Comparison between the Performances of a Time-Averaged Product Array and an Intraclass Correlator

Abstract

Berman and Clay [J. Acoust. Soc. Am. 29, 7 (1957)] have investigated the directional characteristics of a linear array of omnidirectional receiving elements when the output from these elements are multiplied together and time arranged in certain ways. They conclude that the same directional characteristics may be obtained from these “time-averaged product” (TAP) arrays having a small number of detectors as with an additive array with a large number of elements; they also show that there is some economy in terms of the over-all length of the array required to give a specified beam width. Because it is not possible to assess the characteristics of a TAP array solely on the basis of its polar diagram, it is necessary to carry out a detailed analysis to determine its usefulness in applications which require a system with a narrow polar diagram. Three particular applications are investigated, namely the detection of a point source against a noise background, the resolution of the signals from two closely spaced point sources, and the exploration of the distribution of power across an extended source. For comparison purposes a parallel analysis is carried out for an intraclass correlation system. For simplicity, the analyses are confined to investigating the performance of a 4-element linear array with equal spacings between adjacent elements under elementary and idealized conditions. The results so obtained, however, are of general application. Two class I TAP array systems are compared with the intraclass correlator, the detection performance of which was analysed by Faran and Hills [Acoustics Research Laboratory, Harvard University, Techn. Memo. No. 28 (November 1952).] and which is believed to be the most “efficient” detector in this application. {A class I array is defined as one in which the number of time averaging operations lies between (N − 1) and 12N(N − 1), where N is the number of receiving elements. A class II TAP array, which employs true multipliers, is obviously inferior to a class I array in terms of detection performance and will not be considered. It has been shown by Melton et al. [see B. S. Melton and P. R. Kerr, Geophysics 22, 553 (1957), for example] that a class II type of array employing coincidence detectors rather than multipliers has some useful properties but it can be demonstrated that its detection performance is inferior to that of an intraclass correlator. Since class III TAP arrays have the same detection performance as the system prior to the power and sum circuits there is no need to analyse such arrays here.}