On the Asymptotic Efficiency of Distributed Estimation Systems With Constant Modulus Signals Over Multiple-Access Channels

• Published in: IEEE transactions on information theory Vol. 57; no. 10; pp. 7125 - 7130
• Main Authors: Tepedelenlioglu, C., Banavar, M. K., Spanias, A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.10.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Asymptotic efficiency; Channel estimation; characteristic function; Code Division Multiple Access; Data transmission; Detection, estimation, filtering, equalization, prediction; distributed estimation; Electric noise; Estimation; Exact sciences and technology; Fisher information; Information theory; Information, signal and communications theory; Noise; Normal distribution; Phase modulation; Sensor fusion; Sensor phenomena and characterization; Services and terminals of telecommunications; Signal and communications theory; Signal processing; Signal, noise; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Telemetry. Remote supervision. Telewarning. Remote control; Transmission and modulation (techniques and equipments); wireless sensor network; Performance evaluation; Multiple access; distributed estimation; Necessary and sufficient condition; Wireless telecommunication; wireless sensor network; Sensor fusion; Distributed system; Asymptotic efficiency; Remote sensing; Fisher information; Characteristic function; Distributed processing; Information processing; Data fusion; Wireless network; Sensor array; Multiple channel; Signal detection
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2165806

A distributed estimation problem is considered with multiple-access channels between sensors and a fusion center. The sensors phase-modulate their noisy observations before transmitting them to the fusion center, where a signal parameter is estimated. The asymptotic efficiency of this estimator is then determined by using two inequalities that relate the Fisher information and the characteristic function. A necessary and sufficient condition for equality is found for the first time in the literature. The loss in efficiency of the distributed estimation scheme relative to the centralized approach is quantified for different sensing noise distributions. It is shown that this distributed estimation system does not incur an efficiency loss if and only if the sensing noise distribution is Gaussian.