Abstract
In this paper starting from the well known Nakagami-q fading model we are proposing its improvement by introducing an additional flexibility, in the form of a parameter, which is power of the modulus of complex Gaussian process, in order to provide better matching between theoretical results and experimental values measured in a real environment. Within this paper, we will also present the first order statistical analysis of the proposed α-q model. In this paper, a statistical analysis of the first order of the new α-q model that includes derived analytical expressions for: probability density function, cumulative distribution function, moment n-th order are presented, variance and moment genereting function of one α-q process. Results for the probability density function and cumulative distribution function α-q process are graphically presented.
Highlights
well known Nakagami-q fading model we are proposing its improvement by introducing an additional flexibility
experimental values measured in a real environment
Results for the probability density function and cumulative distribution function α-q process are graphically presented
Summary
Obzirom da su X(t) i Y(t) nekorelisani Gauss-ovi procesi, srednje vrednosti nula, i varijansi σ1 i σ2, respektivno, sledi da je njihova združena gustina raspodele data sledećim izrazom p XY X ,Y x2. Združena gustina raspodele može se predstaviti u polarnom koordinatnom sistemu na sledeći način: pR r, J p. Dolazimo do izraza za raspodele gustine verovatnoće procesa R(t):. Zamenom (12) u (11) dolazimo do sledećeg izraza za raspodelu gustine verovatnoće procesa R(t):. Prikaz raspodele gustine verovatnoće procesa R(t) za različite vrednosti parametra α i parametra q prikazan je na slici 1. Sa slike 2 može se videti da kumulativna verovatnoća procesa R(t) teži 1 sa porastom vrednosti parametra r što potvrđuje tačnost izraza (16). Kumulativna verovatnoća znatno brže teži 1 za niže vrednosti parametra α. Sa slike 1 se vidi da sa porastom parametra α dolazi do bržeg opadanja funkcije gustine verovatnoće. Za veće vrednosti parametra q raspodela gustine verovatnoće procesa R(t) ima znatno sporiju promenu u odnosu za niže vrednosti paramezta q
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