Some Properties of Power Sums of Truncated Normal Random Variables

It is common practice in communications engineering to express signal and noise powers on a logarithmic scale. As is well known, such a scale serves both to narrow the numerical range between large and small powers and to simplify some computations by replacing multiplication by addition. The decibel scale is most commonly used. Employing this scale, the power level x of a power w is defined by x = 10 log l0 £ , (1) W0 where w0 is a reference power, and x is expressed in decibels (dB) over the reference power w0. Note from (1) that u'/w0 -- 10' /10 . In the situation where a number of uncorrelated signal sources feed into the same load, the power level p,, of a sum of powers u, . . . , u, is given by pn = 10 logio [10" /10 + ··· + 10' n/, °], 2001 (2)