Generalized marcum q-function
WebJun 13, 2016 · Closed-form solutions for the general integrals in terms of Meijer's G-function are derived and validated by comparing with the analytic expressions for the existing integrals involving the generalized Marcum Q-function, which are the special cases of the general integrals addressed in this letter. WebDec 1, 2003 · First, this paper shows that the incomplete integrals of the type addressed in[11]and [12] are represented by a finite number of elementary functions, generalized Marcum Q functions, and a certain ...
Generalized marcum q-function
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WebWe then apply the derived results to assess the secrecy performance of the system in terms of the average signal-to-noise ratio (SNR) as a function of the $\kappa$ and $\mu$ fading parameters. We observed that for fixed values of the eavesdropper's average SNR, increases in the average SNR of the main channel produce a higher probability of ... WebThe distribution of ∑ i = 1 ν ( Z i + δ i) 2 where Z i are independent standard normal variables and δ i are constants. λ = ∑ i = 1 ν δ i 2 > 0. (In communications it is called the Marcum-Q function). It can be thought of as a Generalized Rayleigh-Rice distribution. The two shape parameters are ν, a positive integer, and λ , a positive real number.
WebAug 1, 2009 · The study of the generalized Marcum function of the second kind is motivated by the importance of the generalized Marcum Q-function in the electrical engineering literature, which was... WebJun 13, 2016 · We investigate analytic solutions for three generalized integrals involving arbitrary powers, generalized Marcum Q-function, and exponential functions, which …
WebJan 25, 2024 · The generalized Marcum Q-function \(Q_{\nu }(a,b)\) and its particular case \(Q_1(a,b)\), the so-called Marcum function, are important functions of the electrical … WebQ = marcumq(a,b) computes the Marcum Q-function of order 1 for noncentrality parameter a and argument b. Use this syntax to calculate the special case of the generalized …
WebQ−function [Marcum 1960]. This is the notation used, for instance, in the MATLAB built-in function marcumq. The relation with the notation we use is simple: Qµ(x,y) = Qeµ(√ 2x, p 2y), (5) and similarly for the P−function. The generalized Marcum Q−function is an important function used in radar detec-
Weband where (,) is the lower incomplete gamma function. The Marcum Q-function (,) can also be used to represent the cdf. (;,) = (,) When the degrees of freedom k is positive odd integer, we ... , is generalized chi-square distributed. If ′ and ′ and is independent of then a … lasten suusta kuultualasten suusta ystävyysWebAug 1, 2009 · In this paper, we study the generalized Marcum Q -function Q nu( a , b ), where a , nu > 0 and b ges 0. Our aim is to extend the results of … lasten suustaWebGeneralized Marcum Q -function collapse all in page Syntax Q = marcumq (a,b) Q = marcumq (a,b,m) Description example Q = marcumq (a,b) computes the Marcum Q -function of order 1 for noncentrality parameter a and argument b. Use this syntax to calculate the special case of the generalized Marcum Q-function of order m with m = 1. lasten sydänsairaudetIn statistics, the generalized Marcum Q-function of order $${\displaystyle \nu }$$ is defined as $${\displaystyle Q_{\nu }(a,b)={\frac {1}{a^{\nu -1}}}\int _{b}^{\infty }x^{\nu }\exp \left(-{\frac {x^{2}+a^{2}}{2}}\right)I_{\nu -1}(ax)\,dx}$$where $${\displaystyle b\geq 0}$$ and See more Finite integral representation The generalized Marcum Q-function can alternatively be defined as a finite integral as However, it is … See more It is convenient to re-express the Marcum Q-function as $${\displaystyle P_{N}(X,Y)=Q_{N}({\sqrt {2NX}},{\sqrt {2Y}}).}$$ See more 1. ^ J.I. Marcum (1960). A statistical theory of target detection by pulsed radar: mathematical appendix, IRE Trans. Inform. Theory, vol. … See more Based on monotonicity and log-concavity Various upper and lower bounds of generalized Marcum-Q function can be obtained using monotonicity and log-concavity of the function $${\displaystyle \nu \mapsto Q_{\nu }(a,b)}$$ and the fact that we have … See more The generalized Marcum Q-function can be used to represent the cumulative distribution function (cdf) of many random variables: • If See more lasten synttäri helsinkiWebApr 10, 2024 · First, we derive the analytical expression of the outage probability with a generalized Marcum Q-function. Then, we develop an alternating optimization algorithm to minimize the outage probability by capitalizing on the generalized eigenvalue-eigenvectors. lasten suzuki pvWebThe generalized Marcum Q-function, Qm (a,b), is here explained geometrically as the probability of a 2m-dimensional, real, Gaussian random vector, whose mean vector has a Frobenius norm of a, lying… Expand 37 Asymptotic and numerical aspects of the noncentral chi-square distribution N. Temme Mathematics 1993 40 PDF lasten synttäreille ohjelmaa