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Unformatted text preview: The Complementary Unit Gaussian Distribution Function Q ( x ) Let ( u ), where ( u ) = 1 2 exp u 2 2 , denote the probability density function (pdf) of a standard (or unit) Gaussian random variable. The cumulative probability distribution function (CDF) of this random variable is denoted ( x ) where ( x ) = Z x ( u ) du = Z x 1 2 exp u 2 2 du. ( x ) is also known as the unit Gaussian distribution function and Q ( x ) = 1 ( x ) = Z x ( u ) du = Z x 1 2 exp u 2 2 du is called the complementary unit Gaussian distribution function. Note that since ( x ) is a monotone increasing function rising from 0 at to 1 at , Q ( x ) is a monotone decreasing function falling from 1 at to 0 at . In many applications in communications and signal processing, Q ( x ) is slightly more convenient to use than ( x ). For example, the bit error rate in some communication systems can be expressed as Q ( SNR) where SNR is the signaltonoise ratio . Since Q ( x ) is a decreasing function of its argument, maximizing the SNR is an important objective in communication system design....
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This document was uploaded on 01/24/2012.
 Spring '09

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