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In wearable optical sensing applications whose target tissue is not superficial, such as deep tissue oximetry, the task of embedded system design has to strike a balance between two competing factors. On one hand, the sensing task is assisted by increasing the radiated energy into the body, which in turn, improves the signal-to-noise ratio (SNR) of the deep tissue at the sensor. On the other hand, patient safety consideration imposes a constraint on the amount of radiated energy into the body. In this paper, we study the trade-offs between the two factors by exploring the design space of the light source activation pulse. Furthermore, we propose BASS, an algorithm that leverages the activation pulse design space exploration, which further optimizes deep tissue SNR via spectral averaging, while ensuring the radiated energy into the body meets a safe upper bound. The effectiveness of the proposed technique is demonstrated via analytical derivations, simulations, andin vivomeasurements in both pregnant sheep models and human subjects.