Opportunistic Function Computation for Wireless Sensor Networks
Function computation over wireless sensor networks is investigated, where a set of K sensors observe their sensor readings and a fusion center wishes to learn a predefined function of the sensor readings via fading multiple access channels (MACs) In this paper, the arithmetic sum and type functions are considered since they can yield various fundamental sample statistics such as mean, variance, maximum, and minimum. We propose a novel opportunistic in network computation (INC) framework in which a subset of sensors with large channel gains opportunistically participate in the transmission at each time, while all sensors simultaneously send their observations or only a single sensor sends its observation in the conventional schemes. We mathematically analyze the long term average computation rate of the proposed INC, and prove that it achieves a nonvanishing computation rate even when the number of sensors K tends to infinity, which is in fact a significant improvement and the first theoretical result in fading MACs. Note that the computation rates of the conventional schemes become zero as K increases. We further show that a similar multiuser diversity gain is still achievable under delay constraints, which implies that the proposed INC is restricted to exploit a fixed and finite number of time slots (or fading instances) for the function computation.
IEEE Transactions on Wireless Communications