Abstract :
The paper is concerned with a more general approach to the problem of the performance of particular directional receiving arrays and their associated signal processing arrangements. It discusses certain physical limitations to the kind of information which can be obtained about a completely unknown far-field distribution, even if noise is assumed to be absent. It is shown, for example, that the ¿fineness of detail¿ which can be discerned by means of a given aperture is determined practically by the dimensions of the aperture in terms of the half-wavelength at a frequency corresponding to half of the total frequency bandwidth of the signal waveform. Additive processing of the outputs of the elements of a spatial array can be shown to give the best result when the field is time-stationary but unknown. More complicated processes, such as multiplication and time averaging, have advantages when the field is either non-stationary in the time domain or when prior information about its form is available (e.g. knowledge that it is due to a limited number of ¿point¿ sources rather than a continuous source distribution). It is shown that, for a field at a single frequency W c/s, a multiplicative (`correlation») process provides the same fineness of detail of the far-field as that obtainable with an additive array of twice the length, provided the field has a time-stationary amplitude distribution and a relatively rapidly time-varying phase distribution. Furthermore, provided the field is of this type, comparable performance can be obtained by retaining only two receiving elements, situated at the extremities of the aperture, and using a `multi-frequency¿ signal waveform whose spectrum occupies a total bandwidth 2W c/s.
