An experiment conducted in the Mediterranean Sea in April 1996 demonstrated that a time-reversal mirror ͑or phase conjugate array͒ can be implemented to spatially and temporally refocus an incident acoustic field back to its origin. The experiment utilized a vertical source-receiver array ͑SRA͒ spanning 77 m of a 125-m water column with 20 sources and receivers and a single source/receiver transponder ͑SRT͒ colocated in range with another vertical receive array ͑VRA͒ of 46 elements spanning 90 m of a 145-m water column located 6.3 km from the SRA. Phase conjugation was implemented by transmitting a 50-ms pulse from the SRT to the SRA, digitizing the received signal and retransmitting the time reversed signals from all the sources of the SRA. The retransmitted signal then was received at the VRA. An assortment of runs was made to examine the structure of the focal point region and the temporal stability of the process. The phase conjugation process was extremely robust and stable, and the experimental results were consistent with theory. INTRODUCTIONPhase conjugation is a process that has been first demonstrated in nonlinear optics 1 and more recently in ultrasonic laboratory acoustic experiments. 2,3 Aspects of phase conjugation as applied to underwater acoustics also have been explored recently. 4-7 The Fourier conjugate of phase conjugation is time reversal; implementation of such a process over a finite spatial aperture results in a ''time-reversal mirror. 2,3 '' In this paper we describe an ocean acoustics experiment in which a time-reversal mirror was demonstrated.In nonlinear optics, phase conjugation is realized using high intensity radiation propagating in a nonlinear medium. Essentially, the incident radiation imparts its own time dependence on the dielectric properties of the medium. The incident radiation is then scattered from this time-varying dielectric medium. The resulting scattered field is a time reversed replica of this incident field propagating in the opposite direction of the incident field. For example, the scattered field that results from an outgoing spherical wave is a spherical wave converging to the original source point; when it passes through the origin it has the time reversed signature of the signal which was transmitted from that point at the originating time. Clearly, this phenomenon can be thought of as a self-adaptive process, i.e., the process constructs a wavefront of the exact required curvature. ͑An alternative would be to use a concave spherical mirror with the precise radius of curvature of the incident wavefront.͒ There is an assortment of nonlinear optical processes which can result in phase conjugation. 1 In acoustics, however, we need not use the propagation medium nonlinearities to produce a phase conjugate field.Because the frequencies of interest in acoustics are orders of magnitude lower than in optics, phase conjugation can be accomplished using signal processing. As in the optical case, phase conjugation takes advantage of reciprocity which is a property of wave...

[1] This paper describes estimation of low-altitude atmospheric refractivity from radar sea clutter observations. The vertical structure of the refractive environment is modeled using five parameters, and the horizontal structure is modeled using six parameters. The refractivity model is implemented with and without an a priori constraint on the duct strength, as might be derived from soundings or numerical weather-prediction models. An electromagnetic propagation model maps the refractivity structure into a replica field. Replica fields are compared to the observed clutter using a squared-error objective function. A global search for the 11 environmental parameters is performed using genetic algorithms. The inversion algorithm is implemented on S-band radar sea-clutter data from Wallops Island, Virginia. Reference data are from range-dependent refractivity profiles obtained with a helicopter. The inversion is assessed (1) by comparing the propagation predicted from the radar-inferred refractivity profiles and from the helicopter profiles, (2) by comparing the refractivity parameters from the helicopter soundings to those estimated, and (3) by examining the fit between observed clutter and optimal replica field. This technique could provide near-real-time estimation of ducting effects. In practical implementations it is unlikely that range-dependent soundings would be available. A single sounding is used for evaluating the radar-inferred environmental parameters. When the unconstrained environmental model is used, the ''refractivity-from-clutter,'' the propagation loss generated and the loss from this single sounding, is close within the duct; however, above the duct they differ. Use of the constraint on the duct strength leads to a better match also above the duct.

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In July 1999, an at-sea experiment to measure the focus of a 3.5-kHz centered time-reversal mirror (TRM) was conducted in three different environments: an absorptive bottom, a reflective bottom, and a sloping bottom. The experiment included a preliminary exploration of using a TRM to generate binary-phase shift keying communication sequences in each of these environments. Broadside communication transmissions were also made, and single-source communications were simulated using the measured-channel response. A comparison of the results is made and time reversal is shown to be an effective approach for mitigating inter-symbol interference caused by channel multipath.

Abstract-The spatial and temporal focusing properties of timereversal methods can be exploited for undersea acoustic communications. Spatial focusing mitigates channel fading and produces a high signal-to-noise ratio (SNR) at the intended receivers along with a low probability of interception elsewhere. While temporal focusing (compression) reduces significantly intersymbol interference (ISI), there always is some residual ISI depending upon the number of transmitters, their spatial distribution (spatial diversity), and the complexity of the channel. Moreover, a slight change in the environment over the two-way propagation interval introduces additional ISI. Using multilevel quadrature amplitude modulation (M-QAM) in shallow water, we demonstrate that the performance of time-reversal communications can be improved significantly by cascading the received time series with an adaptive channel equalizer to remove the residual ISI.Index Terms-Adaptive equalizer, billboard array, decision-feedback equalizer (DFE), decision-feedback phase-locked loop (DFPLL), fractionally spaced equalizer (FSE), intersymbol interference (ISI), multilevel quadrature amplitude modulation (M-QAM), multiple-input-multiple-output (MIMO), time-reversal communication.

Recently, a technique has been developed to image seabed layers using the ocean ambient noise field as the sound source. This so called passive fathometer technique exploits the naturally occurring acoustic sounds generated on the sea-surface, primarily from breaking waves. The method is based on the cross-correlation of noise from the ocean surface with its echo from the seabed, which recovers travel times to significant seabed reflectors. To limit averaging time and make this practical, beamforming is used with a vertical array of hydrophones to reduce interference from horizontally propagating noise. The initial development used conventional beamforming, but significant improvements have been realized using adaptive techniques. In this paper, adaptive methods for this process are described and applied to several data sets to demonstrate improvements possible as compared to conventional processing.

A second phase-conjugation experiment was conducted in the Mediterranean Sea in May 1997 extending the results of the earlier time-reversal mirror experiment ͓Kuperman et al., J. Acoust. Soc. Am. 103, 25-40 ͑1998͔͒. New results reported here include ͑1͒ extending the range of focus from the earlier result of 6 km out to 30 km, ͑2͒ verifying a new technique to refocus at ranges other than that of the probe source ͓Song et al., J. Acoust. Soc. Am. 103, 3234-3240 ͑1998͔͒, and ͑3͒ demonstrating that probe-source pulses up to 1 week old can be refocused successfully.

During the July 2003 acoustic communications experiment conducted in 100 m deep water off the western side of Kauai, Hawaii, a 10 s binary phase shift keying signal with a symbol rate of 4 kilosymbol/s was transmitted every 30 min for 27 h from a bottom moored source at 12 kHz center frequency to a 16 element vertical array spanning the water column at about 3 km range. The communications signals are demodulated by time reversal multichannel combining followed by a single channel decision feedback equalizer using two subsets of array elements whose channel characteristics appear distinct: (1) top 10 and (2) bottom 4 elements. Due to rapid channel variations, continuous channel updates along with Doppler tracking are required prior to time reversal combining. This is especially true for the top 10 elements where the received acoustic field involves significant interaction with the dynamic ocean surface. The resulting communications performance in terms of output signal-to-noise ratio exhibits significant change over the 27 h transmission duration. This is particularly evident as the water column changes from well-mixed to a downward refracting environment.