On Function Computation via Wireless Sensor Multiple-Access Channels

In wireless sensor networks, the identity of a particular sensor node and a complete reconstruction of sensed data at a designated sink node may be not needed. Indeed, the objective is often to compute a certain function of the sensed data. Such desired functions can be for example the arithmetic mean, the geometric mean, polynomials and other functions that adequately match the mathematical characteristic of the underlying multiple-access channel. In this paper, we propose a simple practical approach to compute desired functions of sensor network data, exploiting explicitly the mathematical characteristic of the wireless sensor multiple-access channel (WS-MAC). In contrast to traditional schemes that are designed to combat interference caused by other connections, we exploit this interference with the goal of computing the desired functions, which is in a sense a paradigm shift. This leads directly to a higher data rate in terms of function computation or a higher SNR in comparison to other schemes like time division multiple access (TDMA). Our approach needs no extensive symbol or phase synchronization, since the measured values are converted into the transmit power of a specific random transmit sequence with unit norm. Only a coarse block synchronization is necessary so that the proposed scheme is easy to implement.