HYBRID RAYTRACE MODELLING OF AN UNDERWATER ACOUSTICS COMMUNICATION CHANNEL

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1 Proceedings of the Seventh European Conference on Underwater Acoustics, ECUA 24 Delft, The Netherlands 5-8 July, 24 HYBRID RAYTRACE MODELLING OF AN UNDERWATER ACOUSTICS COMMUNICATION CHANNEL E. Svensson, I. Karasalo and J.-P. Hermand Elin Svensson, KTH, Department of Aeronautical and Vehicle Engineering SE-1 44 Stockholm, Sweden Ilkka Karasalo, Swedish Defence Research Agency, Division of Systems Technology SE Stockholm, Sweden ilkka.karasalo@foi.se Jean-Pierre Hermand, Université Libre de Bruxelles, Dept of Optics and Acoustics av F.-D Roosevelt 5 - CP 194/5, B-15 Brussels, Belgium jhermand@ulb.ac.be A hybrid method is described for modelling sound propagation in range-dependent shallow water environments. The method combines ray tracing in a range-dependent water column with local full-field modelling of interactions with a seabed composed of multiple range-dependent layers of fluid or solid materials. The method is assessed by simulations of the Yellow Shark 94 experiments in the Mediterranean, using environmental parameters available from previous acoustic full-field inversions of the experimental acoustic data, and from an oceanographic survey with a towed-oscillating CTD profiler. Results from applying the method to simulation of transmission and decoding of communication signals in the shallow-water waveguide are presented. 1. INTRODUCTION AND SUMMARY Numerical prediction of the acoustic wavefield in range-dependent shallow-water over a multi-layered seabed is in general nontrivial and computationally demanding. In most applications occurring in practice, methods based on direct discretisation of the governing differential equations with the proper boundary conditions become intractable because of the resulting workload and storage requirements. In such situations methods relying on computationally manageable approximations are required, and the development of such numerical modelling techniques has been intensive in the past decades [1, 2]. A recent contribution to computationally efficient approximative techniques for this problem class was presented by Hovem and Knobles [3]. The method combines ray tracing in the water column with bottom interactions described by the local plane-wave reflection coefficients at the seafloor. The method was applied successfully on test cases with range-dependent depth and

2 non-layered fluid seabeds. In [4] Svensson applied a similar technique for the modelling of an underwater data communication experiment. In this study we describe a fast hybrid technique for modelling of acoustic propagation in range-dependent shallow water over layered seabeds. The method is analoguous to that of Hovem and Knobles [3] but is implemented to allow multi-layered range-dependent geometries with fluid-solid seabeds and fully range and depth dependent material parameters. The method is assessed by comparing numerical predictions of transient propagation with those by an accurate but more time-consuming full field method as well as with experimental data. The experimental data consist of band-limited, medium impulse responses collected at the Yellow Shark 94 experiments in the Mediterranean, a site modelled as midly range-dependent with a two-layer seabed [5, 6]. Our purpose is, in particular, to investigate the applicability of the hybrid technique for the modelling of underwater data communication in shallow water environments. Results from simulations of data communication with a standard QAM modulation scheme and decision feedback equaliser (DFE) decoding are presented, using both experimentally observed and numerically predicted channel transform functions. 2. THE HYBRID METHOD The propagation model (XRAY) used in this study is an extension of that used in [4]. It is applicable on media composed of a water layer above a seabed consisting of an arbitrary number of fluid or solid layers. The depths of all layer interfaces may be range dependent, and all material parameters can be functions of range r and depth z. The layer interfaces z j (r) are required to be smooth functions, and are represented by splines. Similarly, within each layer each material parameter is represented by a spline function of (r, z), constructed from given environmental data by smoothing and interpolation. A ray trajectory (r(s), z(s)) where s is arc length, is a solution to the ODE system [1, Sec ] dr/ds = cos(φ) dz/ds = sin(φ) dφ/ds = {sin(φ) c/ r cos(φ) c/ z}/c. (1) c = c(r, z) is the sound speed and φ = φ(s) the elevation angle of the ray. The principal steps of computing the transfer function H(f) of the channel from a point source at r s to a receiver at r r are then 1. Find all K ray paths (eigenrays) from r s to r r leaving the source within a given interval of launch angles φ = φ(). Denote the number of times ray k hits the seafloor and the surface by n bk and n sk respectively. Then, for eigenray k = 1,..., K, 2. At the seafloor reflection points s = s jk, j = 1,..., n bk, compute the reflection coefficients γ jk = γ(r(s jk ), φ(s jk ), f), j = 1,..., n bk of plane waves incident with elevation angle φ(s jk ) on the seafloor of a range-independent medium with depth-dependence defined by that of the given medium at r = r jk. 3. Solve system (1) augmented with one equation each for the travel time τ(s) along the ray and the partial derivatives r(s)/ φ, z(s)/ φ, φ(s)/ φ with respect to launch angle φ. Determine the number of times n ck ray k passes a caustic, compute the amplitude attenuation factor α k induced by change of the ray tube area from source to receiver, and denote the travel time to the receiver by τ k.

