time-varying wideband underwater acoustic ... - Semantic Scholar
TIME-VARYING WIDEBAND UNDERWATER ACOUSTIC CHANNEL ESTIMATION FOR OFDM COMMUNICATIONS N. F. Josso†, J. J. Zhang, D. Fertonani, A. Papandreou-Suppappola, T. M. Duman †
GIPSA-lab/DIS, Grenoble Institute of Technology, Grenoble, France SenSIP Center, School of ECEE, Arizona State University, Tempe, AZ, USA ABSTRACT We investigate two methods for estimating the matched signal transformations caused by time-varying underwater acoustic channels in orthogonal frequency division multiplexing (OFDM) communication systems. The underwater acoustic channel for this 12-20 kHz medium frequency range OFDM system is best modeled using multipath and wideband Doppler scale changes on the transmitted signal. As a result, our first channel estimation method is based on discretizing the wideband spreading function time-scale representation of the channel output using the Mellin transform. The second method is based on extracting the time-scale features of distinct ray paths in the received signal using a modified matching pursuit decomposition algorithm. We validate and discuss both methods using data from the recent Kauai Acomms MURI 2008 (KAM08) underwater acoustic communication experiment.
may still be distorted as the appropriate matched channel model (wideband or dispersive) is usually not exploited at the receiver for improved processing.
Index Terms— Underwater acoustic channel, wideband spreading function, channel estimation, OFDM.
Our proposed UWA channel estimation approach successfully estimates jointly different Doppler scale components for different multipath propagations, and thus it provides an original approach that can lead to improvements on existing UWA communication schemes. Our methodology makes use of the discrete time-scale channel characterization we have previously proposed in [6, 7] to characterize UWA channels by decomposing a wideband linear time-varying (LTV) channel output into discrete time shifts and time scale changes on the transmitted signal, weighted by a smoothed and sampled version of the wideband spreading function (WSF). We also consider the characterization of UWA channel profiles using an MPD approach with the ray theory model which assumes that the transmitted signal is sparsely scattered into multiple rays, undergoing multipath and Doppler scale changes [8]. Both methods are validated using OFDM communication signals from the KAM08 experiment, and we demonstrate that different arrivals have different Doppler scales associated with them.
1. INTRODUCTION The need for shallow underwater communications is widelyspreading to include communication between autonomous vessels, submarines, or scuba divers. However, the highly time-varying characteristics of underwater acoustic (UWA) channels present many challenges to underwater communication applications. UWA channels exhibit large multipath spreads and Doppler scaling effects on the transmitted signal (for medium carrier frequencies) or nonlinear time-frequency dispersive shifts (for low carrier frequencies). This is because the propagating signal can be subjected to fast varying and undesirable distortion effects due to the time-varying nature of the ocean environment and also due to the relative motion between the transmitter, channel, and receiver. As a result, when classical communication processing techniques, such as sophisticated equalization algorithms, are applied to compensate for the large multipath spread, communication signals The work was supported in part by D´el´egation G´en´erale pour l’Armement under SHOM Grant N07CR0001, ASU SenSIP Center, and Department of Defense MURI Grant No. AFOSR FA9550-05-1-0443. The KAM08 experiment was funded by the MURI Grant No. N00014-07-1-0739.
978-1-4244-4296-6/10/$25.00 ©2010 IEEE
5626
Recently, new techniques have been proposed to estimate fast varying UWA communication channel parameters. For example, in [1], sparse UWA communication channels are estimated using the delay-Doppler spread representation of the received signal and the matching pursuit decomposition (MPD) algorithm to sequentially identify dominant channel taps and estimate their coefficients. In [2, 3], the UWA channel is assumed to have the same Doppler scale on all propagation paths so that the estimated Doppler scaling can be mitigated by resampling the received signal. Although the channel is modeled with multiple Doppler scale paths in [4, 5], their channel estimation approach still assumes a single dominant Doppler scale.
The paper is organized as follows. Sections 2 and 3 present the two time-scale channel estimation methods, and Section 4 demonstrates the application of the proposed channel characterization to real data from the KAM08 experiment.
