Detection of an undersea acoustic communications network by an energy detector

A theory is presented for the upper bound on the mean time τ to the detection of an undersea acoustic communications network by an energy detector whose initial position and heading are uniformly distributed random variables. The network is an infinite square grid of omnidirectional transmit-receive nodes on a flat bottom. Each node transmits to one nearest neighbor at a bit-rate R equal to Shannon's capacity, maximizing τ. The network sets a signaling bandwidth W and node-spacing D. The detector sets a false-alarm rate, integration time, height above the bottom, and speed. For W = 5 kHz and D = 1 km, τ is computed as a function of R in 200 -m water with propagation varying from spherical to cylindrical spreading, volume absorption of 2 dB per km (corresponding approximately to 15 kHz), and illustrative values for other parameters.