Abstract
The point process, a sequence of random univariate random variables derived from correlated bivariate random variables as modeled by Arnold and Strauss, has been examined. Statistical properties of the time intervals between the points as well as the probability distributions of the number of points registered in a finite interval have been analyzed specifically in function of the coefficient of correlation. The results have been applied to binary detection and to the transmission of information. Both the probability of error and the cut-off rate have been bounded. Several simulations have been generated to illustrate the theoretical results.
Highlights
It is known that the detection of an optical field at a low level of power is a sequence of events which is a set of distinct time instants {θj}, 0 ≤ j < ∞, such that θj+1 ≥ θj, for all j
We report some calculations that can be obtained under closed forms depending on the value of the parameter c
The v(t), the relaxed one has been well fitted by the expression v(t)
Summary
It is known that the detection of an optical field at a low level of power is a sequence of events which is a set of distinct time instants {θj}, 0 ≤ j < ∞, such that θj+1 ≥ θj, for all j These {θj}s, which are the time instants of interaction between the photons and the detector device, for example, a photomultiplier, constitute a random point process (RPP) for which a positive instantaneous density λ(θj) can be defined. There are two types of processing that can be utilized to characterize such RPP: the time interval distributions (TIDs) and the probability of number distributions (PNDs) [3].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