ICASSP 2010
2. UWA CHANNEL ESTIMATION USING WSF
3. UAC CHANNEL ESTIMATION USING MPD
For a narrowband signal whose bandwidth is much less than its central frequency, the Doppler effect can be assumed to be a frequency shift. However, for UWA signals, this assumption does not hold because the signal bandwidth is comparable to the central frequency. As a result, transmitted signals over UWA channels, in the 500 Hz to 20 kHz medium-to-high frequency band, will undergo Doppler scalings as well as multipath distortions. The (noiseless) output signal x(t) of such a wideband channel can be modeled as a linear combination of time-shifted and Doppler-scaled versions of the input signal s(t), weighted by the WSF [6, 9], Ts ηmax √ X (τ, η) η s(η(t − τ )) dη dτ. (1) x(t) =
Using ray theory, the (noiseless) output signal of a sparse wideband UWA channel can be represented by [10] N √ ai ηi s(ηi (t − τi )) , (3) x(t) =
0
ηmin
Here, τ and η > 0 are the time delay and Doppler-scale parameters, respectively, and the WSF, X (τ, η), represents the strength of scatterers in the ocean. Due to the physical properties of realistic UWA environments, we assume that X (τ, η) is supported in τ ∈ [0, Ts ] and η ∈ [ηmin , ηmax ], where Ts is the time delay spread of the channel and η ∈ [ηmin , ηmax ] represents the range of possible scale changes. By geometrically sampling the scaling factors of the transmitted signal s(t) using its Mellin transform Ms (β), then it is possible to represent the physical characteristics of the channel in a discrete way and with a minimum number of parameters without loosing significant information. Any signal localized in the time-frequency domain can be shown to also be localized in the Mellin domain [6]. Assuming that s(t) is timefrequency bounded, then we can assume that its Mellin transform Ms (β) is bounded within β ∈ [−β0 /2, β0 /2]. Using the Mellin transform, the scaling factors in (1) are geometrically sampled as η = η0m where m is an integer and η0 = e1/β0 . The time-delay is uniformly sampled for each given scaling factor η0m as τ = n/(η0m W ) for the nth time-delay, where W is the bandwidth of s(t). The resulting discrete time-scale representation of the channel is given by [6] x(t) =
(m) M1 N m=M0 n=0
m
Ψn,m η02 s(η0m t − n/W ),
(2)
where M0 = ln(ηmin )/ ln(η0 ), M1 = ln(ηmax )/ ln(η0 ), N (m) = η0m W Ts , and Ψn,m is a smoothed version of the WSF. It can be shown, under certain assumptions, that the M1 (N (m) + 1) decomposition in (2) can result in M = m=M 0 independent time-scale paths [6]. From (2), it can be seen that estimating the UWA channel corresponds to estimating the WSF coefficients over the specified channel spread. For ˆ = (S T S)−1 S T x, example, an estimate of the coefficients, Ψ can be obtained using the least squares error estimation method, where S is a matrix whose columns consist of timeshift and scale-changed versions of the transmitted signal s(t), and x is the sampled received signal vector.