3 The source to receiver transfer function H(f) is then obtained as the sum of the transfer functions along the K eigenrays H(f) = K H k (f) = k=1 K k=1 α k e i2πfτ k e iπ(n sk+n ck /2) Π n bk j=1 γ jk (2) In step 1 the eigenrays are found by a shooting technique using an adaptive-step 4th order Runge-Kutta method based on the DOPRI5 code by Dormand and Prince [7, Sec. II.5] for tracing individual rays. Thus the spline representation of c(r, z) must have order 5, for not impairing the local error estimates and the high convergence order of the ODE solver. The bottom reflection coefficients γ j in step 2 are computed by an exact finite element method [8], applied on the horizontal wavenumber domain equations of the range-independent medium. 3. A NUMERICAL EXAMPLE Fig. 1 shows modelling of propagation of a 4 Hz Ricker pulse emitted by a source at depth 69.2 m in a waveguide composed of a homogeneous water layer (depth 1 m, c = 151 m/s), a homogeneous fluid sediment layer (thickness 7 m, ρ = 15 m/kg 3, c = 148 m/s, absorption.6 db/λ), and a homogeneous fluid bedrock halfspace (ρ = 18 m/kg 3, c = 153 m/s, absorption.15 db/λ). The two (almost coinciding) curves show the signal as function of time registered by a receiver at range 9 km, depth 67.2 m, computed by XRAY (black) and by XFEM (green) an accurate full-field method for range-independent media [8]. As seen, the agreement of the fast XRAY solution with the correct green curve is quite good. Fig. 1: Propagation of a 4 Hz Ricker pulse in 1 m water over a two-layered seabed: Received signal as function of time at range 9 m depth 67.2 m. Black: Hybrid method XRAY. Green: Full-field method XFEM. 4. EXPERIMENTAL DATA The environmental data and the experimental channel impulse response data were collected in the western part of the Mediterranean during Yellow Shark 94 [5, 6]. The geometry and the conditions used here are from the measurements with a source-receiver distance of ca 9 km (926 m by DGPS). The depth of the water was weakly range dependent with an average of m. The sound speed profile had a well developed thermocline and no sound speed minimum, minimising the surface interaction and maximising the bottom interaction.

4 depth [m] distance [km] sound speed [m/s] Fig. 2: Source and receiver geometry and range-average sound speed profile for the Yellow Shark 94 measurements at 9 km range. The receiving array was positioned below the thermocline and spanned the water between 37.2 and 99.2 m. There were 32 elements equidistantly distributed over the array. The sound source was positioned at a depth of 69.2 m (Fig. 2). Band-limited impulse responses were estimated for two different frequency bands: 2 8 Hz and 8 16 Hz, respectively. The signal used in the experiments was a 12 s long linearly frequency modulated waveform and the impulse response was estimated by matchedfiltered signals. Measurements were performed at two minute intervals as described in Table 1. Day Time Range Frequency Number [km] band [Hz] of signals 1 Sept Table 1: Acoustic data recording periods. 5. IMPULSE RESPONSE DATA VS MODEL Fig. 3 shows an example of experimentally observed and modelled band-limited impulse responses from the source at depth 69.2 m to a receiver at the DGPS measured range 926 m and depth 85.2 m. The propagation channel is modelled as in [5, 6] and consists of a mildly range-dependent water column with average depth m on top of a 7 m thick homogeneous sediment layer (ρ = 15 m/kg 3, c = 148 m/s, absorption.6 db/λ), and a homogeneous fluid halfspace modelling a silty-clay sediment (ρ = 18 m/kg 3, c = 153 m/s, absorption.15 db/λ). The sound velocity profile in the water column is downward refracting as in Fig. 2. The structure and the duration of the model-predicted impulse response is seen to be in reasonable agreement with the experimental data. The cause of the ca 7 ms difference between the model predicted and the observed arrival times is not clear, however possible error sources include bias in the modelled travel time from simplifications in the environmental model, in particular in the model of the sediment, as well as measurement uncertainties in source-receiver range and the sound speed. 6. DATA COMMUNICATION SIMULATIONS In this section we present results from simulations of transmission of data through a communication channel defined by the the experimentally observed and the modelled channel transfer functions. The data, consisting of a sequence of complex-valued symbols, is passed through the channel in the following steps: 1. The piece-wise constant complex signal is passed through a transmitter filter and then up-converted to the passband. The real part of the passband signal is passed through the underwater channel.

