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Age of Information in Energy Harvesting Aided Massive Multiple Access Networks
Zhengru Fang, Jingjing Wang, Yong Ren, Zhu Han, H. Vincent Poor, Lajos Hanzo
TL;DR
The paper tackles the joint freshness and energy problem in EH-aided massive multiple access networks with stochastic status updates and sleep scheduling. It models MV and ST policies across TDMA, FDMA, and NOMA, derives peak-AoI expressions, and solves the resulting allocation problems exactly or approximately. Simulations report lower peak AoI with low power consumption, with sleep scheduling reducing power relative to benchmarks and MV-based NOMA performing best overall.
Problem
Stochastic updates and sleep scheduling make it challenging to meet AoI requirements while controlling power consumption in EH-aided massive access networks.
Method
The paper derives closed-form peak-AoI expressions for MV and ST policies across TDMA, FDMA, and NOMA, then uses exact linear search and low-complexity CCP optimization.
Results
Both MV and ST reduce power consumption versus benchmarks, while MV-based NOMA achieves the lowest average peak AoI and power consumption among the considered access schemes.
Takeaways & Limitations
Sleep scheduling can trade some AoI performance for lower energy consumption, while NOMA provides the strongest reported combined AoI and power outcome under MV.
Abstract
from arXiv · showhide
Given the proliferation of the massive machine type communication devices (MTCDs) in beyond 5G (B5G) wireless networks, energy harvesting (EH) aided next generation multiple access (NGMA) systems have drawn substantial attention in the context of energy-efficient data sensing and transmission. However, without adaptive time slot (TS) and power allocation schemes, NGMA systems relying on stochastic sampling instants might lead to tardy actions associated both with high age of information (AoI) as well as high power consumption. For mitigating the energy consumption, we exploit a pair of sleep-scheduling policies, namely the multiple vacation (MV) policy and start-up threshold (ST) policy, which are characterized in the context of three typical multiple access protocols, including time-division multiple access (TDMA), frequency-division multiple access (FDMA) and non-orthogonal multiple access (NOMA). Furthermore, we derive closed-form expressions for the MTCD system's peak AoI, which are formulated as the optimization objective under the constraints of EH power, status update rate and stability conditions. An exact linear search based algorithm is proposed for finding the optimal solution by fixing the status update rate. As a design alternative, a low complexity concave-convex procedure (CCP) is also formulated for finding a near-optimal solution relying on the original problem's transformation into a form represented by the difference of two convex problems. Our simulation results show that the proposed algorithms are beneficial in terms of yielding a lower peak AoI at a low power consumption in the context of the multiple access protocols considered.
I. INTRODUCTION
The paper addresses AoI and energy-consumption challenges in EH-aided massive multiple access networks with stochastic status updates and sleep scheduling. It proposes adaptive TS allocation and power-control schemes across TDMA, FDMA, and NOMA.
- Motivation: EH-aided MTCD networks must preserve data freshness while operating under limited battery energy and stochastic status updates.AoI captures the elapsed time since the latest received status update, while periodic transmissions can deplete batteries and overflow buffers.
- Research gap: Prior EH massive-access studies largely emphasized throughput and power consumption, leaving AoI insufficiently addressed.The paper identifies a need for multiple access protocols designed specifically for AoI-sensitive EH-aided MTCD networks.
- Approach: The proposed framework jointly optimizes peak AoI and power consumption while MTCDs adaptively switch between active and idle modes under stochastic updates.It uses multiple vacation and start-up threshold sleep-scheduling policies across three access schemes and derives closed-form average peak-AoI expressions.
- Optimization: The non-convex TS and energy-allocation problem is solved exactly by linear search and approximately at lower complexity through DC reformulation and CCP.The exact method obtains the optimal allocation, whereas CCP provides a near-optimal solution from convex subproblems.
- Findings: Both sleep-scheduling policies reduce power consumption relative to benchmarks, while MV-based NOMA achieves the lowest reported average peak AoI and power consumption.The comparison covers EH-aided large-scale multiple access networks using TDMA, FDMA, and NOMA.
C. Transmission Model and Channel Analysis
The transmission model specifies energy costs for active, idle, and data-transmission states, then derives protocol-specific channel-capacity and rate constraints for TDMA, FDMA, and NOMA.
- Energy model: Each MTCD harvests energy and uses it primarily for data transmission, with separate active-state and idle-mode energy constraints.The model defines transmission and active-state battery costs, plus an idle-mode cost adjusted by an EH coefficient.
- Energy model: The EH-aided MTCD transmits one L-bit packet per transmission slot, with a common transmission rate across devices.The packet duration and rate determine the required channel-capacity bound.
- Multiple access protocols: TDMA assigns the complete bandwidth B to each MTCD during its limited transmission period.The resulting capacity bound is derived for each MTCD under time-partitioned access.
