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In this paper, a multihop underwater acoustic line network, which consists of a series of equal-distance hops connected by relay transceivers in a tandem, is considered. Messages are originated as coded packets from a source node at one end, relayed sequentially hop by hop (decoded and re-encoded), and finally received by a destination node at the other end of the network. Several key characteristics of underwater acoustic channels, namely, frequency-dependent signal attenuation and noise, interhop interference, half-duplex modem constraint, and large propagation delay, are taken into account in the analysis. Simple transmission protocols with spatial reuse and periodic transmit/receive schedule are considered. Performance bounds and scheduling design are developed to satisfy the half-duplex constraint on relay transceivers in the presence of long propagation delay. To efficiently cope with frequency-dependent channel characteristic and interhop interference, the power spectral density (PSD) of the signaling is analytically optimized in a way analogous to water filling. Furthermore, the problem of determining the minimum number of hops to support a prespecified rate and reliability with and without a maximum coded packet length constraint is examined. Finally, numerical results are presented to illustrate the analysis.