Age of information in energy harvesting dual-sensor status update systems with HARQ-MRC

We consider an energy harvesting powered wireless sensor network consisting of two sensors and one destination, where the sensors with finite-sized batteries harvest energy to transmit the sensed status update to the destination. A two-stage communication model, containing both control data and status update transmissions, is considered. Specifically, the destination first transmits the control data to the sensors using hybrid automatic repeat request with selection combining (HARQ-SC) for allocating wireless resources. Then, trigged by a common controller, the sensors synchronously sense and transmit the same status update to the destination using truncated HARQ with maximal ratio combining (HARQ-MRC). The system is interested in not only the fresh sensed data (e.g., humidity, temperature, moisture content) as the newest data usually carries the most valuable information, but also the steady harvested energy as the battery-powered sensors are energy-limited. We first present the energy state transition diagram by a Markov chain to characterize the energy harvesting model, and then provide the corresponding energy transition matrix as well as the steady-state distribution. Considering both the preemptive and non-preemptive transmissions, we derive the average age of information (AoI) expression as a function of energy arrival probability, update generation probability, and maximum allowable number of transmissions. Simulation results validate the theoretical results and demonstrate that the preemptive and non-preemptive schemes can outperform each other for minimizing the average AoI in different system configurations.