TABLE OF CONTENTS This section develops a formal model of a network of cognitive radios that is used for the reminder of this chapter, defines the analysis objectives of this chapter, and provides a brief mathematical refresher.
To a large extent, this chapter is self-contained, which means that we believe everything in this chapter can be understood by anyone with an undergraduate exposure to engineering mathematics. However, to go beyond the discussion of this chapter, the reader would benefit from an understanding of real analysis, optimization theory, parallel processing, control theory, and game theory. Before continuing, however, we need to review some symbology and terminology used throughout the remainder of this chapter a necessity for a chapter premised on mathematical analysis. For instance, throughout this chapter, the symbols listed in Table 15.1 express concepts in a more concise manner.
| Symbol | Meaning | Symbol | Meaning |
|---|---|---|---|
| ? | "for all" | ? | "from to" (functions) |
| ? | "contained in" | ? | "there exists" |
| \ | "excluding" | : | "such that" |
| ? | "implies" | N | Set of natural numbers |
| ? | "goes to" (sequences) | R | Set of real numbers |
| . | "norm" "Euclidean distance" | ? | Union of sets |
| . | "magnitude of" [a variable] "number of elements in" [a set] | ? | "is a subset of" |
| ? | "infinity" |
| "Cartesian product" |
| ? | "gradient" | ?j | " j prefers" |
| ? | "is defined as" | ? | "partial derivative" |
| [1]Due to the considerable mathematical treatment in this chapter, we will provide prose explanations as required for readability. |
Additionally,...