- Multiple access protocols: FDMA partitions B into N orthogonal subchannels, while NOMA lets all MTCDs share time, frequency, and space resources.For NOMA, successful decoding additionally requires transmit-power control for successive interference cancellation.
- Multiple access protocols: The average transmission rate accounts for the fraction of time slots designated as legitimate transmission duration.The channel model assumes perfectly known CSI at the BS and MTCDs.
III. PEAK AOI MODEL
The peak-AoI model uses FIFO queueing and vacation-based sleep scheduling to characterize TDMA status updates under MV and ST policies. Closed-form delay and peak-AoI expressions incorporate idle-period effects, switching costs, and stability assumptions.
- AoI and queueing model: The analysis models AoI for TDMA, FDMA, and NOMA using single-server vacation queues representing sleep-scheduling policies.Per-packet AoI is obtained from the area under the FIFO queue’s age curve.
- AoI and queueing model: The average per-packet AoI combines the average data-generation interval with the average system delay under stable queue operation.System delay includes waiting, transmission, and idle periods, while propagation latency is treated as negligible.
- TDMA sleep scheduling: TDMA divides each slot into one EH TS and N transmission TSs, turning off an MTCD when its queue is empty.MV and ST differ in the condition that triggers transmission startup.
- TDMA sleep scheduling: Under MV, an empty-queue MTCD enters an idle period after a switching cost and resumes transmission when packets are available.The resulting queue is modeled as an M/D/1 system with Poisson arrivals and constant service time.
- TDMA sleep scheduling: The MV policy adds idle-mode delay to the corresponding queue delay, and its peak AoI is decomposed into baseline queue age plus idle-period age.The average system delay is derived under stability using probability-generating functions and first-order derivatives.
- TDMA sleep scheduling: The ST policy restarts an idle device when accumulated generated bits reach a threshold, reducing frequent power cycling at the cost of threshold-triggered waiting.FIFO is used because it is standard in multi-service wireless communication systems, despite LIFO often minimizing AoI.
B. FDMA Protocol
FDMA partitions the available bandwidth into orthogonal subchannels and applies MV or ST sleep scheduling independently to MTCD transmission queues. The resulting peak-AoI expressions account for subchannel bandwidth, idle periods, and threshold-triggered service.
- FDMA resource allocation: FDMA divides bandwidth B into orthogonal frequency subchannels, giving each MTCD a subchannel with bandwidth approximately B/N.Each device therefore operates with a reduced bandwidth relative to using the full channel.
- FDMA with MV policy: The FDMA MV policy yields an average peak-AoI expression by applying the queueing model to each MTCD’s subchannel.The sleep-scheduling and EH durations within an FDMA time slot are included in the formulation.
- FDMA with ST policy: Under the FDMA ST policy, transmission begins only after the status-update counter reaches threshold M and continues until the queue empties.This policy is designed to avoid frequent MTCD power cycling across multiple idle time slots.
- FDMA with ST policy: The average FDMA peak AoI under ST is derived using the same queueing framework as the preceding protocol analyses.The formulation distinguishes active and idle mode durations.
C. NOMA Protocol
The NOMA model lets all MTCDs share the same time, frequency, and space resources while reserving EH and transmission portions of each slot. MV and ST sleep scheduling are then incorporated into average peak-AoI expressions.
- NOMA resource model: In PD-NOMA, all MTCDs share time, frequency, and space resources, with each slot partitioned into EH and transmission portions.The slot duration and EH duration determine the available transmission interval.
- NOMA with MV policy: NOMA’s MV formulation uses the queueing model to derive average peak AoI for the EH-aided multiple-access network.The transmission duration is the slot duration minus the EH duration.
- NOMA with ST policy: The NOMA ST policy introduces a start-up threshold to reduce the frequency of MTCD power cycling.Its average peak AoI is expressed using the preceding ST-policy derivations for other access protocols.
- NOMA with ST policy: The NOMA slot duration and start-up threshold are the key parameters in the ST-based formulation.These parameters determine when shared-resource transmission begins under the sleep-scheduling policy.
IV. PROBLEM FORMULATION
The section formulates average peak AoI minimization for TDMA, FDMA, and PD-NOMA under different sleep-scheduling policies. Exact linear search solves convex reformulations, while CCP addresses the original non-convex problems with lower computational complexity.
- Average peak AoI minimization is formulated for TDMA, FDMA, and PD-NOMA under different sleep-scheduling policies.
- The original non-convex problems are represented as difference-of-convex programs and solved using CCP in Algorithm 2.
A. TDMA-based Problem Formulation
The TDMA formulation minimizes average peak AoI and incorporates energy-efficiency, energy, slot-allocation, update-rate, and stability constraints. Fixing the status update rate yields convex subproblems for exact linear search, while CCP provides a lower-complexity locally optimal alternative for DC formulations.
- Exact linear search: Algorithm 1 searches across feasible status update rates and returns the solution with the best objective value.
- TDMA using MV and ST policies: TDMA optimization minimizes average peak AoI subject to energy-efficiency, energy, slot-allocation, update-rate, and stability constraints.
