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Energy-Efficient Resource Allocation in Multiuser OFDM Systems with Wireless Information and Power Transfer
Derrick Wing Kwan Ng, Ernest S. Lo, Robert Schober
TL;DR
The paper addresses resource allocation for multiuser OFDM systems with wireless information and power transfer, where the optimization is non-convex and user selection is combinatorial. It proposes an iterative algorithm using nonlinear fractional programming and Lagrange dual decomposition. In simulations, energy efficiency converges to the optimum within 30 iterations across the considered scenarios.
Problem
Resource allocation for multiuser OFDM information-and-power transfer is difficult because the objective is a ratio and user selection is integer-constrained.
Source: §I · p. 1, §IV · p. 3Method
The paper uses nonlinear fractional programming and Lagrange dual decomposition in an iterative algorithm to maximize system energy efficiency.
Source: §VI · p. 6Results
Energy efficiency converges to the optimum value within 30 iterations in all considered scenarios.
Source: A. Convergence of Iterative Algorithm 1 · p. 5Takeaways & Limitations
Simulations indicate potential benefits from multiple users for energy efficiency, system capacity, and wireless power transfer.
Source: §VI · p. 6
Abstract
from arXiv · showhide
In this paper, we study the resource allocation algorithm design for multiuser orthogonal frequency division multiplexing (OFDM) downlink systems with simultaneous wireless information and power transfer. The algorithm design is formulated as a non-convex optimization problem for maximizing the energy efficiency of data transmission (bit/Joule delivered to the users). In particular, the problem formulation takes into account the minimum required system data rate, heterogeneous minimum required power transfers to the users, and the circuit power consumption. Subsequently, by exploiting the method of time-sharing and the properties of nonlinear fractional programming, the considered non-convex optimization problem is solved using an efficient iterative resource allocation algorithm. For each iteration, the optimal power allocation and user selection solution are derived based on Lagrange dual decomposition. Simulation results illustrate that the proposed iterative resource allocation algorithm achieves the maximum energy efficiency of the system and reveal how energy efficiency, system capacity, and wireless power transfer benefit from the presence of multiple users in the system.
I. INTRODUCTION
The paper develops resource allocation for energy-efficient multiuser OFDM with wireless information and power transfer. Its system model uses downlink channel information to allocate resources in time-slotted transmission.
I. INTRODUCTION
- Prior work on wireless information and power transfer did not establish energy efficiency accounting for RF transmission and circuit power, or cover multicarrier systems with arbitrary user counts.The cited single-carrier schemes may not apply to those multicarrier settings.Source: §I · p. 1
- The work addresses energy-efficient resource allocation for multiuser OFDM systems with wireless information and power transfer.The paper frames the design as a non-convex optimization problem and proposes an iterative algorithm.Source: §I · p. 1
A. Multiuser OFDM Channel Model
- The system comprises a transmitter and K mobile users, each with a single antenna, and divides bandwidth B across nF subcarriers.Scheduling slots are comparable in length to channel coherence time; the channel is assumed time-invariant within a slot.Source: A. Multiuser OFDM Channel Model · p. 1
- Figure 1 depicts a downlink multiuser OFDM system with K = 3 users for wireless information and power transfer.The model obtains downlink channel state information through user feedback in FDD or channel reciprocity in TDD.Source: A. Multiuser OFDM Channel Model · p. 1, Figure 1 · p. 2
B. Information Decoding and Energy Harvesting Receiver
A user either decodes information while served or harvests energy while idle. The resource allocation framework measures delivered bits against system power consumption and accounts for user priorities and power-transfer efficiency.
B. Information Decoding and Energy Harvesting Receiver
- In each scheduling slot, a user either decodes information when active or harvests energy when idle, but cannot do both concurrently.The remaining K −1 idle users harvest energy from the transmitter’s radio signal while one user is served.Source: B. Information Decoding and Energy… · p. 2, A. Instantaneous Channel Capacity · p. 2
A. Instantaneous Channel Capacity
- User weights allow the transmitter to assign different priorities and enforce notions of fairness among mobile users.The power allocation and user selection policies are represented by P and S, respectively.Source: A. Instantaneous Channel Capacity · p. 2
- The power model includes active-transceiver circuit power and power-amplifier consumption, while subtracting power harvested by idle users.The circuit term is independent of transmitted power; idle-user power consumption is omitted as relatively small compared with the active transceiver pair.Source: A. Instantaneous Channel Capacity · p. 2
- System energy efficiency is the total number of bits successfully delivered to selected users per unit energy consumption, measured in bit-per-Joule.The system capacity is the total number of bits delivered to the selected user per second.Source: A. Instantaneous Channel Capacity · p. 2
B. Optimization Problem Formulation
The optimization constraints combine user-specific power-transfer requirements, system power and rate limits, and restrictions on user selection and allocated power.
