Zvezdan M. Marjanovic

On the Effects of Correlation on Outage Performance of FSO-Unbalanced Multibranch SC Receiver

In this letter, we study the outage performance of unbalanced multibranch selection combining receiver operating over free-space optical gamma-gamma turbulence link. The analysis is performed in the case when the position of closely placed photodiodes corresponds to the constant correlation model. Novel analytical expressions for the probability density function and cumulative distribution function of receiver signal-to-noise ratio (SNR) are derived in the infinite series form whose convergence is numerically determined. Based on these analytical results, we examine the simultaneous effects of the spatial correlation, diversity order, photodiodes diameter, and turbulence strength on outage performance. The results illustrate that spatial correlation has a strong effect on SNR gain decreasing, especially for the higher values of diversity order.

On the R-order of some accelerated methods for the simultaneous finding of polynomial zeros

A Gauss-Seidel procedure is applied to increase the convergence of a basic fourth order method for finding polynomial complex zeros. Further acceleration of convergence is performed by using Newtons and Halleys corrections. It is proved that the lower bounds of theR-order of convergence for the proposed serial (single-step) methods lie between 4 and 7. Computational efficiency and numerical examples are also given.ZusammenfassungEin Gauss-Seidel Verfahren wird verwendet zur Beschleunigung der Konvergenz eines Verfahrens vierter Ordnung zur Bestimmung komplexer Polynomwurzeln. Eine weitere Beschleunigung der Konvergenz wird erreicht durch Anwendung von Newton und Halley-Korrekturformeln. Es wird bewiesen, daß die unteren Schranken für dieR-Ordnung der vorgeschlagenen seriellen (Einzelschritt-) Verfahren zwischen 4 und 7 liegen. Die Effizienzzahl und ein numerisches Beispiel wird angegeben.

A family of simultaneous zero finding methods

A class of iterative methods with arbitrary high order of convergence for the simultaneous approximation of multiple complex zeros is considered in this paper. A special attention is paid to the fourth order method and its modifications because of their good computational efficiency. The order of convergence of the presented methods is determined. Numerical examples are given.

Connection of Semi-integer Trigonometric Orthogonal Polynomials with Szegő Polynomials

In this paper we investigate connection between semi-integer orthogonal polynomials and Szegos class of polynomials, orthogonal on the unit circle. We find a representation of the semi-integer orthogonal polynomials in terms of Szegos polynomials orthogonal on the unit circle for certain class of weight functions.

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.

Truncation error analysis in computing of SEP and SEP floor for partially coherent receiver of MPSK signals over composite fading channels

Abstract In this paper, we analyze detection of multilevel phase-shift keying (MPSK) signals transmitted over a Gamma shadowed Nakagami-m fading channel. We derive novel analytical expression, in terms of Meijer’s G function, for Fourier coefficients of the probability density function of the received signal composite phase. Under the assumption of the imperfect reference signal extraction in the receiver, which is performed from the pilot signal, the analytical expression is derived for the symbol error probability (SEP) in the form of convergent series. The existence of the error floor is identified, and expression for its computation is provided. Mathematical proofs for convergence of Fourier series are provided for both SEP and SEP floor, and novel expressions of upper bounds for truncation errors are derived in terms of elementary mathematical functions. The convergence rate of the derived expressions is examined. Numerical results are confirmed independently by Monte-Carlo simulations.

Asymptotic behavior of orthogonal trigonometric polynomials of semi-integer degree

Abstract Orthogonal systems of trigonometric polynomials of semi-integer degree with respect to a weight function w ( x ) on [ 0 , 2 π ) 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 π -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.