Demonstration at sea of the decomposition-of-the-time-reversal-operator technique

This paper presents a derivation of the time reversal operator decomposition (DORT) using the sonar equation. DORT is inherently a frequency-domain technique, but the derivation is shown in the time-frequency domain to preserve range resolution. The magnitude of the singular values is related to sonar equation parameters. The time spreading of the time-domain back-propagation image is also related to the sonar equation. Noise-free, noise-only, and signal-plus-noise data are considered theoretically. Contamination of the echo singular component by noise is shown quantitatively to be very small at a signal-to-noise ratio of 0 dB. Results are shown from the TREX-04 experiment during April 22 to May 4, 2004 in 94 m deep, shallow water southwest of the Hudson Canyon. Rapid transmission of short, 500 Hz wide linear frequency modulated beams with center frequencies of 750, 1250, 1750, 2250, 2750, and 3250 Hz are used. Degradation caused by a lack of time invariance is found to be small at 750 Hz and nearly complete at 3250 Hz. A back-propagation image at 750 Hz shows focusing on the echo repeater. These results are discussed with comments about further research.