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Energy Efficient Joint Resource Allocation and Power Control for D2D Communications
Yanxiang Jiang, Qiang Liu, Fuchun Zheng, Xiqi Gao, Xiaohu You
TL;DR
The paper addresses joint resource allocation and power control for maximizing D2D energy efficiency underlaying cellular networks. It combines fractional programming, penalty functions, and a two-layer iterative optimization scheme. Simulations report improved energy efficiency, including a 66.7% decrease when D2D-pair distance increases from 10m to 100m.
Problem
Joint resource allocation and power control is formulated as a nonconvex, mixed combinatorial optimization problem whose brute-force solution has exponential complexity.
Method
Fractional programming and a penalty function produce an iterative scheme, while a two-layer approach separates power optimization from network-flow resource allocation.
Results
66.7%: the proposed scheme’s energy efficiency decreases as D2D-pair distance increases from 10m to 100m.
Takeaways & Limitations
The proposed scheme achieves remarkable energy-efficiency improvements and reaches optimal energy efficiency after 2 iterations in the considered simulation scenario.
Abstract
from arXiv · showhide
In this paper, joint resource allocation and power control for energy efficient device-to-device (D2D) communications underlaying cellular networks are investigated. The resource and power are optimized for maximization of the energy efficiency (EE) of D2D communications. Exploiting the properties of fractional programming, we transform the original nonconvex optimization problem in fractional form into an equivalent optimization problem in subtractive form. Then, an efficient iterative resource allocation and power control scheme is proposed. In each iteration, part of the constraints of the EE optimization problem is removed by exploiting the penalty function approach. We further propose a novel two-layer approach which allows to find the optimum at each iteration by decoupling the EE optimization problem of joint resource allocation and power control into two separate steps. In the first layer, the optimal power values are obtained by solving a series of maximization problems through root-finding with or without considering the loss of cellular users' rates. In the second layer, the formulated optimization problem belongs to a classical resource allocation problem with single allocation format which admits a network flow formulation so that it can be solved to optimality. Simulation results demonstrate the remarkable improvements in terms of EE by using the proposed iterative resource allocation and power control scheme.
I. INTRODUCTION
D2D communications can improve spectral and energy efficiency but share cellular spectrum, creating a need for coordinated resource allocation and power control. The paper formulates this energy-efficiency problem and develops an iterative solution using fractional programming and a penalty function.
- D2D communications can increase spectrum efficiency and energy efficiency through proximity and reuse gains.
- Because D2D users share spectrum with cellular users, resource allocation and power control must manage their interactions.
- Prior studies separately addressed resource allocation, interference management, throughput, or power control, often under fixed-power or mode-specific settings.
- Rising mobile-device power consumption and slowly improving battery capacity motivate energy efficiency as a performance metric.
- The paper transforms the nonconvex fractional problem into an equivalent subtractive form and proposes an iterative joint allocation and power-control scheme using a penalty function.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The paper models D2D pairs reusing cellular uplink resource blocks in a single cell and maximizes their aggregate energy efficiency under assignment, rate, interference, and power constraints. The formulation includes circuit power and practical interference and channel assumptions.
- The system contains multiple cellular users and D2D pairs in one cell, with D2D pairs reusing cellular uplink resource blocks.
- Resource blocks are represented through cellular-user, RB, and D2D-pair sets, with cellular resource allocation assumed already completed.
- The D2D rate depends on RB bandwidth, direct D2D channel gain, cellular-to-D2D interference gain, transmit power, and noise.
- The objective is aggregate D2D energy efficiency, defined using total D2D throughput and total energy consumption including circuit power.
- Each D2D pair receives one RB, each RB serves at most one D2D pair, and active pairs satisfy minimum-rate, interference, and maximum-power constraints.
- Channel gains are assumed constant across subcarriers within an RB, making power control more practical but yielding a suboptimal solution without single-user diversity.
III. PROPOSED JOINT RESOURCE ALLOCATION AND POWER CONTROL SCHEME
The joint optimization is difficult because integer assignment creates an NP-hard combinatorial problem while the fractional objective is nonconvex. Exhaustive search is therefore computationally impractical as the number of resource blocks grows.
- Integer resource-assignment variables make the optimization combinatorial and NP-hard.
- The fractional objective further increases difficulty because it is nonconvex.
- Brute-force global optimization has exponential complexity in the number of resource blocks and is impractical even for small systems.
A. Problem Equivalence
The paper applies fractional programming to replace the original fractional energy-efficiency objective with an equivalent subtractive formulation. This reformulation enables an iterative solution based on the Dinkelbach method.
- The objective is treated as a nonlinear fractional program over the feasible domain defined by the original constraints.
- The maximum energy efficiency is characterized through an equivalent subtractive objective obtained using fractional programming.
B. Iterative Algorithm for EE Maximization
The iterative algorithm solves the subtractive-form EE problem using Dinkelbach iterations, while penalty functions remove selected constraints during each optimization step.