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i=1
where N is the number of propagation ray paths, and ai , τi and ηi are the attenuation factor, time delay and scale change parameters associated with the ith ray. When the source is moving at a constant speed v, the Doppler scale of the ith ray satisfies ηi = 1/[1−(v/c) cos(θi )], where θi is the declination angle of the ith ray and c is the sound speed in the medium [10]. We note that the ray theory based signal representation in (3) can be shown to be a special case of the time-scale system characterization in (1), with the WSF given by N ai δ(τ − τi )δ(η − ηi ), (4) X (τ, η) = Xray (τ, η) = i=1
where δ(·) is the Dirac delta function. Note that the WSF in (4) still corresponds to a wideband time-varying channel; it however characterizes a sparse wideband channel as its spreading unction is highly-localized in the time-scale plane. Due to the channel-sparse assumption, the MPD can be used to determine the time-scale features associated with the channel. The MPD is an iterative algorithm which expands a signal into a weighted linear combination of elementary functions (or atoms) chosen from a complete dictionary [11]. The resulting L−1expansion of a finite energy signal is given by x(t) = i=0 αi gi (t) + pL (t), where gi (t) is the basis function selected at the ith iteration, αi is the corresponding expansion coefficient, and pL (t) is the residual signal after L MPD iterations. To best fit the UWA model with matched time-scale transformations, the dictionary atoms are designed to match the channel propagating nature by selecting them to be time-delayed and Doppler scaled versions of the transmitted signal s(t) as in (3). We can thus choose them using the wideband ambiguity function (WAF) of the transmitted signal [10,12]. Using the MPD, the ith atom in the dictionary √ will correspond to gi (t) = ηi s(ηi (t−τi )), ηi = 0. Thus, the extracted UWA channel features are simply the MPD parameters (αi , ηi , τi ), i = 0, · · · , L − 1, resulting in highlylocalized and sparse signal characterizations. 4. ALGORITHM VALIDATION USING KAM08 DATA The KAM08 experiment was conducted in shallow water off the western coast of Kauai, Hawaii, in June 2008 [13]. The transmitter was submerged at a depth varying from 20 m to 50 m and towed at a 3 knots (about 1.54 m/s) constant speed. For the analyzed transmission, the source-receiver separation was about 1,500 m and the towing ship was moving towards the fixed receiver. The transmitted signal was sampled at 50 kHz. It consisted of a linear frequency-modulated (LFM) chirp with 8 kHz bandwidth, 16 kHz central frequency, and 100 ms duration, followed by a 100 ms silent interval and eight 276 ms OFDM words with a 20 ms cyclic prefix. The
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Fig. 2. Estimated WSF of the UWA channel.
Fig. 1. Spectrogram of the received LFM and OFDM signals, transmitted by a moving source over an UWA channel.
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4.1. WSF Approach Using the WSF representation for the received OFDM signal, we estimated the channel WSF coefficients as shown in Fig. 2. For the experimental received OFDM signal, the channel time delay spread was Ts ≈ 0.0253 s and the signal bandwidth was W ≈ 10 kHz. From the data Mellin transform, η0 = 1.0001. The possible speed ranged from v = 0 m/s to v = 2 m/s, resulting in ηmin = 1/[1 − (v/c)] = 1 (with v = 0 and c = 1, 500 m/s) and ηmax = 1.00134. The corresponding discrete scale changes in (2) ranged from M0 = 0 to M1 = 13. For this experimental data set, since η0 is close to 1, the number of time shifts is approximately the same for all the different scale factors so that N (m) = η0m W Ts ≈ 253. Thus, the time-delay and Doppler-scale spread are both very large, and the total of possible independent time-scale Mnumber 1 (N (m) + 1) ≈ 3, 542. Once we sampaths is M = m=M 0 ple over the WSF parameters and their approximate bounds, the WSF is estimated using the least squares error estimation approach. Using the estimated WSF and the transmitted OFDM signal s(t) (that was also made available), we can recover the received signal using (2). The recovered signal x ˆ(t) is shown in Fig. 3 superimposed with the received signal x(t). The recovered signal matches the original experimental data very well, with a recovery 9.8%. The recovery error of = error is defined as = |x(t) − x ˆ(t)|2 dt/( |x(t)|2 dt). 4.2. MPD Approach Figure 4 shows the WAF of the received OFDM signal together with the channel time-scale features extracted after 130 MPD iterations (shown as crosses, with scale represented as
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2048 OFDM carrier ranged over 12-20 kHz. The spectrogram of the received signal is depicted in Fig. 1. Instead of the single transmitted LFM chirp, multiple LFM chirps are shown from about 25 ms to 125 ms (represented by sloped lines in the time-frequency plane); this is due to the time-scale effect of the channel in Equation (2).