5 Fig. 3: Band-limited impulse response from a source at depth 67.2 m to a receiver at range 926 m and depth 85.2 m. Frequency range 8 f 16 Hz. Above: Experimentally observed. Below: Modelled. 2. The received signal is down-converted to baseband, low-pass filtered, and demodulated by a receiver filter whose frequency response matches that of the transmitter filter. 3. The signal is cross-correlated with a training sequence to identify its arrival time at the receiver. The arrival time is used for symbol synchronisation, and the signal is then sampled at the symbol rate. 4. The sampled signal is fed to a decision feedback equaliser (DFE) to detect the transmitted message. The DFE in step 4 is controlled by three parameters [9]: the number of coefficients in the feedback filter, the number of coefficients in the feedforward filter and the decision delay, the number of samples that the signal is delayed before the decision is made. The DFE filter coefficients are initialised using the training sequence, and then successively updated using a recursive least squares algorithm [1, Sec. 2.6]. The carrier frequency was set to 12 Hz and the symbol rate to 4 Hz, to maximise the use of the available bandwidth. The length of the training sequence was chosen to 255 symbols to ensure convergence of the DFE filter coefficients before start of symbol estimation. A pseudo random binary bit sequence was used as training sequence, and standard QAM [11, Ch. 7] modulation was used to transfer a bit sequence into complex-valued symbols. The bit sequences of the symbol points were Gray encoded. Fig. 4 shows constellations of the complex symbols for five receivers, obtained with the experimentally observed (above) and the modelled (below) impulse responses at different receiver depths. The points are those fed into the decision step of the DFE. The lengths of the forward and backward filters of the DFE were 1, with a decision delay of 5 samples. As seen in Fig. 4, the spread of the points in the constellation plots obtained with the modelled and the experimental transfer functions are similar, indicating that the model transfer functions are satisfactorily realistic. The point spread reflects the success of the channel equalisation filter of the DFE, and must be sufficiently small for correct symbol identification by the subsequent decision step. In all cases shown in Fig. 4 all symbols were identified correctly, i.e. the bit error rate, BER, was zero. 7. ACKNOWLEDGEMENTS This work was supported by the Swedish National Defence College and by the Royal Netherlands Naval College. The data were collected by Saclantcen, La Spezia, Italy.

6 m 85.2 m 69.2 m 53.2 m 37.2 m Fig. 4: Symbol constellations at the input of the decision step of the DFE. Experimentally observed (above) and model-predicted (below) impulse responses, respectively. REFERENCES [1] F. Jensen, W. Kuperman, M. Porter, H. Schmidt, Computational Ocean Acoustics, AIP Press, New-York, [2] P. Etter, Underwater Acoustics Modelling and Simulation, Third edition, Spon Press, London, 23. [3] J. Hovem, D. Knobles, A range-dependent propagation model based on a combination of ray theory and plane wave reflection coefficients, Tenth Int. Congress on Sound and Vibration, pp , July 23. [4] E. Svensson Acoustic Signal Transmission in Shallow Water, TRITA-FKT-22:1, KTH, 22. [5] J.-P. Hermand, Inversion of Broad-Band Multitone Acoustic Data from the YELLOW SHARK Summer Experiments, J. Oceanic Eng., volume 21 (number 4), pp , [6] J.-P. Hermand, Broad-Band Geoacoustic Inversion on Shallow Water from Waveguide Impulse Response Measurements on a single Hydrophone: Theory and Experimental Results, J. Oceanic Eng., volume 24 (number 1), pp , [7] E. Hairer, S.P. Norsett, G. Wanner, Solving Ordinary Differential Equations I, Springer Verlag, [8] I. Karasalo Exact finite elements for wave propagation in range-independent fluid-solid media, Journal of Sound and Vibration, Vol 172(5), pp , [9] P.A. Voois, I. Lee, J.M. Cioffi The Effect of Decision Delay in Finite-Length Decision Feedback Equalization, IEEE Transactions on Information Theory, volume 45 (number 2), pp , [1] T. Kailath, A.H. Sayed, B. Hassibi, Linear Estimation, pp , Prentice-Hall, 2. [11] J.G. Proakis, M. Salehi, Communication Systems Engineering, pp 35-36, Prentice- Hall, 22.