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Abstract-Sparse intersymbol-interference (ISI) channels are encountered in a variety of high-data-rate communication systems. Such channels have a large channel memory length, but only a small number of significant channel coefficients. In this paper, trellis-based equalization of sparse ISI channels is revisited. Due to the large channel memory length, the complexity of maximumlikelihood detection, e.g., by means of the Viterbi algorithm (VA), is normally prohibitive. In the first part of the paper, a unified framework based on factor graphs is presented for complexity reduction without loss of optimality. In this new context, two known reduced-complexity algorithms for sparse ISI channels are recapitulated: The multi-trellis VA (M-VA) and the parallel-trellis VA (P-VA). It is shown that the M-VA, although claimed, does not lead to a reduced computational complexity. The P-VA, on the other hand, leads to a significant complexity reduction, but can only be applied for a certain class of sparse channels. In the second part of the paper, a unified approach is investigated to tackle general sparse channels: It is shown that the use of a linear filter at the receiver renders the application of standard reduced-state trellisbased equalizer algorithms feasible, without significant loss of optimality. Numerical results verify the efficiency of the proposed receiver structure.

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Today research interests in underwater (UW) communication and navigation technologies are steadily growing. However, the design of robust UW communication and navigation systems demands a deep knowledge of the transmission medium. Acoustic UW (AUW) communication is widely used due to the good propagation characteristics of sound waves in water compared to electromagnetic waves that are highly attenuated. Besides its advantage -the low attenuation compared to electromagnetic waves -AUW communication suffers from multipath propagation, severe Doppler spread due to the low propagation speed of sound, and shadow zones, to name some of the most challenging effects. Evaluation of new communication devices under realistic conditions in sea trials is expensive and time-consuming. Therefore, a simulator modeling the AUW communication channel accurately is a valuable tool for development and evaluation of AUW communication devices. In this paper an Acoustic Underwater Channel and Network Simulator is proposed that uses ray tracing to model the AUW channel. It uses channel impulse responses (CIRs) generated by theBELLHOP ray tracing model to simulate multipath propagation. These CIRs for static constellations of receiver and transmitter are post-processed to be in agreement with the mobility of transmitters and receivers. Thereby, Doppler spread is introduced into the channel model. An empirical noise model is used to superimpose received signals with noise. Different modulation schemes can be evaluated using this AUW channel model in laboratory before expensive sea trials are conducted. In this paper a frequency hopping and an OFDM implementation are realized besides the channel model. Multiple mobile transmitters and receivers can be considered to simulate UW networks.