Performance of Distributed Space-Time Cooperative Schemes for Underwater Acoustic Communications Madhavan Vajapeyam and Urbashi Mitra Communication Sciences Institute, University of Southern California 3740 McClintock Avenue, Los Angeles, 90089 Email: {vajapeya,ubli}@usc.edu Abstract— In resource limited, large scale underwater sensor networks, cooperative communication over multiple hops offers opportunities to save power when intermediate nodes between source and destination act as cooperative relays. Herein, protocols coupled with space-time block code (STBC) strategies are ana- lyzed for distributed cooperative communication in underwater channels. Amplify-and-forward type protocols are considered, in which the relays do not attempt to decode the information. The Alamouti-based cooperative scheme proposed by Hua et al (2003) for flat-fading channels is modified in order work in the presence of multipath. A time-reversal distributed space- time block code (TR-DSTBC) is employed, which extends the classical TR-STBC approach from Lindskog and Paulraj (2000) to a cooperative communication scenario. Furthermore, the performance of the scheme employing a DFE equalizer at the destination is analytically investigated in terms of bit error rate (BER) bounds and achievable spatial diversity. I. I NTRODUCTION Underwater sensor networks form an emerging technology paradigm that promises to enable or enhance several key appli- cations in oceanic research, such as: data collection, pollution monitoring, tactical surveillance and disaster prevention [1]. In such networks, acoustic signaling will be employed to achieve underwater communication [1], [2]. In addition, the multihop nature of sensor networks provides several advantages over single hop schemes [3]: a) combating the severe signal decay over long distances, thus saving trans- mission power; b) providing signal paths between terminals which do not have a direct line of sight between them; and c) providing multiple communication links for applications with a high data rate requirement which cannot be satisfied via a single link. Multihop networks can also provide additional capacity and/or performance gains through cooperation between termi- nals, by taking advantage of their inherent richness in spatial diversity [4]. Hence, a natural way to exploit this diversity is via Distributed Space-Time Block Coding (DSTBC) originally proposed in [4]. The goal of a DSTBC-based protocol is to allow the cooperating terminals to act, from the destination point of view, as a multi-antenna array employing a well de- signed Space-Time Block Code (STBC), originally proposed for co-located antennas in [5]. Several DSTBC schemes have been recently proposed (e.g, [4], [6] and others). 0 This research has been funded in part by one or more of the following grants: ONR N-000140410273, NSF ITR CCF-0313392 and NSF OCE 0520324. The idea that DSTBC schemes could be applied to un- derwater networks suggests itself naturally. The underwater acoustic channel, however, poses extra difficulties to the design of communication protocols. Typical major challenges posed by underwater channels are [1]: severe range-dependent at- tenuation, extensive multipath propagation (resulting in severe intersymbol interference-ISI) and highly variable propagation delays (due to slow sound propagation). In this work, we consider the problem of underwater com- munication between single source (S) and destination (D) terminals. Data is relayed in a multihop fashion, through intermediate sensor nodes placed between S and D. Commu- nication protocols based on DSTBC are considered. The time reversal STBC (TR-STBC) approach proposed in [7] for co- located antennas, is extended to a distributed antenna scenario. We show that, just like in the STBC case [7], [8], TR along with the orthogonality of the DSTBC essentially allows for decoupling of a vector ISI detection problem into separate scalar problems, without loss of optimality (neglecting ”border effects” [8]) and, therefore, significant complexity reduction. A performance analysis of the proposed TR-STBC system is carried out in order to obtain an upper bound on the BER at high SNR, assuming the receiver employs a standard decision feedback equalizer (DFE) [9]. Furthermore, the DFE performance is compared to that of the optimal maximum- likelihood sequence estimator. Throughout this paper, the distribution of a complex Gaussian random variable with mean µ and variance σ 2 will be denoted by CN (µ, σ 2 ). II. SIGNAL MODEL We first consider the discrete-time signal model for a scenario with a single source terminal (S) communicating to a destination terminal (D) via a stage of two wireless relays as depicted in Figure 1. Since the channels between the multiple links contain ISI, we will employ discrete-time filter notation to represent them. To exemplify the notation, for a generic input u(t) and channel filter a(q −1 ) - with q −1 denoting the delay operator - the output v(t) is given by v(t)= a(q −1 )u(t)= Lc X i=0 a i u(t − i), t =1,...,N (1) where L c +1 is the number of channel taps and N is the block size. Denoting the time-reversed input and output by © 1-4244-0357-X/06/$20.00 2006 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE GLOBECOM 2006 proceedings.