Application of DORT to active sonar

Active sonar in shallow water is often reverberation-limited and the detectability is often limited by the presence of too many false alarms. The problem of improving detection, and classification, in shallow water is being worked on in several different ways. The time reversal operator decomposition (DORT) is a technique that has recently been applied to the problem of discriminating echoes in shallow water based on the different depths of the scatterers. DORT uses scattering data from a multiple source and multiple receiver sonar arrangement to separate scatterers that are resolvable by the source and receiver arrays. DORT is the application of the singular value decomposition of the frequency-domain data. This paper presents a derivation of DORT from the sonar equation. DORT is inherently a frequency-domain technique. In order to preserve range-resolution, the sonar equation is transformed into the time-frequency domain. With that representation, DORT can be applied to the frequency domain signal within a range resolution cell. Following the derivation of DORT from the sonar equation, numerical simulations are shown that demonstrate the depth resolution of a vertical line array of sources and receivers. Sufficient depth resolution is shown using few sources at frequencies near 500 Hz in water with a depth of 100 m. Problems that are encountered with the implementation of the technique are discussed. Target motion causes leakage of signal energy into several singular values. Motion of the source or receiver is shown to have little effect. The problems and constraints that arise from different multiplexing techniques, including frequency, code and time division, are shown. Results are shown with data taken on the Atlantic shelf, east of Cape May, NJ, during Geoclutter 03 and TREX-04 experiments