Robust Analog Function Computation via Wireless Multiple-Access Channels

TL;DR

This paper proposes a novel analog computation scheme for wireless sensor networks that directly computes functions like mean and max over the wireless channel, avoiding inefficient reconstruction of individual sensor readings.

Contribution

It introduces a practical analog computation method that exploits channel properties for efficient function estimation, outperforming traditional separation-based schemes.

Findings

Significant reduction in estimation error asymptotically.

Numerical simulations demonstrate large performance gains.

Method effectively computes linear and nonlinear functions over wireless channels.

Abstract

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.