OPTIMAL MODAL BEAMFORMING OF BANDPASS SIGNALS USING AN UNDERSIZED SPARSE VERTICAL HYDROPHONE ARRAY - THEORY AND A SHALLOW-WATER EXPERIMENT

Conventional methods for modal beamforming of underwater acoustic sign als using a vertical-line hydrophone array (VLA) can suffer significan t degradation in resolution when the array is geometrically deficient, i.e., consists of sparsely spaced elements and spans the water column partially or is poorly navigated. Designed for estimating the coeffic ients of the normal modes, these conventional methods include the dire ct projection (DP) of the data on the calculated mode shapes and least -squares (LS) fitting of the mode sum to the data, The degradation, in the form of modal cross talk or sidelobes, Is a result of an undersam pling in depth. This cross talk may be mitigated with the application of proper space-time filter constraints in the case of a pulse transmi ssion. In this paper, a generalized least-squares (GLS) mode beamforme r, capable of incorporating physical space-time constraints on the pro pagation of sound, is presented. The formulation is based on the well- known theorem of Gauss and Markov. Initialized by a model prediction o f the basic arrival structure of the normal modes and incorporating, i teratively, refined estimates of the statistics of the modal fluctuati ons, this GLS technique strives to boost the resolution of a geometric ally deficient VLA. The improvement is demonstrated using the VLA data collected during a shallow-water tomography experiment in the Barents Sea. The superiority of the GLS method over the conventional DP and L S methods is evident, providing a high-quality time series of modal ar rivals as a function of geophysical time, which, in turn, reveals the dominant time scales of the oceanic processes associated with the Pare nts Sea Polar Front.