 classified? What are those useful properties? How well do they work? Preliminary answers are forthcoming in this introductory chapter. We will motivate the study of spread-spectrum systems by analyzing a sim- ple game, played on a finite-dimensional signal space by a communications system and a jammer, in which the signal-to-interference energy ratio in the communication receiver's data detection circuitry serves as a payoff func- tion. The reader is hereby forewarned that signal-to-interference ratio cal- culations alone cannot illustrate many effects which, in subtle ways, degrade more realistic performance ratios, e.g., bit-error-rate in coded digital SS sys- items. However, the tutorial value of the following simple energy calculations soon will be evident. 1.1 A BASIS FOR A JAMMING GAME The following abstract scenario will be used to illustrate the need for spec- trum spreading in a jamming environment, to determine fundamental design characteristics, and to quantify one measure of SS system perfor- mance. Consider a synchronous digital communication complex in which the communicator has K transmitters available with which to convey infor- mation to a cooperating communicator who possesses K matching receivers (see Figure 1.1). Assume for simplicity that the communication signal space has been "divided equally" among the K transmitters. Hence, with a band- width Wss available for communicating an information symbol in a Ts sec- ond interval (0, Ts), the resultant transmitted-signal function space of dimension approximately 2TWSs is divided SO that each transmitter has a A Spread-Spectrum Overview JAMMER m,(f) m2(+) SOURCE mk(i) COMMON CLOCKS AND KEYS Figure 1.1. The scenario for a game between a jammer and a communication sys- tem complex. D-dimensional subspace, D = 2TWWI, in which to synthesize its output signal. Denote an orthonormal basis for the total signal space by 4k(t), k = 1, 2, , 2T Wss, i.e., (1.1) where the basis functions may be complex valued, and ()* denotes conju- gation. Then the signal em