Analog computation via wireless multiple-access channels: Universality and robustness

Recently, it has been shown that the superposition property of wireless multiple-access channels can be exploited to compute functions in sensor networks much more efficiently. By using appropriate pre- and post-processing functions operating on real sensor readings and the superimposed signal received by a fusion center, every function of the measurements is in principle computable by means of the wireless channel in which the pre-processing functions, and therefore the transmitting nodes, do not depend on the function of interest. In this paper we extend these general considerations by examining how robust this kind of universality is against variations in network topology due to nodes that drop out of the network or due to new nodes that connect to the network.