Using Resampling to Combat Doppler Scaling in UWA Channels With Single-Carrier Modulation and Frequency-Domain Equalization

In this paper, we study the performance of single carrier (SC) modulation with frequency-domain equalization (FDE) over underwater acoustic (UWA) channels. The underlying channels are time-varying intersymbol interference (ISI) channels, where time variation arises from the relative motion between the transceivers, which induces one or more Doppler scaling factors. We study two scenarios: a point-to-point (P2P) system, where each cluster of paths has its own distinct Doppler scaling factor, and a multiple access (MAC) system, where $M$ users communicate with a multiple-antenna common receiver in which each user has its own Doppler scaling factor. First, the maximum likelihood (ML) receiver is derived for both scenarios, and it is shown that a preprocessing stage is necessary to reduce the time variation; this is referred to as multiple resampling (MR). The proposed receiver consists of multiple branches where each branch corresponds to a cluster/user and performs frequency shifting and resampling followed by an integrator. Since the output of the MR stage is contaminated by ISI for P2P systems and ISI and interuser interference for MAC systems, an additional equalization stage is necessary, which is ideally the ML sequence detector (MLSD). Since the complexity of MLSD exponentially grows with the number of symbols per block, the alphabet size, and the number of users, a linear minimum-mean-square-error FDE equalizer is used instead. To further reduce the complexity, instead of resampling the received signal multiple times by different scaling factors, it is resampled only by one scaling factor, which is a function of all Doppler scaling factors. The resulting suboptimal preprocessing scheme is called single resampling (SR). Simulation results for uncoded systems show that MR outperforms its SR counterpart at the expense of some additional hardware complexity. Moreover, it is shown that SC-FDE is more resilient than orthogonal frequency-division multiplexing (OFDM) to the Doppler scaling effect in UWA channels at lower overall complexity for the MR case, whereas both have the same overall complexity for the SR case.