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- Title
Estimation of Truncation Error in Statistical Description of Communication Signals over mm-Wave Channels.
- Authors
Marjanović, Zvezdan; Milić, Dejan N.; Đorđević, Goran T.
- Abstract
This paper presents an illustration of how knowledge from the field of special functions, orthogonal polynomials and numerical series can be applied to solve a very important problem in the field of modern wireless communications. We present the formulas for the probability density function (PDF) and cumulative distribution function (CDF) of the composite signal envelope over an m m -Wave channel. The formulas for the PDF and CDF are expressed in the convergent infinity series form. The main contribution of the paper is in estimating the upper bounds for absolute truncation error in evaluating PDF and CDF of the signal envelope. We also derive the formulas for the required number of terms in the summation under the condition of achieving a given accuracy for typical values of channel parameters. In deriving these formulas, we use the alternating series estimation theorem, as well as some properties of orthogonal polynomials in order to derive upper bounds for hypergeometric functions. Based on the newly derived formulas, numerical results are presented and commented upon. The analytical results are verified by Monte Carlo simulations. The results are essential in the designing and performance estimating of the fifth-generation (5G) and beyond wireless networks.
- Subjects
STATISTICAL errors; PROBABILITY density function; CHANNEL estimation; MONTE Carlo method; ORTHOGONAL polynomials; CUMULATIVE distribution function; HYPERGEOMETRIC functions
- Publication
Axioms (2075-1680), 2022, Vol 11, Issue 10, pN.PAG
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms11100569