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Fig. 3. Recovered signal using WSF and received signal. the inverse of velocity). Figure 5 shows a zoomed region of Fig. 4 around 0.049 s. Each propagated ray family can be seen as a high energy area in the WAF [10]. The relatively sparse multipath-scale profile obtained using the MPD is represented by crosses in Fig. 6. The solid line represents the multipath profile obtained using an approach proposed in [10]. Using the MPD, the recovery of the received OFDM signal, rˆ(t), can be computed directly from the functions used in the MPD signal decomposition. The reconstruction error after the first M = 130 MPD iterations was ε = 14.9%. Note that the higher error was expected as this approach assumed that the WSF of the channel is in the form of (4). 5. CONCLUSION We investigated two approaches for estimating wideband underwater acoustic channels for use in communication applications with a stationary receiver and a moving transmitter. The first method considers all possible wideband spreading function representations for the channel through a discretization process for implementation. The second method assumes a sparse channel representation and only estimates time shifts and Doppler scales corresponding to a fixed number of rays using the MPD. Both methods were successfully validated using OFDM communication data from the KAM08 experiment. Our approach demonstrated that, indeed, underwater acoustic channels using medium range frequencies result in different arrivals with different Doppler scales. Therefore,
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Fig. 6. Multipath profile using MPD approach (crosses).
channels with Doppler spread,” in IEEE DSP Workshop, Marco Island, FL, 2009, pp. 138–143.
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[6] Y. Jiang and A. Papandreou-Suppappola, “Discrete time-frequency models of generalized dispersive systems,” IEEE Trans. on Signal Processing, vol. 3, pp. 349–352, May 2006.
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Fig. 5. Zoomed region of the WAF in Fig. 4, around 0.049 s. time-scale diversity could be exploited if the receiver is properly designed, a subject now under investigation. Acknowledgments We would like to thank C. Ioana (GIPSAlab/DIS) and K. Tu (ASU) for fruitful discussions. 6. REFERENCES [1] W. Li and J. C. Preisig, “Estimation of rapidly timevarying sparse channels,” IEEE Journal of Oceanic Engineering, vol. 32, pp. 927–939, October 2007. [2] M. Stojanovic, “Low complexity OFDM detector for underwater acoustic channels,” in Proc. IEEE Oceans, Boston, MA, Sept. 2006, pp. 1–6. [3] K. Tu, D. Fertonani, T. M. Duman, M. Stojanovic, J. G. Proakis, and P. Hursky, “Mitigation of intercarrier interference for OFDM over time-varying underwater acoustic channels,” IEEE J. Oceanic Eng., submitted, 2009. [4] B. Li, S. Zhou, M. Stojanovic, L. Freitag, and P. Willett, “Multicarrier communication over underwater acoustic channels with nonuniform Doppler shifts,” IEEE Journal of Oceanic Eng., vol. 33, pp. 198–209, April 2008. [5] S. Mason, C. Berger, S. Zhou, K. Ball, L. Freitag, and P. Willett, “An OFDM design for underwater acoustic
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[7] S. Rickard, Time-frequency and Time-scale Representations of Doubly Spread Channels, Ph.D. thesis, Princeton, 2003. [8] N. F. Josso, J. Zhang, A. Papandreou-Suppappola, C. Ioana, J. I. Mars, C. Gervaise, and Y. Stephan, “On the characterization of time-scale underwater acoustic signals using matching pursuit decomposition,” in Proc. IEEE Oceans, October 2009. [9] A. Papandreou-Suppappola, C. Ioana, and J. Zhang, “Time-varying wideband channel modeling and applications,” in Wireless Communications over Rapidly TimeVarying Channels, F. Hlawatsch and G. Matz, Eds. Academic Press, 2009. [10] N. F. Josso, C. Ioana, J. I. Mars, C. Gervaise, and Y. Stephan, “On the consideration of motion effects in the computation of impulse response for underwater acoustics inversion,” The Journal of the Acoustical Society of America, in print, 2009. [11] S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Transactions on Signal Processing, vol. 41, pp. 3397–3415, Dec. 1993. [12] N. F. Josso, C. Ioana, C. Gervaise, Y. Stephan, and J. I. Mars, “Motion effect modeling in multipath configuration using warping based lag-Doppler filtering,” in IEEE ICASSP, Taiwan, 2009, pp. 2301–2304. [13] W. S. Hodgkiss, H. C. Song, M. Badiey, A. Song, and M. Siderius, “Kauai Acomms MURI 2008 (KAM08) experiment,” Trip Report, July 2008.
