 signal transmitted at 1 W is typically 0.0000000000001 W, or 100 fW, at the base-station receiver. Losing 99.99999999999 percent of the energy sounds wasteful, but our receivers are able to demodulate this tiny signal to recreate the signal modulated at the transmitting end. We can demodu- late and understand such a weak signal by engineering our wireless systems so that the other signals competing with it are even weaker. The crucial issue in getting a signal through is not the amount of power; it is the ratio between the power of the signal and the power of the noise or interference, the signal-to-noise (S/N) ratio or the signal-to-interference (S/I) ratio. As long as this ratio is high enough at the receiver, the amount of power received is irrelevant. Since every electrical amplifier has its own noise, the receiver has some internal noise level, and we want our signal to be stronger than the noise. Maximizing the ratio is the key to good radio design. Electrical engineers are designing superb noise receivers, and it is the job of the wireless telephone system planners to get as much signal and as little that is not our own signal to the receiver as possible. 1.6 Decibel Notation The power ratios in radio are often huge. We broadcast 100 W of power only to have 10 fW get into the receiver. Throwing numbers like 10,000,000,000,000, 1013 around gets tiresome and confusing. The Americans and British do not even agree on what to call such a large number; it is called 10 trillion in the United States, but it is called 10 billion in England. There is a more fundamental point, however. Ratios are often the essential matter, and we need some notation for describing ratios as ratios and articulating the differ- ences between ratios. Fortunately, the decibel scale does the job nicely. Named after Alexander Graham Bell, the bel is defined as a factor of 10, so 2 bels is a factor of 100 and 3 bels is a factor of 1000. As shown in Table 1.1, bels add where the 5 A summary of units and notation is in the "Physical Units" s