we have two log-normal distributions with 10-dB standard deviations whose means differ by 30 dB. The S/I ratio, the difference in decibels, has a standard devia- tion of 14 dB (V102 + 102.). In evaluating wireless telephone service, we tend to use the tenth percentile of the distribution, the level where 90 percent of the calls are better and 10 percent of the calls are worse. In the case of a normal distribution, the tenth percentile is 1.3 stan- dard deviations worse than the mean, SO this particular example has a tenth percentile S/I ratio of 12 dB, quite acceptable performance for GSM. 5 It is an important observation that the signal and interfering radio paths are all be- tween base stations and wireless telephones. The radio paths between base stations and the radio paths between user terminals are not a factor in the AMPS or GSM FDD radio environments. 6 The signal distribution depends on the cell radius but generally is independent of the antenna radiation pattern or how the channel is reused. The interference distributions, on the other hand, are highly dependent on which cells reuse the channels and the an- tenna radiation patterns used at the base stations. In the next section we will examine how channel reuse is related to S/I distribution. 4There are two noteworthy comments here for those interested in the convolution integral. First, the units of s(x), i(x), and q(x) are all logarithmic decibels. A calculus student could perform a change of variables from decibels to power using Eq. (1.3), but there is no reason to do so. Sec- ond, this is a convolution of the difference rather than the sum, so we have i(x + t) instead of i(x - t) as we would have in a normal convolution. 5This is a mean S/I ratio of 30 dB minus 1.3 times a standard deviation of 14 dB. 6Time division duplex (TDD) systems can have significant other interference components because both forward and reverse directions share the same frequencies at different times. If one cell is using its forward link at the same time and on the same fr