Active Sonar Detector in Sparse Time Dispersive Channel

When a sonar operates in a shallow water condition, echo from the interested target contains a direct path signal as well as the top-bottom reflections from ocean boundaries. These multi-path arrivals distort the target echo and affect the detection performance of the sonar system. Replica correlator (matched filter) is a commonly used detector, which is optimal in a scenario when the scaled version of transmitted signal is mixed with additive white Gaussian noise. However, in the multi-path scenarios, the performance of the replica correlator degrades due to this echo distortion. To handle the delay spread, the replica correlator integrator (RCI) was proposed in the literature. In many scenarios, the impulse response of the acoustic channel can be modeled as a sparse vector with a few multi-path components. In a sparse acoustic channel, the RCI is sub-optimum, which does not utilize the sparsity of the channel in the detector design. In this paper, we introduce a new generalized likelihood ratio test (GLRT) detector named as sparse RCI for sparse underwater acoustic channels. The proposed detector enhances the performance by using multiple arrivals of target echo. We also derive a closed form expression of the upper bound of the detection threshold (DT), which is useful to compare the performance of sparse RCI with other commonly used detectors. The simulation results show superior performance of sparse RCI in sparse time dispersive channels.