On the use of delays for wide-band superdirective beam forming in endfire and broadside arrays

In algebra, the values of a polynomial over a wide span of time can be inferred from its value and that of its derivatives, measured over a very short span of time. Somewhat analogously, closely-spaced measurements, defining the fine structure of the phase and amplitude distribution over a narrow antenna aperture, can provide the information conventionally obtained from a similar number of elements spaced at half-wavelength intervals over a wider aperture. Superdirective beam patterns, exploiting this principle, are conveniently synthesized by defining the directions in which zero (or minimum) response is required. The correlation between closely-spaced measurements will then cause some reduction of gain, even at the wanted peak of the directional response pattern, but the directivity, i.e. the gain in the wanted direction relative to that in other directions, can be significantly enhanced. Each direction of arrival produces a corresponding pattern of relative propagation delays to the different elements of an array. By suitably equalizing these with non-dispersive delay circuits and then subtracting for null-forming (in place of the usual phase changers), such superdirective arrays can be designed for bandwidths of up to several octaves. Thus superdirectivity can be of considerable value, in certain circumstances, for h.f. radio, sonar or radar.