B. Optimization Problem Formulation
- C1 requires minimum power transfer mink for user k when that user is idle.C2 limits transmit power, while C3 caps total system power at the power-grid supply.Source: B. Optimization Problem Formulation · p. 3
- C4 enforces minimum system data rate Rmin, while C5 and C6 ensure that at most one user is served in a scheduling slot.C6 also imposes binary user-selection variables.Source: B. Optimization Problem Formulation · p. 3
- C7 requires non-negative power allocation variables Pi,k.The selection variables sk are binary.Source: B. Optimization Problem Formulation · p. 3
IV. SOLUTION OF THE OPTIMIZATION PROBLEM
The resource-allocation problem is mixed non-convex and combinatorial, and the proposed solution begins by simplifying its objective with nonlinear fractional programming.
IV. SOLUTION OF THE OPTIMIZATION PROBLEM
- The optimization problem combines non-convexity from a ratio objective with combinatorial user selection through integer constraints.These characteristics make the problem a mixed non-convex and combinatorial optimization problem.Source: §IV · p. 3
- The first solution step simplifies the objective function using nonlinear fractional programming.The paper applies this transformation to the considered optimization problem.Source: §IV · p. 3
- The formulation’s combinatorial nature comes from the integer constraint on user selection.The ratio of two functions in the objective is the source of non-convexity.Source: §IV · p. 3
A. Transformation of the Objective Function
The section recasts the fractional energy-efficiency objective as an equivalent subtractive objective, enabling the optimization to focus on the transformed form while preserving the optimal resource allocation policy.
A. Transformation of the Objective Function
- The feasible set F contains the solutions satisfying the optimization problem’s constraints, and the power constraints make F compact.Source: A. Transformation of the Objective… · p. 3
- The maximum energy efficiency is attained when the subtractive objective U(P, S) − q*UT P(P, S) satisfies the stated condition for feasible solutions.The condition applies when U(P, S) ≥ 0 and UT P(P, S) > 0.Source: A. Transformation of the Objective… · p. 3
- For a fractional objective, an equivalent subtractive-form objective can yield the same optimal resource allocation policy.Source: A. Transformation of the Objective… · p. 3
B. Iterative Algorithm for Energy Efficiency Maximization
The algorithm applies Dinkelbach’s method to maximize energy efficiency, solving a transformed problem at each iteration. Time-sharing relaxes user selection so the inner problem can be treated as concave and solved through its dual.
B. Iterative Algorithm for Energy Efficiency Maximization
- Convergence to maximum energy efficiency is guaranteed if each iteration’s inner problem is solved.The iterative algorithm uses the Dinkelbach method and an equivalent objective function.Source: B. Iterative Algorithm for Energy… · p. 3
- Setting q = 0 turns the transformed objective into aggregate weighted system capacity maximization.Source: B. Iterative Algorithm for Energy… · p. 3
- Relaxing the Boolean user-selection constraint to 0 ≤ sk ≤ 1 lets sk represent a time-sharing factor across users.The relaxation balances computational complexity against optimality compared with brute force or branch-and-bound approaches.Source: Solution of the Main Loop Problem · p. 3
Solution of the Main Loop Problem:
- The relaxed solution’s duality gap becomes zero with sufficiently many subcarriers, for example nF = 128.Source: Solution of the Main Loop Problem · p. 4
- Under time-sharing, the problem is jointly concave in power allocation and user selection, so solving its dual is equivalent to solving the primal under mild conditions.Source: Solution of the Main Loop Problem · p. 4
C. Dual Problem Formulation
For a fixed energy-efficiency parameter, the resource-allocation problem is solved through Lagrange dual decomposition. KKT-based subproblems and gradient updates iteratively determine power allocation, user selection, and the dual variables.
