Radiation with Multiple Scattering

In this chapter we illustrate how the physical constraints imposed by propagation in complex environments limit the amount of information that can be transported by a propagating wave.

We consider the stochastic diversity of signals propagating in a time-invariant random medium and relate it to the parameters of the stochastic model used to describe the medium. We rely on the stochastic frequency representations developed in Chapter 6, and provide additional insights into the design trade-offs discussed in Chapter 7.

From a physical perspective, the general effect of multiple scattering is a damping of the transmitted coherent wave and the creation of an incoherent energy coda – see Figure 10.1. The term “coherent” is used to denote the part of the waveform whose frequency components are not significantly distorted by propagation filtering, so that the waveform retains the original transmitted shape. On the other hand, the term “incoherent” is used to denote the part of the waveform whose frequency components are significantly distorted, so that the original transmitted shape is broadened in time. The transfer of coherent energy into incoherent energy through multiple scattering, as well as the absorption associated with the multiple-scattering process, are responsible for the exponential attenuation of the coherent part of the response. The incoherent response appears delayed and spread, due to the delayed arrival of the different multiple-scattered contributions that combine at the receiver.

From an information-theoretic perspective, as the signal loses coherence due to multiple scattering, it becomes more unpredictable in frequency, increasing the stochastic diversity of the process used to model its frequency variation. From a practical perspective, as the coherence bandwidth decreases, communication using a sequence of short pulses is somewhat inhibited by the multiple scattering process, due to the overlap of the broadened pulses at the receiver.