding user m’s signal to be at least user m’s own received SINR.
  • A. Weighted System Throughput: When the paired DL users and UL users coincide, the FD MC-NOMA throughput expression reduces to the instantaneous weighted throughput of FD MC-OMA.

B. Optimization Problem Formulation

The optimization problem maximizes weighted system throughput over joint power and subcarrier allocation. Its mixed binary and non-convex structure motivates a monotonic-optimization solution, with an extension for minimum user-rate requirements.

  • The system objective is to maximize the weighted sum of the entire system throughput.
  • The optimal policy jointly allocates transmit power and subcarriers subject to SIC, BS and UL power, and multiplexing constraints.
  • Constraints C4 and C5 ensure that each subcarrier is allocated to at most two DL users and two UL users, respectively.
  • The formulation is mixed combinatorial and non-convex because subcarrier allocation uses binary variables and the objective function is non-convex.
  • The proposed strategy exploits problem monotonicity to design an optimal resource allocation method.
  • The optimization framework can incorporate minimum required transmission rates for individual DL and UL users with more involved notation.

IV. SOLUTION OF THE OPTIMIZATION PROBLEM

The paper solves the non-convex allocation problem optimally through monotonic optimization and outer polyblock approximation, then proposes a lower-complexity suboptimal scheme. The optimal method provides a benchmark, while the suboptimal method balances complexity and performance.

  • IV. SOLUTION OF THE OPTIMIZATION PROBLEM: Monotonic optimization transforms the allocation problem into a form whose increasing objective reaches an optimum on the feasible-set boundary.
  • B. Joint Power and Subcarrier Allocation Algorithm: The outer polyblock algorithm constructs nested polyblocks containing the feasible set, projects selected vertices onto the feasible boundary, and iteratively refines the approximation.
  • B. Joint Power and Subcarrier Allocation Algorithm: Each iteration replaces a selected vertex with D new vertices generated using its feasible-set projection and coordinate unit vectors.
  • B. Joint Power and Subcarrier Allocation Algorithm: The projection step is a fractional programming problem solved by the Dinkelbach algorithm, with the resulting convex problem solvable using standard convex-programming solvers.
  • B. Joint Power and Subcarrier Allocation Algorithm: The optimal vertex determines the optimal subcarrier allocation by restoring allocation indicators according to the prescribed variable mapping.
  • B. Joint Power and Subcarrier Allocation Algorithm: The monotonic-optimization algorithm achieves one globally optimal solution in a finite number of iterations and supplies an upper bound for suboptimal methods.
  • B. Joint Power and Subcarrier Allocation Algorithm: Its computational complexity grows exponentially with the number of vertices D used in each iteration.
  • B. Joint Power and Subcarrier Allocation Algorithm: A suboptimal iterative resource-allocation scheme is proposed with polynomial-time complexity to balance complexity and system performance, achieving close-to-optimal simulation performance.

C. Suboptimal Solution

The suboptimal scheme transforms the non-convex allocation problem and repeatedly solves convex approximations to obtain a locally optimal solution with polynomial-time complexity.

  • Suboptimal scheme: The proposed suboptimal scheme targets lower computational complexity while retaining a locally optimal resource allocation solution.It addresses the non-convex optimization arising from the objective and allocation constraints.
  • Problem reformulation: The integer subcarrier-allocation constraint is reformulated using continuous variables constrained between zero and one.The reformulation enables subsequent convex-approximation steps.
  • Problem reformulation: A sufficiently large penalty factor η penalizes non-binary allocation variables in the reformulated optimization problem.The penalized problem is stated as equivalent to the original formulation.
  • Successive convex approximation: The reformulated problem belongs to difference-of-convex programming because its objective remains non-convex.The method uses convex functions and affine global under-estimators within successive convex approximation.
  • Successive convex approximation: Algorithm 3 iteratively solves a convex upper-bound problem, updates the resource allocation, and generates a sequence of feasible solutions.Each iteration solves problem (40) and stores the resulting allocation before updating the next iterate.
  • Convergence and complexity: The proposed suboptimal iterative algorithm converges to a locally optimal solution of (40) with polynomial time computational complexity.Convex subproblems can be solved efficiently by standard convex-program solvers.

V. SIMULATION RESULTS

The simulations evaluate the proposed resource allocation schemes in a single-cell FD MC-NOMA setting and compare them with three FD or HD baseline configurations.

  • Simulation setup: The simulation model uses a single cell with ring-shaped user regions, with DL and UL users randomly and uniformly distributed.The BS is located at the cell center, and the stated region radii are 30 meters and 600 meters.
  • Simulation setup: User weights are based on normalized distance to the FD BS to provide resource-allocation fairness, especially for cell-edge users.The weighting choice is intended to address poorer conditions for cell-edge users.
  • Simulation setup: The fading model includes independent Rayleigh channels and independent Rician self-interference channels with a 5 dB Rician factor.Results are averaged over different path-loss and multipath-fading realizations.
  • Baseline schemes: The baselines include an FD MC-OMA scheme, an HD MC-NOMA scheme with orthogonal DL and UL time intervals, and a traditional HD MC-OMA scheme.The FD MC-OMA baseline permits at most one DL and one UL user per subcarrier, while the HD schemes separate transmissions in time or radio resources.
  • Baseline schemes: The proposed framework jointly optimizes subcarrier, DL-power, and UL-power allocation for the compared schemes where specified.The FD MC-OMA baseline is treated as a special case of the proposed optimal resource allocation scheme.
  • Baseline schemes: For fair comparison, throughputs of the HD baseline schemes are divided by two because transmission occurs in only one direction at a time.The baseline allocation policies use algorithms specified for their respective DL and UL settings.

