 Signal dBm Figure 27.3 Signal distribution for a cell sector. path distribution between a base station's antenna face and a community of wireless user terminals. This distribution is typically log-normal, as described in Sec. 1.6, and it looks like a normal bell-shaped distribution on the decibel scale. Figure 27.3 shows a typical received signal distribution for AMPS or GSM calls. This is the signal S part of the S/I ratio, the received radio power, the product of the trans- mit power and the radio path gain, or their sum in decibels. In this case, the average received signal power is -90 dBm, 1 pW, and the standard deviation is about 10 dB. Figure 27.4 shows the same signal distribution with an interferer I superimposed on the picture. In this case, the average received interferer power is - 120 dBm, 1 fW, and the standard deviation is about 10 dB. Received Power dBm Figure 27.4 Signal and interference for a cell sector. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Conventional Reuse Principles Conventional Reuse Principles While it is tempting to suggest that the overlap of the two curves represents the lost call rate, the actual mathematical relationship is more complicated. If s(x) is the signal density function and i(x) is the interference density function, then the distribution of S/I ratio q(x) is the convolution of s(x) and i(x), as shown in Eq. (27.1)4: s(t)i(x + dt (27.1) Even with the complexity of mathematical convolution, the bottom line is that the closer these curves are, the more signal and interference overlap, the more likely an AMPS or GSM system is to have poor sound quality and to lose calls. The statistical convolution of two normal distributions is another normal distribu- tion whose standard deviation og is the root-mean-square of the first two standard de- viations Os and Oi, as shown in Eq. (27.2): (27.2) Thus 