On Numerical Evaluation of Packet-Error Rate for Binary Phase-Modulated Signals Reception over Generalized-K Fading Channels

We present a numerical evaluation of packet error rate (PER) for digital binary phase modulations over wireless communication channels. The analysis is valid for a quasistatic fading communication channel, where multipath fading and shadowing appear simultaneously. The approach is based on numerical evaluation of signal-to-noise ratio threshold that is further used in PER computation. We analyze the threshold and PER dependence on signal power, multipath fading and shadowing severity, as well as packet length

Estimation of Truncation Error in Statistical Description of Communication Signals over mm-Wave Channels

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 mm-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

Asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree

Orthogonal systems of trigonometric polynomials of semi-integer degree with respect to a weight function w(x) on (0, 2 pi) have been considered firstly by Turetzkii [A.H. Turetzkii, On quadrature formulae that are exact for trigonometric polynomials, East J. Approx. 11 (2005) 337-359 (translation in English from Uchenye Zapiski, Vypusk 1(149), Seria Math. Theory of Functions, Collection of papers, Izdatel'stvo Belgosuniversiteta imeni V.I. Lenina, Minsk, (1959) pp. 31-54)]. Such orthogonal systems are connected with quadrature rules with an even maximal trigonometric degree of exactness (with an odd number of nodes), which have application in numerical integration of 2 pi-periodic functions. In this paper we study asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree with respect to a strictly positive weight function satisfying the Lipschitz-Dini condition

Error Probability of a Coherent <i>M</i>-ary PSK FSO System Influenced by Phase Noise

In this paper, we aim to develop an analytical framework for design and analysis of new generation mobile networks fronthaul/backhaul links based on the application of free-space optical (FSO) technology. Taking the receiver hardware imperfections into account, we present an efficient analytical approach in analyzing average symbol error probability (SEP) of the coherent FSO system employing M-ary phase-shift keying (PSK). Optical signal transmission is influenced by pointing errors and atmospheric turbulence. The signal intensity fluctuations caused by atmospheric turbulence are modeled by general Málaga (M) distribution, which takes into account the effect of multiple scattered components. We estimate the range of the signal-to-noise ratio at which the SEP floor appears, as well as the value of this non-removable error floor. The results illustrate that the effect of imperfect phase error compensation on the SEP is more critical under weaker turbulence conditions and for higher order modulation formats. Based on the analytical tools presented here, it is possible to estimate tolerable value of standard deviation of phase noise for the given value of SEP. This value of standard deviation is an important parameter in designing the phase-locked loop filter in the receiver