Fluctuations of Random Noise Power

A random quantity of interest in many communication and detection systems is the average power, y = Trf'~ Nt)dt, (1) 1 J-T/2 of a sample of finite time duration, T, of a Gaussian noise, N(t). This quantity has been discussed in some detail by Rice in his classic paper1 where he obtains expressions for the first few moments of y and an approximate probability density function. In this paper the exact probability density function, f(y), and the cumulative distribution function, F(y), of the average power are computed for a number of ergodic Gaussian noises and for a number of values of T. The results are presented as a series of curves which are discussed in the next section. It is hoped that they will be of use to those designing specific systems.