This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 1 Optimal Time-Resource Allocation for Energy-Efficient Physical Activity Detection

The optimal allocation of samples for physical activity detection in a wireless body area network for health-monitoring is considered. The number of biometric samples collected at the mobile device fusion center, from both device-internal and external Bluetooth heterogeneous sensors, is optimized to minimize the transmission power for a fixed number of samples, and to meet a performance requirement defined using the probability of misclassification between multiple hypotheses. A filter-based feature selection method determines an optimal feature set for classification, and a correlated Gaussian model is considered. Using experimental data from overweight adolescent subjects, it is found that allocating a greater proportion of samples to sensors which better discriminate between certain activity-levels can result either a lower probability of error or energy-savings ranging from 18 % to 22%, in comparison to equal allocation of samples. The current activity of the subjects and the performance requirements do not significantly affect the optimal allocation, but employing personalized models results in improved energy-efficiency. As the number of samples is an integer, an exhaustive search to determine the optimal allocation is typical, but computationally expensive. To this end, an alternate, continuous-valued vector optimization is derived which yields approximately optimal allocations and can be implemented on the mobile fusion center due to its significantly lower complexity