The cumulative distribution function (CDF) of the T-X family is given by R{W(F(x))}, where R is the CDF of a random variable T, F is the CDF of X and W is an increasing function defined on [0, 1] having the support of T as its range. This family provides a new method of generating univariate distributions. Different choices of the R, F and W functions naturally lead to different families of distributions. This paper proposes the use of quantile functions to define the W function. Some general properties of this T-X system of distributions are studied. It is shown that several existing methods of generating univariate continuous distributions can be derived using this T-X system. Three new distributions of the T-X family are derived, namely, the normal-Weibull based on the quantile of Cauchy distribution, normal-Weibull based on the quantile of logistic distribution, and Weibull-uniform based on the quantile of log-logistic distribution. Two real data sets are applied to illustrate the flexibility of the distributions.
This paper presents the capacity analysis of unmanned aerial vehicles (UAVs) communications supported by flying intelligent reflecting surfaces (IRSs). In the considered system, some of the UAVs are equipped with an IRS panel that applies certain phase-shifts to the incident waves before being reflected to the receiving UAV. In contrast to existing work, this letter considers the effect of imperfect phase knowledge on the system capacity, where the phase error is modeled as a von Mises random variable with parameter κ. Analytical results, corroborated by Monte Carlo simulations, show that the achievable capacity is dependent on the phase error, however, the capacity loss becomes negligible at high signal-to-noise ratio (SNR) and when κ ≥ 6.
This letter considers the exact bit error rate (BER) analysis of a two-user non-orthogonal multiple access (NOMA) system using square quadrature amplitude modulation (QAM). Unlike existing work, no constraints are imposed on the modulation order of the QAM symbols for any user. Closedform expressions are derived for the BER of the successive interference cancellation (SIC) receiver in Raleigh fading channels. The analytical BER results corroborated by Mote Carlo simulation show that the power control becomes challenging for high order QAM. Moreover, the BER of each user is approximately independent of the modulation scheme used by the other user for certain power settings.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.