Active source detection in a dispersive multiple-reflection environment

A signal propagating in a shallow water waveguide is subjected to (a) multiple re ections o the ocean boundaries and (b) distortion because of the dispersive properties of the propagation medium. Because of these corruptions, the received signal di ers substantially from the transmitted signal. Although the transmission is sometimes exactly known, the received signal cannot be described in detail because of inadequate knowledge of the ocean impulse response. Ignoring the e ects of the ocean on the signal, or representing them inaccurately, can lead to deterioration of the detection statistics. This paper compares the performance of methods designed for distortion-free, multiple-re ection transmission in realistic, dispersive environments. Two existing methods, the RCI processor and the simple sourcereceiver matchedlter, and a new detector are evaluated. The impact of distortion on signal transmission is assessed by comparing the distortion-free methods to the optimal processor, which models the e ects of the propagation medium on the signal. 1. OPTIMAL DETECTION IN A KNOWN OCEAN FOR AN EXACTLY KNOWN SOURCE SIGNAL In active sonar problems, a known and controlled source transmits a waveform, which is then received at a controlled set of receivers. Based on the measurements at the receiving hydrophones, a decision is made as to whether a target is present in the insoni ed region of the ocean. A simple detection tool is the correlation between the received and transmitted waveforms. This correlation detector (referred to here as a standard source-receiver matchedlter) would be optimal if the received waveform was a simple replica of the transmitted signal corrupted by white Gaussian noise. The problem considered here is more complex, because the ocean, through which the signal propagates, distorts the signal. This work was supported by ONR Ocean Acoustics, through grant number N00014-97-1-0600. Speci cally, assuming signal s(t) is transmitted, the received signal r(t) will be described by equation r(t) = h(t) s(t) + w(t), where h(t) is the impulse response of the propagation channel connecting source and receiver and w(t) is additive, white, Gaussian noise. The standard source-receiver matchedlter, which correlates s(t) and r(t), is a suboptimal detector because it ignores the distortion (described by h(t)) imposed on the signal during propagation through the ocean. The optimal detector is a matchedlter between the received signal r(t) and the convolution of the oceanic impulse response and the source signal, h(t) s(t). This `model-based matchedlter' [1] is signi cantly superior to the suboptimal, standard source-receiver matchedlter for underwater target detection. 2. DETECTION IN A MULTIPLE REFLECTION ENVIRONMENT A singular di culty in signal detection in the ocean is the uncertainty about the ocean environment through which the sound propagates. The optimal detector described in Section 1 requires knowledge of the impulse response (or, equivalently, the transfer function) of the ocean, which depends on several parameters many of which are unknown or uncertain. As has been shown in [2, 3], assumptions about the impulse response that do not re ect reality can cause a serious performance degradation, making, under certain circumstances, the simple suboptimal source-receivermatched lter preferable to the theoretically optimal model based matched lter. In order to overcome the adverse mismatch effects, multiple model-based matchedlters are recommended. Speci cally, following the methodology used in passive matchedeld processing [4], replicas of h(t) for many candidate values of the unknown parameters are calculated, and correlations are computed between the received signal and quantities h(t) s(t) for all di erent h(t)'s. Maximization of the correlation over all parameters yields the detection statistic [5]. This process can be very computationally intensive depending on the number of the uncertain parameters and the sensitivity of the ocean response to these parameters (which determines the required resolution of the search). Implementation of such a scheme is environmentdependent and therefore non-portable. Calculation of the ocean impulse response for multiple sets of parameters has to be performed every time detection is desired in a di erent environment. E orts have been made to develop techniques that are less dependent on the properties of the propagation medium. Proposed techniques include the Segmented Replica Correlation (SRC) and the Replica Correlation Integration (RCI) [6, 7]. The SRC method has been designed for cases where the transmitted signal is distorted by a frequency domain convolution process resulting from temporal coherence characteristics of the ocean. The RCI method has been developed for signals that travel through a multiple reection medium. The RCI method is more suitable than the SRC method for detection in shallow water environments. Since the signal bounces o the ocean boundaries several times, a combination of the direct arrival and a series of re ections arrive at the receiving phone. The RCI processor assumes that the received signal is a linear combination of attenuated and delayed exact replicas of the transmitted signal and that there is adequate temporal separation between consecutive arrivals for them to be resolvable. The RCI processor is a likelihood ratio test derived for an unknown ocean impulse response. It is optimum when the received signal is a sum of undistorted replicas of the transmitted signal and the duration of the impulse response is known. The statistic calculated for the RCI detection processor is y(n) = P M 1