A sparse random array with self-organizing properties is proposed as a communications relay. The relay consists ofNrandomly deployed, low-power transmit/receive elements with capabilities for phasing their retransmissions to arrive coherently at the ultimate destination. Signal-to-noise ratio results for conventional modulation schemes corrupted with additive noise are given, together with possible system block diagrams. It is concluded that, in spite of the complexity, practical systems can be built with extremely low electromagnetic radiation densities with point-to-point characteristics at least as good as with conventional systems employing high power relays. The novel characteristics make the proposed system particularly suitable for tactical military communication, and variants thereof may find application in urban communication.

A new technique for finding the frequency spectrum of a carrier frequency modulated by a periodic signal is presented. The technique is based on the frequency modulation (FM) equation due to Hess, which in the frequency domain is a double convolution equation. The technique reduces the FM spectrum problem to the solution of a set of linear equations in which the FM side-band amplitudes are the unknowns. The results obtained through this new technique can, in most cases, be obtained by other means. However, the technique is simple and as a result its implementation on a standard computer is both simple and fast. Furthermore, it is especially suitable when the modulating signal is in the form of a Fourier series with a large number of terms or requires a large number of terms to approximate it. Numerical results obtained using the technique for a large number of complex modulating signals are presented.

The estimate of the entropy of a language by assuming that the word probabilities follow Zipf's law is discussed briefly. Previous numerical results [3] on the vocabulary size implied by Zipf's law and entropy per word are corrected. The vocabulary size should be 12 366 words (not 8727 words) and the entropy per word 9.27 bits (not 11.82).