- Iterative algorithm: The Dinkelbach method iteratively solves the equivalent subtractive-form objective until the convergence condition is met.The algorithm initializes s = 1 and q_s = 0, then repeats optimization and updates until |F(q_s)| < ǫ.
- Iterative algorithm: The resulting iterative procedure alternates between solving the optimization problem for a given temporary EE and updating the iteration state.The algorithm is presented as the Iterative Resource Allocation and Power Control Algorithm.
- Penalty-based reformulation: Penalty functions remove constraints (4d) and (4f) from the optimization problem in each iteration.Feasible RB sets satisfying constraint (4e) are obtained from measured interference power on different resource blocks.
C. The Novel Two-Layer Joint Resource Allocation and Power Control Scheme
The proposed two-layer scheme decomposes each iteration’s mixed resource-allocation and power-control problem into separate power and allocation optimizations, with variants that account for cellular-rate loss.
- Two-layer decomposition: Theorem 2 transforms the original two-dimensional nonconvex problem into two separate optimization problems in each iteration.The decomposition follows from constraints (4a)–(4c).
- First layer: power control: In the first layer, each D2D pair determines the maximum value of f_i,j(P_i,j) on candidate RBs satisfying constraint (4e).The corresponding power value is then determined for each candidate resource block.
- Second layer: resource allocation: In the second layer, each RB is allocated to one D2D pair according to the first-layer results to maximize EE and avoid interference among D2D pairs.The allocation uses the power-control outcomes as inputs.
- Cellular-rate loss: The scheme studies both cases with and without considering the loss of cellular users’ rates.When rate loss is considered, R(P_i,j) and f_i,j(P_i,j) are replaced by modified functions that incorporate cellular-rate effects.
1) The First Layer (Power Control):
The first layer optimizes each D2D pair’s transmit power on feasible RBs by solving derivative-based equations, with separate formulations depending on whether cellular-rate loss is included.
- Without cellular-rate loss: Without cellular-rate loss, the optimal transmit power is obtained by differentiating f_i,j(P_i,j) under the relevant power and rate constraints.The resulting solution is selected within the constraining interval.
- Feasibility conditions: If the candidate solution falls outside the constraining interval, the corresponding minimum-rate or maximum-power requirement cannot be satisfied for maximum EE.A left-bound violation indicates that the minimum rate requirement cannot be satisfied.
- With cellular-rate loss: With cellular-rate loss, the first-layer objective changes from f_i,j(P_i,j) to θ_i,j(P_i,j), whose maximum is likewise obtained through derivative analysis.The modified derivative expression incorporates interference from D2D transmission toward the base station.
- Root finding: The unconstrained power solution can be found from a cubic equation whose candidate roots depend on the value of y_N.One real root exists when y_N > h^2, while three real roots exist when y_N < h^2.
2) The Second Layer (Resource Allocation):
The second layer assigns resource blocks to D2D pairs using the first layer’s optimized power values, yielding a classical single-allocation problem solvable to optimality.
- Optimal solution: The resulting resource-allocation problem admits a network-flow formulation and can be solved to optimality.It is also an assignment problem solvable by the Hungarian or branch-and-bound method.
- Scope and limitation: The complete two-layer scheme is claimed to attain the optimal solution of the original mixed combinatorial and nonconvex problem with low complexity.The approach assumes centralized operation, which incurs signaling overhead whose impact is left for future research.
IV. SIMULATION RESULTS
Simulations evaluate the proposed scheme against alternative schemes and across system conditions. The results show improved EE, rapid convergence, and strong sensitivity to D2D-user distance and minimum rate requirements.
- Scheme comparison: The proposed scheme greatly improves D2D EE compared with the rate-adaptive and margin-adaptive schemes in and.Its complexity is polynomial in the problem dimensions, O(NdM), supporting practical implementation.
- Scheme comparison: EE decreases slightly as PB/N0 increases because CU-to-D2D interference increases, although the effect remains small under the interference constraint.The allowed interference from the sharing CU is constrained below a threshold.
- Convergence: Only 2 iterations are required to converge to the optimal EE in the considered simulation scenario.EE also increases with the number of D2D pairs.
- Distance sensitivity: 66.7%: EE decreases as D2D-user distance increases from 10m to 100m.The paper attributes this decrease to increased fading with distance.
- Rate requirement: EE versus γi shows a saturation point beyond which EE no longer increases, indicating that the minimum rate requirement affects optimal transmit power.γi is the minimum rate requirement of each D2D pair.
V. CONCLUSIONS
The paper formulates joint resource allocation and power control for energy-efficient D2D communications underlaying cellular networks as a nonconvex optimization problem. Using fractional programming and a penalty function, it derives an iterative scheme that maximizes D2D EE, with simulations showing remarkable EE improvements.
- The study formulates joint resource allocation and power control for energy-efficient D2D communications underlaying cellular networks as a nonconvex optimization problem.
- Fractional programming and a penalty function yield an efficient iterative joint resource allocation and power control scheme for maximizing D2D EE.
- The proposed scheme achieves remarkable improvements in D2D EE according to the simulation results.