A Time-Varying Opportunistic Multiple Access for Delay-Sensitive Inference in Wireless Sensor Networks

We consider distributed transmission scheduling for inference over multiple access channels (MAC) using a wireless sensor network (WSN). The sensors transmit their data simultaneously using common shaping waveforms through finite-state Markovian fading channels, and the fusion center (FC) receives a superposition of the analog transmitted signals. The inference task is computed by the FC and is based on data received from the sensors. We study the case of delay-sensitive inference, where each sensor must schedule its transmission in one of D consecutive time slots. The essence of the problem is to schedule transmissions by exploiting the channel diversity over time slots to minimize the expected transmission energy consumed during the inference task. We formulate the transmission scheduling problem as a finite-horizon Markov decision process (MDP) with a continuous state space. By judiciously exploiting the inherent structure of the associated dynamic programming (DP) problem, we prove that the optimal solution obeys a time-varying threshold-based policy with low complexity (thus avoiding the general intractable complexity of DP with the problem size). We then establish a novel Time-varying Opportunistic Multiple Access (TOMA) protocol based on the structured DP solution.