AN OFDM DESIGN FOR UNDERWATER ACOUSTIC CHANNELS WITH DOPPLER SPREAD Sean Mason 1 , Christian Berger 1 , Shengli Zhou 1 , Keenan Ball 2 , Lee Freitag 2 , and Peter Willett 1 1 Dept. of Elec. and Comp. Engr., University of Connecticut, Storrs, CT, 06269 2 Applied Ocean Physics and Engr. Dept., Woods Hole Oceanographic Institution, MA 02543 ABSTRACT In this paper, we study the performance of orthogonal frequency division multiplexing (OFDM) over underwater acoustic multipath channels with different Doppler scales on different paths. We first derive an exact inter-carrier- interference (ICI) expression after incorporating the com- pensation of nonuniform Doppler shifts across OFDM sub- carriers. Based on the assumption that the residual ICI is dominantly from immediate neighbors, we suggest a practi- cal design that divides subcarriers into groups, where each group of eight subcarriers consists of three contiguous data subcarriers, one pilot subcarrier, and five carefully spaced null subcarriers. We use the orthogonal matching pursuit (OMP) algorithm for sparse channel estimation that identifies distinct physical paths with different Doppler scales. Sys- tem performance is evaluated using data recorded from the GLINT08 and SPACE08 experiments. Relative to the re- ceiver that ignores the residual ICI, we observe that explicitly suppressing the residual ICI induced by Doppler spread leads to improved performance for the SPACE08 data, while not for the GLINT08 data. Index Terms— Underwater acoustic communication, OFDM, Doppler spread, sparse channel estimation 1. INTRODUCTION Underwater acoustic (UWA) channels exhibit long delay spreads and significant Doppler effects due to sea-surface motion and internal waves [1]. In general, the signals arriving from different propagation paths will be scaled differently due to different path variation rates. However, the receiver designs of [2, 3, 4] for multicarrier modulation over UWA channels are based on the assumption that all paths have similar Doppler scales. Inter-carrier-interference (ICI) was ignored for data demodulation after proper compensation of nonuniform Doppler shifts on OFDM subcarriers [2, 3]. Explicitly accounting for ICI caused by Doppler spread could further improve the system performance. Various ap- proaches have been pursued in e.g., [5, 6, 7] based on a basis S. Mason, C. R. Berger, S. Zhou, and P. Willett are supported by the ONR YIP grant N00014-07-1-0805, the NSF grant ECCS-0725562, the NSF grant CNS-0721834, and the ONR grant N00014-07-1-0429. K. Ball and L. Freitag are supported by the ONR grant N00014-07-1-0229. expansion model (BEM) for time-varying channels such that ICI is limited to neighboring subcarriers. In this paper, we first derive an exact ICI expression for zero-padded (ZP) OFDM signals received over a UWA chan- nel with different Doppler scales on different paths, where the effect of the two-step compensation of nonuniform Doppler shifts across OFDM subcarriers [3] is also included. We then assume that the residual ICI is limited to immediate neigh- bors and present a practical ZP-OFDM design that leads to decoupled low-complexity channel estimation and demodula- tion. Using channel outputs on and around the pilot subcarri- ers, the orthogonal matching pursuit (OMP) algorithm [8, 9] is used for sparse channel estimation that identifies distinct paths with different Doppler scales. Based on data collected in the GLINT08 and SPACE08 experiments, we compare the system performance using two receivers, one explicitly considering the residual ICI due to Doppler spread, and the other of [3] that ignores residual ICI. We observe that explicitly considering the residual ICI does not improve performance in the GLINT08 data, and hence the approach in [3] is adequate for the UWA chan- nels in this experiment. On the other hand, the performance in the SPACE08 data benefits considerably from explicitly suppressing the residual ICI, which reveals the potential of receiver design tailored for channels with large Doppler spread. The rest of this paper is organized as follows, in Section 2 we derive our signal model, in Section 3 we present our pro- posed design, detailing signal design, channel estimation and data demodulation, in Sections 4 and 5 we evaluate the perfor- mance based on experimental data, and we conclude in Sec- tion 6. 2. SYSTEM MODEL 2.1. ZP-OFDM Let T denote the symbol duration and T g the guard interval for the zero-padded (ZP) OFDM. The total OFDM block du- ration is T ′ = T + T g and the subcarrier spacing is 1/T . The kth subcarrier is at frequency f k = f c + k/T, k = −K/2,...,K/2 − 1, (1)