Measurement Complexity of Rayleigh Fading Channels

• Published in: IEEE transactions on vehicular technology Vol. 58; no. 7; pp. 3776 - 3781
• Main Authors: Xinjia Chen, Xinjia Chen, Guoxiang Gu, Guoxiang Gu, Kemin Zhou, Kemin Zhou
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Access methods and protocols, osi model; Applied sciences; Asymptotic properties; Channels; Confidence intervals; Detection, estimation, filtering, equalization, prediction; Electrical engineering. Electrical power engineering; Electrical machines; Error analysis; Estimates; Exact sciences and technology; Fading; Information, signal and communications theory; Intervals; Mathematical models; Noise measurement; Parameter estimation; Path loss; Power control; Power system modeling; Random variables; Rayleigh channels; Rayleigh fading channels; Regulation and control; Signal and communications theory; Signal to noise ratio; Signal, noise; Size measurement; Studies; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Transmission and modulation (techniques and equipments); Wireless communication; Wireless communications; Fading channels; Access control; Mobile radiocommunication; wireless communications; Parameter estimation; Logarithmic function; Wireless telecommunication; Rayleigh channels; Data transmission; Rayleigh fading channels; Coverage; Power electronics; Path loss; Modeling; Confidence interval; Power control; Channel estimation; Handover; Relative error; Rayleigh fading; Mathematical model; Transmission loss; Random variable
• ISSN: 0018-9545; 1939-9359
• DOI: 10.1109/TVT.2009.2015952

Rayleigh fading is a widely used channel model in wireless communications. The mean channel power is of practical importance in channel access, power control, handoff, modeling, and coverage analysis of wireless systems. A fundamental problem naturally arises: How many measurements are sufficient to estimate these parameters with the prescribed margin of error and confidence level? We first study the noise-free case in which only the second moment of the Rayleigh random variable is subject to measurement and estimation. It is demonstrated that the measurement sample size is roughly inversely proportional to the square of the margin of relative error and is linear with respect to the logarithm of the inverse of the gap between the confidence level and one. A closed-form formula is also obtained for the interval estimate of the second moment that is shown to be asymptotically tight. These sample complexity results are extended to the noisy case for interval estimation of the path loss and noise power. Our study shows that a typical margin of relative error can be achieved with near certainty and modest sample size.