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Optimal Joint Power and Subcarrier Allocation for MC-NOMA Systems
Yan Sun, Derrick Wing Kwan Ng, Zhiguo Ding, Robert Schober
TL;DR
MC-NOMA resource allocation must jointly manage power and subcarrier assignment to maximize weighted system throughput under cochannel interference. The paper solves this non-convex problem optimally with monotonic optimization and proposes a lower-complexity alternative. Simulations show close-to-optimal performance for the suboptimal scheme and substantial throughput improvement over MC-OMA.
Problem
MC-NOMA requires careful joint power allocation and subcarrier assignment because multiplexing users on each subcarrier creates cochannel interference.
Method
The paper formulates weighted-throughput maximization as a non-convex optimization problem, solves it with monotonic optimization, and proposes a low-complexity suboptimal scheme.
Results
The suboptimal scheme achieves close-to-optimal performance, while the proposed MC-NOMA schemes substantially outperform conventional MC-OMA in system throughput.
Takeaways & Limitations
The optimal allocation policy provides a performance benchmark, and efficient resource-allocation optimization is important for MC-NOMA system performance.
Abstract
from arXiv · showhide
In this paper, we investigate the resource allocation algorithm design for multicarrier non-orthogonal multiple access (MC-NOMA) systems. The proposed algorithm is obtained from the solution of a non-convex optimization problem for the maximization of the weighted system throughput. We employ monotonic optimization to develop the optimal joint power and subcarrier allocation policy. The optimal resource allocation policy serves as a performance benchmark due to its high complexity. Furthermore, to strike a balance between computational complexity and optimality, a suboptimal scheme with low computational complexity is proposed. Our simulation results reveal that the suboptimal algorithm achieves a close-to-optimal performance and MC-NOMA employing the proposed resource allocation algorithm provides a substantial system throughput improvement compared to conventional multicarrier orthogonal multiple access (MC-OMA).
I. INTRODUCTION
MC-NOMA multiplexes multiple users on shared subcarriers to improve spectral efficiency, but requires careful power allocation and user scheduling because of cochannel interference. The paper develops optimal and low-complexity resource-allocation approaches for this setting.
- MC-NOMA multiplexes multiple users on the same frequency resource, using successive interference cancellation to remove undesired interference.This contrasts with conventional multicarrier systems, where each subcarrier is allocated to at most one user.
- Careful power allocation and user scheduling are necessary in MC-NOMA because multiplexing users creates unavoidable cochannel interference.
- The proposed formulation maximizes weighted system throughput through joint power and subcarrier allocation for MC-NOMA systems.
- The paper considers a downlink single-antenna MC-NOMA system with a base station, K users, and orthogonal subcarriers.
III. PROBLEM FORMULATION
This section defines the performance measure and formulates the joint power and subcarrier allocation problem for the considered MC-NOMA system.
- The section first defines the adopted performance measure and then formulates the power and subcarrier allocation problem.
- The formulation targets joint power and subcarrier allocation for the considered MC-NOMA system.
- The problem is structured to evaluate resource allocation through the system's adopted performance measure.
A. Weighted System Throughput
Weighted throughput is defined using channel quality, power allocation, user priorities, and SIC behavior on each subcarrier. The formulation also captures MC-OMA as a special case while limiting each subcarrier to two users.
- A better-channel user decodes and removes the cochannel interference from a worse-channel user through SIC on a shared subcarrier.
- The weighted throughput accounts for each user's priority through the positive weight w_m, with 0 ≤ w_m ≤ 1.
- Each subcarrier is limited to at most two multiplexed users to reduce cochannel interference and hardware complexity.SIC also increases processing delay as more users are multiplexed on one subcarrier.
- When a subcarrier serves only one user, the instantaneous weighted throughput reduces to the conventional MC-OMA case.
B. Optimization Problem Formulation
The paper maximizes weighted system throughput under power and subcarrier-allocation constraints. The resulting mixed combinatorial non-convex problem is addressed using monotonic optimization.
- The optimization objective is to maximize weighted system throughput by jointly choosing power and subcarrier allocation.
- The formulation includes a base-station power limit, binary subcarrier-allocation variables, at-most-two-user allocation constraints, and non-negative transmit powers.
- Conventional MC-OMA is a subcase of the MC-NOMA formulation when each subcarrier is exclusively assigned to one user.
- The problem is mixed combinatorial and non-convex because subcarrier allocation is integer-constrained and the objective function is non-convex.
IV. SOLUTIONS OF THE OPTIMIZATION PROBLEM
The paper solves the MC-NOMA resource allocation problem optimally with monotonic optimization and then introduces a lower-complexity alternative.
- Monotonic optimization is applied to solve the joint power and subcarrier allocation problem optimally.
- The proposed solution targets the weighted system throughput objective in MC-NOMA systems.
