As a prelude to subsequent discussion, it will be useful to introduce the concept of the deviation. We want to compute the quantiles of transmission loss at distance ,. The distributions involved are nearly normal, so it simplifies the calculation to express the fractions in terms of standard normal deviates. The complementary normal distribution is given by: (4.1) and the standard normal deviate, is obtained from the inverse function: z, (4.2) If the field strength, is a normally distributed random variable with mean (also equal to its median) E (dB), and standard deviation , then its quantiles are given by: . (4.3) Note the convention that the positive direction of deviation corresponds to an increase in field strength, hence a decrease in loss. To obtain the twofold quantile of basic transmission loss,, we write: (4.4) the overall median value, , and the deviations, and may be written: YL YT, (4.5a) for (4.5b) and where the deviation” of the time variability, , is a function of the distance, A method x. “pseudostandard for computing the deviation” of the time variability, , is given below, since it is not “pseudostandard explicitly given in the Recommendations. For certain interference and/or sharing studies involving mobile services, it may be necessary to calculate the combined time and location variability. In those cases, the root sum square approximation may be used to the combined variability. To obtain the deviation” of the time variability,, use the “pseudostandard 10% time and 50% time quantiles of the field strengths [dB]: (4.6a) or, in terms of the corresponding quantiles of basic transmission losses in dB,
As a prelude to subsequent discussion, it will be useful to introduce the concept of the deviation. We want to compute the quantiles of transmission loss at distance ,. The distributions involved are nearly normal, so it simplifies the calculation to express the fractions in terms of standard normal deviates. The complementary normal distribution is given by: (4.1) and the standard normal deviate, z, is obtained from the inverse function: (4.2) If the field strength, E (dB), is a normally distributed random variable with mean (also equal to its median) and standard deviation , then its quantiles are given by: . (4.3) Note the convention that the positive direction of deviation corresponds to an increase in field strength, hence a decrease in loss. To obtain the twofold quantile of basic transmission loss,, we write: (4.4) the overall median value, , and the deviations, YL and YT, may be written: (4.5a) for (4.5b) and where the “pseudostandard deviation” of the time variability, , is a function of the distance, x. A method for computing the “pseudostandard deviation” of the time variability, , is given below, since it is not explicitly given in the Recommendations. For certain interference and/or sharing studies involving mobile services, it may be necessary to calculate the combined time and location variability. In those cases, the root sum square approximation may be used to the combined variability. To obtain the “pseudostandard deviation” of the time variability,, use the 10% time and 50% time quantiles of the field strengths [dB]: (4.6a) or, in terms of the corresponding quantiles of basic transmission losses in dB,
R-HDB-58-2012-OAS-MSW-E.docx