Improvement on Age of Information for Information Update Systems With HARQ Chase Combining and Sensor Harvesting-Transmitting Diversities

Abstract

The age of information (AoI) has attracted increasing attentions as a new metric and tool to capture the timeliness of reception and freshness of data, which is different from the conventional metric such as outage, delay, and throughput. While most existing works focused on AoI analysis and optimizing method, the information update system design by utilizing diversity to reduce AoI is not fully exploited so far. Inspired by this fact, a novel information status update system is designed by jointing wireless energy harvesting diversity, status update transmitting diversity, and hybrid automatic repeat request (HARQ). Specially, the update system consists of two sensors that can be seen as an unified entity from the destination's perspective, and one destination. The two sensors, which have finite-size batteries and synchronously operate in half-duplex mode, harvest energy from a Bernoulli process source, and cooperatively deliver the status update to destination by sharing a common information source. To exploit the information of the unsuccessfully decoding update packet, the HARQ and chase combining (HARQ-CC) are jointly used at destination so that the HARQ-CC receiving diversity is also exploited. By using Bernoulli process energy arrival probability and sensor transmission probability, we first propose one novel sensor energy harvesting and update delivering model that can be represented by Markov Chain (MC) and develop one novel construction method of the transition matrix of sensor battery energy states. Considering the developed energy state transmission matrix column stochastic, irreducible, and aperiodic, we obtain the stationary distribution of sensor battery energy states so that the steady transmitting power is derived. Secondly, the average AoI of the dual-sensor status update system is derived in terms of a closed-form expression by accurately calculating the statistical descriptions of the maximum retransmission number (time) in HARQ-CC and the service time of one packet. The analytical results are validated by using the comparison from simulations. Moreover, compared with traditional single sensor system, the dual-sensor system not only harvests more energy, but also has smaller average AoI because of the joint exploitation of multi-diversity. Besides, the impact of the system parameters on harvested energy and average AoI is provided, which provides insights in terms of the optimal design of Internet of things system.

AoI-Constrained Transmission Scheduling with HARQ and Heterogeneous Sampling Processes

“…where Π D is the set of all deterministic policies. Let π * β denote an optimal policy that solves problem (10) for a given β, which is called a β-optimal policy.…”

“…The following remark expresses the relation between the optimal values of CMDP problem (9) and the MDP problem (10).…”

“…where L * (β) is the optimal value of the MDP problem (10) for a given β, defined as L * (β) = min π∈ΠD L(π, β).…”

“…One of the earliest studies to analyze AoI under an HARQ protocol is [9], where the authors derived the closed-form expression of the average AoI for an HARQ-based M/G/1/1 queueing system. Besides the analysis, the AoI has been studied in the retransmissionbased status update systems from the perspective of sampling and transmission policies [10]- [15]. The most related works to our paper are [14], [15].…”

Optimization on information freshness for multi‐access users with energy harvesting cognitive radio networks

“…From the Reference 29, it is clear that for any scheduling policy, $$$ {\lim}_{t\to \infty }E\left[\frac{1}{t}{\sum}_{v=0}^{t-1}H(v){b}_2(v) As(v)\right]=1 $$$ can be guaranteed for a finite AoI. The average PAoI minimization problem $$$ \min {A}_p^{ave} $$$ is equivalent to $$$$ \underset{x>0}{\max}\kern.41em x, $$$$ $$$$ s.t.\kern0.60em \underset{t\to \infty }{\lim}\operatorname{inf}E\left[\frac{1}{t}\sum \limits_{v=0}^{t-1}H(v){b}_2(v)\right]\ge x, $$$$ $$$$ {Q}^{ave}<\infty, $$$$ …”