Active Sonar Detector in Doubly Dispersive Acoustic Channel

The acoustic channel in a shallow ocean condition can be modeled as a doubly dispersive channel with significant Doppler and delay spread. Commonly used detector in active sonar system is known as replica correlator. The relative movements between own platform and interested target introduce Doppler shift in the received target echo. In such scenario, a bank of correlator with different Doppler shifted replicas is implemented in active sonar signal processor and the maximum value among different correlator output is chosen as the detector output. The plane wave assumption does not hold in shallow water condition with wide-band active transmitted signal. More-over, the Doppler shift introduced in each ray path depends on the arrival and departure angles at the transmitter and receiver side. In this paper, we derive a generalized likelihood ratio test (GLRT) detector for the doubly dispersive underwater acoustic channel, which can utilize the multiple arrivals to enhance the detection performance. Detection threshold (DT) of a detector is an important parameter involved in the design of the sonar figure of merit (FOM). We derive the closed form expression of the detection threshold of introduced detector and compare it with other detectors. The derived expression shows that the performance of the detector for shallow water waveguide depends on the
$l_{2}$
norm of the channel vector.