Robust Analog Function Computation via Wireless Multiple-Access Channels

• Published in: IEEE transactions on communications Vol. 61; no. 9; pp. 3863 - 3877
• Main Authors: Goldenbaum, Mario, Stanczak, Slawomir
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Channels; Computation; Computation over multiple-access channels; Computer simulation; Detection, estimation, filtering, equalization, prediction; Digitization; distributed computation; Exact sciences and technology; function estimation; in-network processing; Information, signal and communications theory; Mathematical analysis; Mathematical models; Protocols; Receivers; Reconstruction; Robustness; Sensors; Services and terminals of telecommunications; Signal and communications theory; Signal, noise; Synchronization; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Telemetry. Remote supervision. Telewarning. Remote control; Transmission and modulation (techniques and equipments); Wireless communication; Wireless sensor networks; Performance evaluation; function estimation; wireless sensor networks; Noise reduction; Wireless telecommunication; Computation over multiple-access channels; Non linear function; Distributed computing; Remote sensing; Signal detection; Multiple access; Estimation error; in-network processing; Measurement sensor; Error function; distributed computation; Mean value; Interference suppression; Simulation; Code division multiple access; Telecommunication channels; Signal processing; Wireless network; Sensor array; Multiple channel
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2013.072913.120815

Wireless sensor network applications often involve the computation of pre-defined functions of the measurements such as for example the arithmetic mean or maximum value. Standard approaches to this problem separate communication from computation: digitized 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 at the fusion center is not necessary to compute a function of them. In particular, if the mathematical structure of the channel is suitably matched (in some sense) to the function of interest, then channel collisions induced by concurrent transmissions of different nodes can be beneficially exploited for computation purposes. This paper proposes an analog computation scheme that allows for an efficient estimate of linear and nonlinear functions over the wireless multiple-access channel. A match between the channel and the function being evaluated is thereby achieved via some pre-processing on the sensor readings and post-processing on the superimposed signals observed by the fusion center. After analyzing the estimation error for two function examples, simulations are presented to show the potential for huge performance gains over time- and code-division multiple-access based computation schemes.