- A suboptimal scheme is subsequently proposed to achieve close-to-optimal performance with low computational complexity.
A. Monotonic Optimization
This section introduces monotonic optimization through normal sets, polyblocks, projections, and increasing objective functions.
- A polyblock is formed by the union of boxes associated with its vertex set, while a normal set contains the box below each of its points.
- Projection maps a point onto the boundary of a normal feasible set using the largest feasible positive scaling factor.
- A monotonic optimization problem is represented over a non-empty normal closed set with an increasing objective function.
B. Joint Power and Subcarrier Allocation Algorithm
The proposed allocation algorithm reformulates the weighted-throughput problem as monotonic optimization, approximates the feasible-set boundary with shrinking polyblocks, and obtains power and subcarrier allocations from the resulting optimum.
- The weighted throughput is rewritten in an equivalent vector form, yielding a monotonic optimization problem over a feasible set defined by the system constraints.
- Outer polyblock approximation constructs a sequence of shrinking polyblocks that contain the feasible set and selects vertices whose projections maximize the objective.
- The approximation terminates when the normalized distance between the selected vertex and its projection is at most the error tolerance ǫ.
- The initial polyblock uses maximum transmit power while omitting cochannel interference, and although this intermediate policy is generally infeasible, the polyblock contains the feasible set and converges to the optimum.
- Projection is solved as a fractional programming problem with the Dinkelbach algorithm, while the optimal vertex is mapped back to power and subcarrier allocations.
- The monotonic optimization algorithm achieves a globally optimal solution, but its complexity grows exponentially with the number of vertices D.
C. Suboptimal Solution
The suboptimal scheme transforms the non-convex resource-allocation problem using big-M reformulation and successive convex approximation, producing a low-complexity local solution. Its iterative convex upper-bound procedure converges to a local optimum with polynomial-time complexity.
- The scheme uses big-M reformulation to decompose product terms that obstruct computationally efficient resource-allocation design.
- The integer subcarrier-allocation constraint is rewritten through an equivalent reverse-convex formulation with continuous variables constrained between zero and one.
- A large penalty factor η enforces binary-like allocation variables by penalizing values that differ from zero or one.
- Algorithm 3 initializes the penalty, iteration limit, and feasible point, then repeatedly solves the convex subproblem until convergence or Imax.
- Successive convex approximation replaces convex terms with affine global underestimators, yielding a convex upper-bound problem solved iteratively.
- The proposed iterative algorithm converges to a local optimal solution with polynomial-time computational complexity.
V. SIMULATION RESULTS
The simulations evaluate the proposed resource-allocation schemes in a single-cell downlink MC-NOMA setting with randomly distributed users, distance-based weights, and fading channels. Results are averaged over path-loss and multipath-fading realizations.
- The simulation uses a single cell with users uniformly distributed between 30-meter inner and 600-meter outer boundaries, and NF = 64 subcarriers.
- User weights are based on normalized distance to the base station to promote fairness, particularly for cell-edge users with poor channel conditions.
- Results are averaged over different realizations of both path loss and multipath fading.
A. Average System Throughput vs. Maximum Transmit Power
The proposed schemes achieve higher throughput than the baseline allocation methods and retain close performance between the optimal and suboptimal policies. Their MC-NOMA allocation also exploits additional power-domain and frequency-domain degrees of freedom as the user population grows.
- Average throughput increases with Pmax because optimal additional transmit power can improve users' SINR, while the proposed suboptimal scheme closely approaches the optimal scheme.
- At Pmax = 46 dBm, the proposed optimal scheme achieves roughly 20% and 56% higher average throughput than baseline schemes 1 and 2, respectively.
- For a given target throughput, the proposed schemes enable power reductions of more than 10 dB compared with the baseline schemes.
- At Pmax = 45 dBm, throughput generally increases with user count for the proposed schemes and baselines 1 and 3, whereas random-scheduling baseline 2 is insensitive to user count.
- The proposed schemes grow faster with user count than baselines 1 and 3 because MC-NOMA exploits both frequency and power domains for user selection and power allocation.
- The suboptimal scheme achieves performance similar to the optimal scheme even for relatively large numbers of users.
VI. CONCLUSION
The paper develops optimal joint power and subcarrier allocation for MC-NOMA through monotonic optimization and proposes a lower-complexity alternative. Simulations show close-to-optimal suboptimal performance and substantial throughput improvement over MC-OMA.
- The resource-allocation design maximizes weighted system throughput through a non-convex optimization formulation solved optimally using monotonic optimization.
- A low-complexity suboptimal scheme achieves close-to-optimal performance.
- The proposed MC-NOMA resource allocation substantially improves system performance compared with conventional MC-OMA.
- The results demonstrate the importance of efficient resource-allocation optimization in NOMA systems.