Timely and Energy-Efficient Information Delivery in Heterogeneous Correlated Random Access Networks

This paper characterizes and jointly optimizes Age of Information (AoI) and energy efficiency in heterogeneous correlated random access networks, where each sensor adopts a distinct transmission probability and its observations are correlated with those of other sensors. An analytical model is proposed to analyze AoI and energy efficiency for each sensor. Closed-form expressions for long-term average AoI and energy efficiency are derived, explicitly accounting for spatial correlation and state-dependent power consumption. By constraining sensors to adopt the same transmission probability, three unified transmission strategies are derived: the age-optimal strategy (q_A^), the energy-efficiency optimal strategy (q_E^), and the Pareto-optimal strategy (q^), which jointly optimizes AoI and energy efficiency. A bounded exhaustive search with O(1/(n q_epsilon)) complexity guarantees efficient computation of q^. Theoretically, the correlation gain is proven to significantly enhance both metrics under spatial correlation. To exploit sensor heterogeneity, a gradient-based iterative algorithm, Multi-Start Projected Adaptive Moment Estimation (MS-PAdam), is proposed to jointly optimize all sensors' transmission probabilities, efficiently converging to the optimal AoI-energy-efficiency tradeoff. Crucially, MS-PAdam adaptively suppresses transmissions where marginal gains are outweighed by correlated neighbors' contributions, substantially alleviating competition. Numerical results show MS-PAdam outperforms unified strategies, achieving harmonious operation that mitigates AoI/energy degradation in contention-intensive scenarios.