A. Convergence of Proposed Algorithms

Both proposed algorithms converge to the optimal solution across different DL and UL user counts, while the suboptimal algorithm converges substantially faster.

  • Convergence: Both proposed optimal and suboptimal algorithms converge to the optimal solution for different values of K and J.The convergence comparison varies the numbers of DL and UL users.
  • Convergence: For K = 12 and J = 12, the optimal algorithm converges in less than 300 iterations on average, whereas the suboptimal algorithm reaches a stationary point after 30 iterations on average.These iteration counts illustrate the computational advantage of the suboptimal approach.
  • Convergence: The proposed suboptimal algorithm converges significantly faster than the proposed optimal algorithm.The optimal algorithm searches a larger feasible solution space as the user count increases.

B. Average System Throughput versus Maximum Transmit Power

Average system throughput generally increases with the maximum DL transmit power, but self-interference limits the UL benefit; the proposed schemes outperform the baselines and approach the optimal benchmark.

  • Throughput versus power: Average system throughput increases monotonically with the maximum DL transmit power because additional power can improve DL-user SINR.The improvement is achieved through optimal allocation of the available transmit power.
  • Throughput versus power: Higher DL transmit power makes self-interference more severe, decreasing UL throughput and partially offsetting the DL-throughput improvement.The resulting throughput trend exhibits diminishing returns at higher DL transmit powers.
  • Scheme comparison: The proposed suboptimal algorithm closely approaches the performance of the proposed optimal power and subcarrier allocation scheme.This supports its use as a lower-complexity alternative to the optimal benchmark.
  • Scheme comparison: Baseline scheme 3 has the lowest spectral efficiency because it assigns radio resources orthogonally in both time and frequency.Baseline scheme 2 also loses spectral efficiency by separating DL and UL transmissions in time.
  • Scheme comparison: At a target system throughput of 6 bit/s/Hz, the proposed schemes enable power reductions of more than 4 dB, 8 dB, and 12 dB compared with baseline schemes 1, 2, and 3.The reported reductions correspond to the same three baseline schemes.

C. Average System Throughput versus Total Number of Users

Average system throughput increases with the total user population, and the proposed FD MC-NOMA schemes scale faster than the baseline schemes. The proposed optimal and suboptimal schemes also outperform the baselines while the suboptimal scheme remains close to optimal.

  • Average system throughput increases with the total number of users because all schemes exploit multiuser diversity.
  • The proposed schemes grow faster with increasing users than all baseline schemes by exploiting frequency-domain and power-domain resources.
  • The proposed schemes achieve higher throughput than FD MC-OMA and other baselines, while HD MC-OMA has the lowest average throughput.
  • The suboptimal scheme achieves similar performance to the optimal scheme even with a relatively large number of users.
  • Scheduled users increase monotonically but sub-linearly with total users because poorly conditioned users may receive no resources.
  • At K + J = 100, the proposed schemes serve 70%, 96%, and 226% more users than baseline schemes 1, 2, and 3, respectively.

E. Fairness versus Total Number of Users

Fairness declines as the user population grows, reflecting stronger competition and more users with poor channels or lower priorities. The proposed FD MC-NOMA schemes nonetheless achieve higher fairness than the baselines and retain near-optimal throughput with lower-complexity allocation.

  • Fairness indices decrease as the total number of users increases because competition becomes more intense.
  • More users with poor channel conditions or lower priorities may remain unserved as the population grows.
  • The proposed schemes achieve higher fairness than baseline schemes 1 and 3 because NOMA multiplexes more users per subcarrier.
  • The proposed schemes exceed baseline scheme 2 in fairness because simultaneous DL and UL service distributes per-user throughput more evenly.
  • The proposed suboptimal scheme achieves the same fairness index as the optimal scheme even for large user populations.
  • As SI cancellation worsens, proposed-scheme throughput decreases monotonically and accelerates beyond ρ = −110 dB because residual SI becomes the bottleneck.
  • Monotonic optimization yields an optimal allocation benchmark, while successive convex approximation provides a lower-complexity alternative with close-to-optimal performance.
  • The proposed FD MC-NOMA scheme provides substantial throughput improvement over FD MC-OMA, HD MC-NOMA, and HD MC-OMA while balancing throughput and fairness.

APPENDIX-PROOF OF THEOREM 1

Theorem 1 is established by comparing equivalent primal and dual formulations through weak and abstract Lagrangian duality. The proof concludes that the primal-dual gap is zero under the stated conditions.

  • The proof begins by applying abstract Lagrangian duality and defining two cases for the dual problem.
  • Weak duality supplies one inequality between the equivalent primal and dual problems.
  • The dual objective is bounded above by the optimal value of the primal problem through the monotonicity and boundedness of Θ(η).
  • Feasibility of the constructed solution is used to establish the reverse inequality between the equivalent primal and dual formulations.
  • The gap between the equivalent primal problem (47) and dual problem (48) is zero, confirming Theorem 1.
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