Towards an Information Theory of Spread-Spectrum Systems

A novel definition of a spread-spectrum signal as a signal whose Fourier bandwidth is much greater than its Shannon bandwith (one-half the number of dimensions of signal space required per second) is proposed. Six different communication systems are analyzed in terms of this definition. It is shown that there is a fundamental difference between the bandwidth expansion due to coding and that due to "spectrum spreading". It is further shown that spectrum spreading plays no role in increasing channel capacity, but can perform other useful roles such as providing low probability of interception of the signal, good electromagnetic compatibility, and a multiple-access capability. The effects of linear and nonlinear filtering on bandwidth are considered and seen to be quite different for Fourier bandwidth and for Shannon bandwidth. The concepts developed are used to resolve two paradoxes in spread-spectrum communications: the apparent increase in capacity when users become unsynchronized in a code-division multiple-access (CDMA) system and the fact that a heavily loaded CDMA system is as energy-efficient for transmitting information as a single-user system with the same (total) average power constraint. Areas of spread-spectrum communications where further information-theoretic development is needed are indicated.