Opportunistic in-network computation for wireless sensor networks

Function computation over wireless sensor networks is investigated, where K sensors measure their observations and a fusion center wishes to estimate a pre-defined function of the observations via fading multiple access channels (MACs). The arithmetic sum and type functions are considered since they yield various fundamental sample statistics such as mean, variance, maximum, minimum, etc. We propose a novel opportunistic in-network computation (INC) scheme in which a subset of sensors with large channel gains opportunistically participate in the transmission at each time slot, while all sensors in a network simultaneously send their observations or only a single sensor sends its observation in the conventional INC schemes. We analyze the ergodic computation rate of the proposed INC scheme and prove that it achieves a non-vanishing computation rate even when the number of sensors K tends to infinity, which provides a significant rate improvement compared to the conventional INC schemes whose computation rates converge to zero as K increases.