C. Dual Problem Formulation
- The Lagrangian for the primal problem in (10) uses multipliers for power-transfer, transmit-power, grid-power, data-rate, and user-selection constraints.Source: C. Dual Problem Formulation · p. 4
D. Lagrange Dual Decomposition
- The dual decomposes into parallelizable subcarrier subproblems and an outer master minimization, solved iteratively using KKT conditions and gradient updates.Source: D. Lagrange Dual Decomposition · p. 4
Layer 1 (Subproblem Solution):
- KKT conditions give a closed-form optimal power allocation for each subcarrier and user for a fixed q.Source: Layer 1 (Subproblem Solution) · p. 4
- Power allocation has a multilevel water-filling form, with water levels varying by user and subcarrier and reflecting user priority and effects on other users.Source: Layer 1 (Subproblem Solution) · p. 4
- The data-rate and idle-user power-transfer requirements influence power allocation through multipliers γ and αj, respectively.Source: Layer 1 (Subproblem Solution) · p. 4
- The user-selection criterion uses each user’s marginal system benefit Qk, while circuit power affects the dual solution through updates to q.Source: Layer 1 (Subproblem Solution) · p. 4
Layer 2 (Master Problem Solution):
- The master problem updates its multipliers by gradient steps; convergence to the primal optimum of (10) is guaranteed when step sizes satisfy the infinite travel condition.Source: Layer 2 (Master Problem Solution) · p. 5
- The gradient updates act as resource shadow-price adjustments, and combining them with the selection criterion eventually selects only one user despite the time-sharing relaxation.Source: Layer 2 (Master Problem Solution) · p. 5
V. SIMULATION RESULTS
The simulations evaluate the algorithm in an indoor OFDM setting with specified channel, power, and rate parameters. Failed channel realizations are assigned zero energy efficiency and system capacity when minimum rate or power-transfer requirements cannot be met.
V. SIMULATION RESULTS
- The simulation uses an indoor system with a 10-meter maximum service distance, 5 MHz bandwidth, and 128 subcarriers.Users are uniformly distributed from 2 to 10 meters; the model uses TGn path loss and 14 dB effective antenna gain.Source: §V · p. 5
- The setup assumes a 40 dBm circuit power, 50 dBm maximum grid supply, 10 Mbits/s minimum system rate, and −10 dBm minimum power transfer per user.Energy-harvesting efficiency is 0.8 per user and power-amplifier efficiency is 40%.Source: §V · p. 5
- A channel realization receives zero energy efficiency and system capacity if the transmitter cannot meet the minimum system rate or required power transfer.Source: §V · p. 5
A. Convergence of Iterative Algorithm 1
The proposed algorithm reaches its optimum energy efficiency within 30 iterations across the considered scenarios, with a zero duality gap. The results use 30 iterations for subsequent performance evaluations.
A. Convergence of Iterative Algorithm 1
- Within 30 iterations, the algorithm reaches optimum energy efficiency with zero duality gap across all considered user counts and transmit-power allowances.The gap measures the difference between primal and dual optima and reflects constraint relaxation and insufficient iterations.Source: A. Convergence of Iterative Algorithm 1 · p. 5
- The convergence and zero duality gap support the practicality of the proposed algorithm.Source: A. Convergence of Iterative Algorithm 1 · p. 5
- Subsequent performance results use 30 iterations to illustrate the proposed algorithm.Source: A. Convergence of Iterative Algorithm 1 · p. 5
B. Average Energy Efficiency and Average System Capacity
Energy efficiency rises with the transmit-power allowance until additional allowance yields no further gain, and it also benefits from more users. Capacity comparisons show that the proposed and baseline schemes are similar at low allowance, while the baseline performs better at high allowance.
B. Average Energy Efficiency and Average System Capacity
- Energy efficiency increases with Pmax until it reaches an upper limit, after which additional transmit power yields no further gain.The proposed algorithm’s energy efficiency also increases with user count.Source: B. Average Energy Efficiency and… · p. 5
- More users improve energy efficiency through multiuser diversity and because idle users harvest radiated power, reducing total system power consumption.Source: B. Average Energy Efficiency and… · p. 6
- In the high transmit-power regime, the capacity-maximizing baseline outperforms the proposed algorithm, while both schemes benefit from more users.At low allowance, the proposed algorithm achieves virtually the same capacity as the baseline.Source: B. Average Energy Efficiency and… · p. 6, Figure 4 · p. 6
- At high transmit-power allowance, the baseline’s capacity advantage comes from using all available power, which impairs energy efficiency.Source: B. Average Energy Efficiency and… · p. 6
C. Average Harvested Power
The paper reports that harvested power rises with transmit-power allowance and user count, and concludes that multiple users can benefit energy efficiency, capacity, and wireless power transfer. Its resource-allocation problem is non-convex and combinatorial, addressed by an iterative algorithm.
C. Average Harvested Power
- Harvested power increases with Pmax and with the number of users, as more idle users participate in energy harvesting.Source: C. Average Harvested Power · p. 6, Figure 5 · p. 6
VI. CONCLUSIONS
- The resource-allocation problem for concurrent information and power transfer is non-convex and combinatorial.Source: §VI · p. 6
- The proposed iterative algorithm uses nonlinear fractional programming and Lagrange dual decomposition to maximize system energy efficiency.Source: §VI · p. 6
- Simulations show convergence within a small number of iterations and potential multiuser benefits for energy efficiency, capacity, and wireless power transfer.Source: §VI · p. 6