Experimental Study of the Space-Time Properties of Acoustic Channels for Underwater Communications Beatrice Tomasi * , Giovanni Zappa ‡ , Kim McCoy ‡ , Paolo Casari * , Michele Zorzi * * Department of Information Engineering, University of Padova, Italy — {tomasibe, casarip, zorzi}@dei.unipd.it ‡ NATO Undersea Research Centre (NURC), La Spezia, Italy — {zappa, mccoy}@nurc.nato.int Abstract—In this paper, we present an analysis of the space- time correlation and power-delay profile (PDP) properties of the underwater acoustic channel in the nearabouts of the Pianosa Island, off the north-western coast of Italy. Our data has been collected during sea trials which took place from May to September 2009. Using the results from this evaluation, we compare the measured bit error rates affecting the transmission of Frequency-Hopping Binary Frequency Shift Keying (FH- BFSK) against those obtained by simulating the same digital modulation scheme over synthesized channels whose spread in time has the same statistical properties as those found in the trials, and whose channel taps are Rayleigh-distributed. The results show a generally good accordance of the simulated performance with the outcomes of the experiments. Moreover, given the absence of a widely agreed upon under- water channel model, and the recent interest in incorporating more accurate propagation simulators into network simulators, we compare the measured channel impulse responses against those obtained through the ray tracing tool Bellhop, and give some observations about the suitability of the tool for the purpose of reproducing realistic channel traces. I. I NTRODUCTION Underwater acoustic networks are of great interest for both civilian and military applications; however, they still represent a challenge due to the limited bandwidth available for com- munication and the high amount of time- and space-varying reverberation affecting signals in most scenarios of practical interest. Because of the amount of money and resources required for deployment and maintenance of a test system, simulation is still the most widely employed investigation tool for underwater networks. What still lacks to make up a full- rounded simulator is a widely agreed upon channel model representing the behavior of the underwater channel at least from a statistical point of view. Following similar efforts [1], [2], in this paper we make some steps in this direction by performing an estimation of the space and time correlation, and power-delay profile (PDP) properties of an underwater acoustic channel. Our estimates are derived from a large data set collected during the SubNet 2009 sea trials, which took place from May to September 2009 in waters around Pianosa Island, located in the Tyrrhenian sea, off the north-western coast of Italy (about 42.585 ◦ N, 10.1 ◦ E). Broadly speaking, the underwater channel coherence time is the period over which the propagation paths of the acous- tic energy and their intensity incur little changes, resulting in approximately stationary channel realizations as seen at the receiver; the power-delay profile (and a measure of its “length”, i.e., the channel time spread) 1 represents instead the period over which separately detectable arrivals reach the receiver, and can be measured as the standard deviation of the probability distribution obtained by normalizing the average squared magnitude of the impulse response. A measure of the channel coherence time, as well as of the time spread of the channel response, is of practical importance in many communication-related tasks. For example, when simulating underwater communications, channel realizations (and there- fore fading and other channel variability phenomena) are assumed to be approximately stationary within a certain period of time, whose length should be estimated depending on the expected channel coherence time. The latter measure can also help tune signal processing algorithms, e.g., by setting the update period of filter coefficients in adaptive equalizers: the frequency of such updates must be directly dependent on the channel coherence time. Also, when simulating underwater communications, channel estimates are assumed to be stable within a certain time period, whose length should be tuned to the expected channel coherence time. In this paper, we consider a JANUS version 0.0 wave- form [3] transmitted in the 9–14 kHz band. In particular we focus on the wideband hyperbolic frequency modulated (HFM) sine wave portion within the JANUS signal preamble: such signal has a very narrow autocorrelation function, which provides fine resolution in the computation of the channel responses at the output of a filter matched to the waveform. Based on this output, we estimate the PDP and the time correlation function of the channel. Similar evaluations of the channel coherence have been conducted in the past [4]–[7], at various frequencies and using different kinds of probe signals. Unlike most previous work, our data set contains data gathered over a period of three months, which allows to draw conclu- sions on the long-term stability of channel parameters and PDPs. We also give a measure of spatial channel coherence across the three receivers of the vertical hydrophone array, and compare the measured channel impulse responses against those obtained by simulating channel propagation through the Bellhop ray tracing tool [8]. We finally study the Bit Error Rate (BER) of the Frequency- Hopping Binary Frequency-Shift Keying (FH-BFSK) modula- tion used for the JANUS signals versus the Signal to Noise 1 In the following, we will use the terms time spread and delay spread interchangeably