On analog computation of vector-valued functions in clustered wireless sensor networks

It is already known that the superposition property of wireless multiple-access channels can profitably be exploited for computing linear functions of the measurements in sensor networks. If appropriate pre- and post-processing functions are employed to operate on sensor readings and the superimposed signal received by a fusion center, respectively, then every function of the measurements is essentially computable by means of the channel at a single channel use, provided that pre- and post-processing functions are not confined to be continuous. If the continuity property is required, then it has been recently shown that in general extra resources are necessary, thereby reducing the computation efficiency. In this paper we extend these results to the problem of computing vector-valued functions in clustered sensor networks (i.e., in networks of multiple-access channels) and show that if interference is appropriately harnessed, the component-functions can be computed much more efficiently than with standard approaches that avoid interference, even in the case of continuous pre- and post-processing functions.