The Journal of Korean Institute of Communications and Information Sciences (한국통신학회논문지)

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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A Geometric Derivation of the Craig Representation for the Two-Dimensional Gaussian Q-Function

이변량 가우시안 Q-함수의 Craig 표현에 대한 기하학적인 유도

  • 박승근 (한국전자통신연구원 전자파환경연구팀) ;
  • 이일규 (공주대학교 전기전자제어공학부)
  • Received : 2010.11.12
  • Accepted : 2011.02.08
  • Published : 2011.04.30
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Abstract

In this paper, we present a new and simple derivation of the Craig representation for the two-dimensional (2-D) Gaussian Q-function in the viewpoint of geometry. The geometric derivation also leads to an alternative Craig form for the 2-D Gaussian Q-function. The derived Craig form is newly obtained from the geometry of two wedge-shaped regions generated by the rotation of Cartesian coordinates over two correlated Gaussian noises. The presented Craig form can play a important role in computing the probability represented by the 2-D Gaussian Q-function.

본 논문에서는 기하학적인 관점으로 이변량 가우시안 Q-함수의 Craig 표현에 대한 새롭고 간단한 유도를 제시하고 있다. 또한, 이러한 기하학적인 유도는 이변량 가우시안 Q-함수의 또 다른 Craig 표현 식을 제시하고 있다. 새롭게 유도된 이변량 가우시안 Q-함수의 Craig 식은 2개의 상관 가우시안 잡음에서 직교좌표의 변환으로 생성되는 2개 웨지 영역의 기하학으로부터 새롭게 구한 것이다. 제시된 Craig 형태는 이변량 가우시안 Q-함수로 표현되는 확률을 계산하는데, 중요한 역할을 할 수 있다.

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References

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