 minutes of roaming and talking. Of course, this is based on the simple union bound and gives a more pessimistic probability than a more precise calculation of the true probabilities, which will be smaller. It seems that if we allow ourselves an average of one -40-dB fade once every 16 minutes, then we must compensate for the Rayleigh fading chan- nel by 40 dB of power contol. This assumes no diversity and does not take into account any of the frequency diversity effects that occur with spread- spectrum signals. Note that in comparing this application with the cellular radio application in which the radio can be in an automobile traveling at 100 km/hr, the rate of change may be more than 20 times faster than the roaming pace in PCS applications. This means that deep fades occur more often with cellular appli- cations, and thus the IS-95 design must overcome deeper fades to achieve the same rate of deep fades as a PCS system. Impact of Diversity The results above are based on a single-channel output signal. In practice, we may have more than one-channel output, with diversity owing to Antenna diversity in which two or more receiver antennas are used. Frequency diversity in which a wideband signal experiences frequency- selective fading. Fast frequency-hopping spread-spectrum systems can also exhibit frequency diversity. Path diversity in which multipath owing to different delays may be resolved as separate signals at the in-phase and quadrature spread-spec- trum codeword-matched filter outputs. Time diversity in which different time samples are interleaved in an error- correction coding technique. Appendix 3A. Multipath and Diversity The purpose of diversity is to obtain more than one output signal with independent random amplitudes in each signal. Suppose there are N independent random variables owing to N diversity signals. Suppose R1, R2, , RN are the independent random amplitudes for these N diversity signals. There are many ways to combine the N output signals. The simplest tech- nique is to take the signal w