- Exact linear search: Fixing λ_n converts the non-convex problem into a convex subproblem, enabling exact linear search for the optimal solution.The search initializes λ_n at its minimum, repeatedly solves convex subproblems, and outputs the best solution found.
- CCP formulation: The average peak AoI objective can be decomposed into convex and concave components, forming a difference-of-convex programming problem.
- CCP solution: CCP iteratively linearizes the concave component and solves convex subproblems to obtain a locally optimal solution with reduced computational complexity.The paper motivates CCP because increasing the accuracy of exact search increases complexity for EH-aided MTCDs with finite computational resources.
B. FDMA-based Problem Formulation
The FDMA formulation applies the same average peak AoI and energy-efficiency optimization framework to MV and ST policies. Algorithm 1 provides optimal solutions after convex reformulation, while CCP offers a tractable iterative alternative for the resulting DC programs.
- FDMA using MV and ST policies: FDMA allocates subchannel bandwidth and time slots while optimizing average peak AoI and energy efficiency under MV and ST policies.
- FDMA optimization: The FDMA optimization problems define average peak AoI as the objective while incorporating the associated resource-allocation variables.
- FDMA using the ST policy: Under the ST policy, an MTCD wakes from idle mode when its queue contains more than M status updates.
- FDMA solution methods: Algorithms 1 and 2 respectively provide optimal-search and lower-complexity CCP procedures for the FDMA MV and ST problems.
C. NOMA-based Problem Formulation
The NOMA formulation optimizes average peak AoI under MV and ST sleep-scheduling policies while accounting for shared-spectrum operation, transmit-power constraints, and common update parameters. Algorithms 1 and 2 provide exact-search and lower-complexity CCP solutions.
- NOMA using the MV policy: NOMA assumes MTCDs share the same spectrum, status update rate, and time-slot allocation under the MV policy.
- NOMA using the MV policy: NOMA optimization must accurately control transmit power and energy harvesting across MTCDs because successive interference cancellation is used at the base station.
- NOMA power constraint: Unlike TDMA and FDMA, NOMA imposes the transmit-power constraint specified by Eq. (6).
- NOMA using the ST policy: The ST formulation minimizes average peak AoI under transmit-power and time-slot allocation constraints.
- NOMA solution methods: Algorithms 1 and 2 obtain exact-search and lower-complexity CCP solutions for the NOMA MV and ST optimization problems.
V. SIMULATION RESULTS AND DISCUSSIONS
The simulations evaluate both sleep-scheduling policies against unscheduled TDMA, FDMA, and NOMA benchmark designs.
- The numerical study verifies the performance of both sleep-scheduling policies.
- TDMA, FDMA, and NOMA without sleep-scheduling serve as benchmark designs.
- The evaluation therefore compares scheduling policies with corresponding unscheduled multiple-access protocols.
A. Parameters Settings
The simulations compare MV and ST sleep scheduling across TDMA, FDMA, and NOMA under varied packet lengths, update-rate constraints, and network sizes. Results show an AoI–energy trade-off, with NOMA generally strongest and MV often preferable for low-delay operation.
- Packet length: Increasing packet length under MV raises peak AoI because throughput and tell-traffic load increase.
- Packet length: NOMA achieves lower peak AoI than FDMA and TDMA, while CCP results remain close to exact optimal solutions.
- Packet length: Shorter packets save energy, and NOMA with MV generally consumes less power than the other protocols.
- Status update rate: At λ_max = 1.4 kbps, ST increases peak AoI by 37.5%, 36.6%, and 40.4% for TDMA, FDMA, and NOMA, respectively.
- Status update rate: At λ_max = 1.4 kbps, MV increases peak AoI by 5.8%, 5.6%, and 5.7% for TDMA, FDMA, and NOMA, respectively.
- Status update rate: Sleep scheduling reduces power consumption but increases AoI, while MV is better suited than ST to low-delay scenarios.
- Number of MTCDs: Increasing the number of MTCDs raises optimal peak AoI because higher total throughput causes longer queues and greater energy requirements.
- Overall comparison: Under fair rate allocation, NOMA outperforms TDMA and FDMA in peak AoI and power consumption.
APPENDIX A PROOF OF LEMMA 2
The appendix derives the stationary distribution and probability-generating function for the ST-policy model, then uses them to obtain queueing quantities and establish the convexity properties needed for optimization.
- The proof starts from the stationary distribution of Π_ST,n and its equilibrium equation with transition matrix P_0.
- The stationary distribution is converted into a probability-generating function, with normalization yielding π_0 = (1 − λ_nτ_b)^(M−1).
- The proof derives the average generated-packet count and system delay using the stationary quantities and Little’s Law.
- The objective is decomposed into functions whose convexity and concavity are established through nonnegative sums and Hessian conditions.
- These curvature results establish convexity for constraints (32) and (33a)–(33c), while constraint (33d) requires convexification.