ABSTRACT
Spread spectrum∗ transmission works by taking a signal that has most of its energy at low frequencies and smearing the signal’s spectral content in such a way that its energy is nearly uniform over a broad range of frequencies. The smearing is done in such a way that to people who know how the smearing is done, it is relatively simple to “unsmear” the message, while to others it is well nigh impossible to recover the message. Often, because the power of the signal at any given frequency can be less than the power of the background noise at that frequency, an uninitiated observer may not even be aware that a signal has been transmitted. The main idea behind direct sequence spread spectrum (the only type of
spread spectrum that we consider) is to take a signal of interest, X(t), and to multiply it by a second signal R(t) that satisfies R2(t) = 1. That is, one multiplies X(t) by a signal that is always equal to ±1. Clearly the more frequently the sign of R(t) changes the more high frequency content R(t) will have. Also, after multiplying X(t) by R(t) the product will also have a lot of energy in its high-frequency region; the product will also have many sign changes. Demodulation-unspreading-is accomplished by multiplying
is X(t)—the original signal. In this chapter, we develop the theory of spread spectrum communications
in two ways. In §9.2-§9.4 we take a probabilistic approach and in §9.5-§9.13 we take a deterministic approach. The probabilistic approach allows us to use what we have learned about stationary stochastic processes to talk about spread spectrum in a particularly nice way. The deterministic approach allows us to describe how spread spectrum is actually implemented (with some of the details left out). The deterministic approach also allows us to develop some of the ideas that underlie the generation of pseudo-random numbers by deterministic techniques-a fascinating subject in its own right.
