Abstract
To identify or equalize wireless transmission channels, or alternatively to evaluate the performance of many wireless communication algorithms, coefficients or statistical properties of the used transmission channels are often assumed to be known or can be estimated at the receiver end. For most of the proposed algorithms, the knowledge of transmission channel statistical properties is essential to detect signals and retrieve data. To the best of our knowledge, most proposed approaches assume that transmission channels are static and can be modeled by stationary random variables (uniform, Gaussian, exponential, Weilbul, Rayleigh, etc.). In the majority of sensor networks or cellular systems applications, transmitters and/or receivers are in motion. Therefore, the validity of static transmission channels and the underlying assumptions may not be valid. In this case, coefficients and statistical properties change and therefore the stationary model falls short of making an accurate representation. In order to estimate the statistical properties (represented by the high-order statistics and probability density function, PDF) of dynamic channels, we firstly assume that the dynamic channels can be modeled by short-term stationary but long-term non-stationary random variable (RV), i.e., the RVs are stationary within unknown successive periods but they may suddenly change their statistical properties between two successive periods. Therefore, this manuscript proposes an algorithm to detect the transition phases of non-stationary random variables and introduces an indicator based on high-order statistics for non-stationary transmission which can be used to alter channel properties and initiate the estimation process. Additionally, PDF estimators based on kernel functions are also developed. The first part of the manuscript provides a brief introduction for unbiased estimators of the second and fourth-order cumulants. Then, the non-stationary indicators are formulated. Finally, simulation results are presented and conclusions are derived.
Highlights
Unlike discrete transmission channels which have limited practical value, continuous random transmission channels are widely accepted and used to illustrate practical concepts [1]
The transmission channels can no longer be considered as static channels, i.e., they cannot be modeled by stationary random variables
We developed a non-stationary transition indicator based on the variance and the fourth-order cumulant
Summary
Unlike discrete transmission channels which have limited practical value, continuous random transmission channels are widely accepted and used to illustrate practical concepts [1]. In various applications, transceiver units are in motion For such systems, the transmission channels can no longer be considered as static channels, i.e., they cannot be modeled by stationary random variables. Most researchers assume that the transmission channels are static during the processing timea [28,29,30] In this manuscript, the proposed models are improved by considering that transmission channels are dynamic channels that can be modeled as non-stationary variables. To the best of our knowledge, there is no such PDF estimator for nonstationary random variables It is the aim of this paper to propose a PDF estimator based on a smooth kernel PDF estimator that assumes known transition times
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