Higher Order Statistics of Sampled Fading Channels With Applications

• Published in: IEEE transactions on vehicular technology 2012-09, Vol.61 (7), p.3342-3346
• Main Authors: López-Martínez, F. J., Martos-Naya, E., Paris, J. F., Fernández-Plazaola, U.
• Format: Article
• Language: English
• Subjects: Applied sciences; Average fade duration (AFD); Channels; Correlation; Equivalence; Exact sciences and technology; Exact solutions; Fading; fading channels; Frequency domain analysis; Higher order statistics; Information, signal and communications theory; level crossing rate (LCR); Mathematical analysis; OFDM; performance analysis; Random processes; Rayleigh channels; Sampling; Sampling, quantization; Signal and communications theory; Statistics; Studies; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments)
• ISSN: 0018-9545; 1939-9359
• DOI: 10.1109/TVT.2012.2199528

In this paper, we present a novel analytical framework for the calculation of the level crossing rate (LCR) and the average fade duration (AFD) of fading channels sampled at a certain sampling period T S . These expressions are valid for arbitrary fading distributions with arbitrary correlation and can be easily computed in terms of the cumulative distribution function (cdf) of the fading envelope and its bivariate cdf. This approach yields interesting insights into the effect of finite sampling in the higher order statistics of fading processes. We also demonstrate that the proposed expressions for sampled fading process converge with the existing expressions for continuous fading processes as the sampling period tends to zero. As a direct application, exact closed-form expressions are given for the LCR and AFD of sampled Rayleigh fading processes, which are suitable to characterize the higher order statistics of the equivalent frequency-domain fading process in multipath Rayleigh fading.