  Detection of hydroacoustic transmissions is a key enabling technology in
applications such as depth measurements, detection of objects, and undersea
mapping. To cope with the long channel delay spread and the low signal-to-noise
ratio, hydroacoustic signals are constructed with a large time-bandwidth
product, $N$. A promising detector for hydroacoustic signals is the normalized
matched filter (NMF). For the NMF, the detection threshold depends only on $N$,
thereby obviating the need to estimate the characteristics of the sea ambient
noise which are time-varying and hard to estimate. While previous works
analyzed the characteristics of the normalized matched filter (NMF), for
hydroacoustic signals with large $N$ values the expressions available are
computationally complicated to evaluate. Specifically for hydroacoustic signals
of large $N$ values, this paper presents approximations for the probability
distribution of the NMF. These approximations are found extremely accurate in
numerical simulations. We also outline a computationally efficient method to
calculate the receiver operating characteristic (ROC) which is required to
determine the detection threshold. Results from an experiment conducted in the
Mediterranean sea at depth of 900~m agree with the analysis.
