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This subsection will focus on the received signal envelope having a central chi-square distribution and will use 2SRL to analyze the physical-layer TS packets outputting behavior.
Based on an analysis of the error rate and on simulations using a wireless Rayleigh fading channel with received signal envelope having a central chi-square distribution, an approximation of the performance improvement has been obtained.
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It works on the principle that if all measurements are performed under LOS channel conditions, the residuals have a central Chi-Square distribution and the residuals are the squared differences between the estimates and the true positions.
If effects are random, then X = (1 − ι) Q has a central chi-square distribution.
Under homogeneity, with large n k, Q has a central chi-square distribution with df degrees of freedom.
As ι gets small, we converge toward the homogeneous situation where Q itself has a central chi-square distribution with df degrees of freedom.
Thus, follows the central chi-square distribution with degrees of freedom and is a central chi-square random variable with one degree of freedom.
The probability density function of a central chi-square distribution is defined in [23] as.
where χ 2 w 2 and χ 2 w 2 ( 2 γ ) represent a central chi-square distribution and a non-central chi-square distribution with 2w degrees of freedom and the non-centrality parameter 2γ, respectively.
(chi _{2u}^{2}) follows a central chi-square distribution with 2u degrees of freedom, and (chi _{2u}^{2} ({2gamma _{p,k}^{n}})) follows a non-central chi-square distribution with 2u degrees of freedom and a non centrality parameter (2gamma _{p,k}^{n}) [4].
The second term of (12) represents the right-tail probability of a central chi-square with l = N + 2k degrees of freedom.
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