Some Properties of Power Sums of Truncated Normal Random Variables

The power sum of Pnn components X1, X2, …, Xnis defined by the relationpₙ\ = \ 10 log₁₀\ [10^X₁/10 + … + 10^Xₙ/10]The distributions of such power sums are studied both analytically and by Monte Carlo simulation techniques for the case where the components are independent, identically distributed, truncated normal random variables. Results are given in terms of distributions and moments of Pn. The number of components varies from 2 to 256, and the standard deviation of the component variables before truncation ranges from 1 to 10 dB. The dependence of the results on the choice of truncation point is also investigated.