istics course tells us that a normal distribution is more than 2.236 standard devia- tions high 1.3 percent of the time, more than 2.236 standard deviations low 1.3 percent of the time, and in the fat middle part of the curve the other 97.4 percent of the time. This gives us a BER of 1.3 percent. There is an alternative to using more power. We could send each bit five times instead of only once and have the receiver add up all five signals. This gives us better BER per- formance, and we use the term processing gain to describe the increase in performance Probability Density Voltage Figure 8.2 BPSK with a 7-dB S/N rato. Downloaded from Digital Engineering Library @ McGraw-Hil (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. The CDMA Principle Key Radio Concepts from repeated sending of the same bit. The magic of processing gain is that this five- fold repeating gives us the same statistical advantage as a fivefold power increase. In both cases we have increased the energy per bit five times while keeping the noise constant. It is the ratio of bit energy to noise that is important here. We denote this ra- tio by Eb/No, and we will have more to say on Eb/No in Sec. 27.1. The important con- cept for processing gain is that the Eb/No increase by increasing power and the Eb/No increase by sending multiple samples of each bit yield the same BER improvement; they are exactly the same, statistically speaking. In this example, the processing gain is 7 dB, a factor of 5, enough to change the BER from 16 to 1.3 percent. We call the sub-bit samples chips, and we refer to the chip transmission rate or the chip- ping rate. The cdmaOne standard created by Qualcomm sends 1,228,800 chips per second to deliver 19,200 bits per second, a processing gain of 64 (64 chips per bit), or 18 dB. For discussions about digital radio, it is customary to refer to bits as +1 and -1 rather than 1 and 0. It makes it much easier to ta