lar systems. Like the rules-of-thumb formulas for how to invest in stocks or how many calories you use playing tennis, these are not rigorously derived results. However, rules of thumb help us understand the relationships among various components of cellular design. 27.11.1 Channel bandwidth The simplest rule is that narrow channels are more efficient. All other things being equal, a 10-kHz channel uses one-third the radio spectrum resource that a 30-kHz channel uses. For this calculation, we have to use the per-channel bandwidth rather than the per-carrier bandwidth, so the GSM channel counts as 25 kHz. This means that GSM is 30/25 as efficient as AMPS at the same S/I distribution. That the GSM channel is one-eighth of a 200-kHz carrier does not affect this estimate. 27.11.2 6 dB of S/N is a factor of 2 The big background rule of conventional reuse is that 6 dB of radio performance is worth a factor of 2 in reuse. 16 Why is this? Because a factor of 2 in reuse means using each channel twice as often in the same number of cells. Since cells are spread out over a two-dimensional service area, doubling the reuse of each channel means reducing the 16 This is a logarithmic relationship, SO 10 dB is a factor of 3 (close enough to 3.162), 12 dB is a factor of 4, and 20 dB is a factor of 10. 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 Capacity and Quality Principles cochannel reuse distance by the square root of two (V2). Using the fourth-power-of- distance rule from Sec. 1.7, reducing the distance by V2 creates four times the inter- ference, 6 dB more. We can express the 6-dB rule is Eq. (27.3): (27.3) where C1 = first channels per base station C2 = second channels per base station d1 = first S/N ratio in decibels d2 = second S/N ratio in decibels As an example, let us compare the AMPS and GSM channels. The GSM ch