In this paper, a clustered wireless sensor network is considered that is modeled as a set of coupled Gaussian multiple-access channels. The objective of the network is not to reconstruct individual sensor readings at designated fusion centers but rat
her to reliably compute some functions thereof. Our particular attention is on real-valued functions that can be represented as a post-processed sum of pre-processed sensor readings. Such functions are called nomographic functions and their special structure permits the utilization of the interference property of the Gaussian multiple-access channel to reliably compute many linear and nonlinear functions at significantly higher rates than those achievable with standard schemes that combat interference. Motivated by this observation, a computation scheme is proposed that combines a suitable data pre- and post-processing strategy with a nested lattice code designed to protect the sum of pre-processed sensor readings against the channel noise. After analyzing its computation rate performance, it is shown that at the cost of a reduced rate, the scheme can be extended to compute every continuous function of the sensor readings in a finite succession of steps, where in each step a different nomographic function is computed. This demonstrates the fundamental role of nomographic representations.
This invited paper presents some novel ideas on how to enhance the performance of consensus algorithms in distributed wireless sensor networks, when communication costs are considered. Of particular interest are consensus algorithms that exploit the
broadcast property of the wireless channel to boost the performance in terms of convergence speeds. To this end, we propose a novel clustering based consensus algorithm that exploits interference for computation, while reducing the energy consumption in the network. The resulting optimization problem is a semidefinite program, which can be solved offline prior to system startup.
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.
