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Abstract

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.