ny users k the two matrices M1(k) and M2(k) can take be- fore their systems reach overload status. Let k1 be the overload point where det[M1(k1)] = 0, and let k2 be the overload point where det[M2(k2)] = 0. The combination of Eqs. (28.23) and (28.25) and some algebra gives us Eq. (28.26): det[M1(k)]=D-ka+ 1 - (1 B2)(22) (28.26) det[M(k)] ]=D-k(a- = 1) It is convenient that the factors of and 1/3 cancel out to unity in the equation for det[M2(k). We can solve for k1 and k2 to get Eq. (28.27)5: (28.27) So long as < 1 and O2 > 0, we have k1 > k2. This means that this simple CDMA system will serve more users on the right cell than on the wrong cell before it becomes overloaded and unstable. 6 This example gives us insight that there are unlikely to be any reasonable CDMA systems where overflowing traffic to other cell sectors is good for system capacity. 28.1.5 Assumptions The above equations make several assumptions as we present them in this section. While these assumptions are not exactly true, these equations still give us insight into the behavior of channels within a CDMA radio carrier. In the rest of this chapter we ex- plore the differences between these assumptions and real CDMA systems, how we can modify the equations to take these differences into account, and how these differences affect our calculations. 4If this brings back too many linear algebra classes from too long ago, then the reader can trust our analysis. 5At first glance, the reader may wonder how the formula k2 = D/(a + 1) could have reference to user population 1 or O2 or radio conditions B. However, the original determinant D depends on 01, O2, and B. 6The condition = 1 means that the two cells are exactly the same for both user communities, and the condition O2 = 0 means that there are no users in the service area of cell 2. Thus we are comfortable that B<1 and 2 > 0 are reasonable assumptions for this example. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Comp