Title :
A simpler form of the Craig representation for the two-dimensional joint Gaussian Q-function
Author :
Simon, Marvin K.
Author_Institution :
Jet Propulsion Lab., Pasadena, CA, USA
Abstract :
We derive a simpler form for the Craig (1991) representation of the two-dimensional joint Gaussian Q-function which dispenses with the trigonometric factor that precedes the exponentials in the integrands and furthermore results in an exponential argument that is precisely in the same simple form as that in the Craig representation of the one-dimensional Gaussian Q-function. As such, the entire dependence on the correlation parameter now appears only in the limits of integration. The resulting single integral form is particularly useful in evaluating the outage probability for dual diversity selection combining over correlated identically and nonidentically distributed log normal channels.
Keywords :
AWGN channels; Gaussian distribution; correlation methods; diversity reception; error statistics; integral equations; log normal distribution; 1D Gaussian Q-function; 2D joint Gaussian Q-function; AWGN channel; Craig representation; Gaussian probability function; additive white Gaussian noise channel; average error probability; correlated identically distributed log normal channels; correlated nonidentically distributed log normal channels; correlation parameter; dual diversity selection combining; exponential argument; integral form; outage probability; two-dimensional joint Gaussian Q-function; AWGN; Additive white noise; Constellation diagram; Diversity methods; Diversity reception; Fading; Gaussian distribution; Integral equations; Random variables; Two dimensional displays;
Journal_Title :
Communications Letters, IEEE
DOI :
10.1109/4234.984687
