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The single-element spectrogram for a continuous broadband signal, plotted as a function of range, has been shown to exhibit striated bands of intensity maxima and minima. The slope of the striations is an invariant of the modal interference and is described by a waveguide invariant parameter "beta." The striation pattern is analyzed and modeled in this paper for the beam outputs of a horizontal line array obtained by conventional beamforming. Array beamforming makes it possible to measure the waveguide invariant parameter for weak signals due to the enhancement of signal levels by the array gain over that of a single element. It is shown that the signal beam spectrogram as a function of range exhibits the same striation pattern as that (predicted) for a single element. Specifically, for a broadside signal, the beam striation is identical to that of a single-element plus a constant signal gain. For a nonbroadside target, the signal beam intensity will be modified by a frequency-bearing dependent signal gain due to the signal spread over multiple beams, nevertheless the beam spectrogram retains the same striation pattern (slope) as for a single element. The sidelobe beams (outside the canonical cones containing the signal arrivals) exhibit an entirely different striation pattern as a function of frequency and range. For array processing, it is shown that a fast range-rate, close range target and a distant, slow range-rate interference source will have a different striation pattern (slope) in the corresponding beam spectrograms as a function of time, assuming no prior knowledge of the source ranges. The difference in the striations between the beam spectrograms can be used in array processing to suppress the interference contribution. A 5-7 dB interference suppression is demonstrated using simulated data.
T. C. Yang (2003) studied this question.