  Various wireless sensor network applications involve the computation of a
pre-defined function of the measurements without the need for reconstructing
each individual sensor reading. Widely-considered examples of such functions
include the arithmetic mean and the maximum value. Standard approaches to the
computation problem separate computation from communication: quantized sensor
readings are transmitted interference-free to a fusion center that reconstructs
each sensor reading and subsequently computes the sought function value. Such
separation-based computation schemes are generally highly inefficient as a
complete reconstruction of individual sensor readings is not necessary for the
fusion center to compute a function of them. In particular, if the mathematical
structure of the wireless channel is suitably matched (in some sense) to the
function, then channel collisions induced by concurrent transmissions of
different nodes can be beneficially exploited for computation purposes.
Therefore, in this paper a practically relevant analog computation scheme is
proposed that allows for an efficient estimate of linear and nonlinear
functions over the wireless multiple-access channel. After analyzing the
asymptotic properties of the estimation error, numerical simulations are
presented to show the potential for huge performance gains when compared with
time-division multiple-access based computation schemes.
