ormance of a radio link almost always defined in terms of the S/N or S/I ratio. These concepts are important in any radio engineering, but CDMA makes it partic- ularly important because small changes in signal make comparable changes in capac- ity. The connection is often direct: 0.5-dB change in signal quality is a 0.5-dB change in system capacity, which should be a 12 percent difference in revenue. (Before you scoff at 12 percent, ask yourself what a 12 percent change in your own salary is worth to you.) And there is a more subtle reason to think in terms of ratios. There is a statistical notion, the law of large numbers, that tells us when we add a large number of random variables the sum tends toward a particular statistical shape called a normal distribu- tion, the famous bell-shaped curve we read about.6 6 Another term for a normal distri- bution is a gaussian distribution, named after the mathematician Karl Friedrich Gauss (1777-1855). In a radio path, the random variables are path losses from line-of-sight distance, buildings, trees, hills, and even rainy weather, and these path losses multi- ply in absolute numbers and add in decibel-ratio units. If distance path loss averages 80 dB, for example, buildings add another 15 dB of path loss, trees add 10 dB, and hilly terrain another 25 dB, then the total path loss will average 130 dB with a normal, bell- shaped, statistical variation in the decibel scale. We call this a log-normal distribution because it is normal in the logarithmic decibel scale. Because of the fundamental difference between voltage and power, we have two equations for decibels that look different but are really telling us the same thing: = 10 log (wz) (1.3) d = 20 log (uz) (1.4) Equation (1.3) tells us the decibel expression for the ratio of two power levels W1 and W2 in watts, whereas Eq. (1.4) tells us the decibel expression for the ratio of two 'We are glossing over a great deal of deep and interesting statistical theory here, but the point is still a valid one. Downloaded from Digital