GIPSA-lab/DIS, Grenoble Institute of Technology, Grenoble, France SenSIP Center, School of ECEE, Arizona State University, Tempe, AZ, USA ABSTRACT We investigate two methods for estimating the matched signal transformations caused by time-varying underwater acoustic channels in orthogonal frequency division multiplexing (OFDM) communication systems. The underwater acoustic channel for this 12-20 kHz medium frequency range OFDM system is best modeled using multipath and wideband Doppler scale changes on the transmitted signal. As a result, our first channel estimation method is based on discretizing the wideband spreading function time-scale representation of the channel output using the Mellin transform. The second method is based on extracting the time-scale features of distinct ray paths in the received signal using a modified matching pursuit decomposition algorithm. We validate and discuss both methods using data from the recent Kauai Acomms MURI 2008 (KAM08) underwater acoustic communication experiment.
may still be distorted as the appropriate matched channel model (wideband or dispersive) is usually not exploited at the receiver for improved processing.
Index Terms— Underwater acoustic channel, wideband spreading function, channel estimation, OFDM.
Our proposed UWA channel estimation approach successfully estimates jointly different Doppler scale components for different multipath propagations, and thus it provides an original approach that can lead to improvements on existing UWA communication schemes. Our methodology makes use of the discrete time-scale channel characterization we have previously proposed in [6, 7] to characterize UWA channels by decomposing a wideband linear time-varying (LTV) channel output into discrete time shifts and time scale changes on the transmitted signal, weighted by a smoothed and sampled version of the wideband spreading function (WSF). We also consider the characterization of UWA channel profiles using an MPD approach with the ray theory model which assumes that the transmitted signal is sparsely scattered into multiple rays, undergoing multipath and Doppler scale changes [8]. Both methods are validated using OFDM communication signals from the KAM08 experiment, and we demonstrate that different arrivals have different Doppler scales associated with them.
1. INTRODUCTION The need for shallow underwater communications is widelyspreading to include communication between autonomous vessels, submarines, or scuba divers. However, the highly time-varying characteristics of underwater acoustic (UWA) channels present many challenges to underwater communication applications. UWA channels exhibit large multipath spreads and Doppler scaling effects on the transmitted signal (for medium carrier frequencies) or nonlinear time-frequency dispersive shifts (for low carrier frequencies). This is because the propagating signal can be subjected to fast varying and undesirable distortion effects due to the time-varying nature of the ocean environment and also due to the relative motion between the transmitter, channel, and receiver. As a result, when classical communication processing techniques, such as sophisticated equalization algorithms, are applied to compensate for the large multipath spread, communication signals The work was supported in part by D´el´egation G´en´erale pour l’Armement under SHOM Grant N07CR0001, ASU SenSIP Center, and Department of Defense MURI Grant No. AFOSR FA9550-05-1-0443. The KAM08 experiment was funded by the MURI Grant No. N00014-07-1-0739.
978-1-4244-4296-6/10/$25.00 ©2010 IEEE
5626
Recently, new techniques have been proposed to estimate fast varying UWA communication channel parameters. For example, in [1], sparse UWA communication channels are estimated using the delay-Doppler spread representation of the received signal and the matching pursuit decomposition (MPD) algorithm to sequentially identify dominant channel taps and estimate their coefficients. In [2, 3], the UWA channel is assumed to have the same Doppler scale on all propagation paths so that the estimated Doppler scaling can be mitigated by resampling the received signal. Although the channel is modeled with multiple Doppler scale paths in [4, 5], their channel estimation approach still assumes a single dominant Doppler scale.
The paper is organized as follows. Sections 2 and 3 present the two time-scale channel estimation methods, and Section 4 demonstrates the application of the proposed channel characterization to real data from the KAM08 experiment.
ICASSP 2010
2. UWA CHANNEL ESTIMATION USING WSF
3. UAC CHANNEL ESTIMATION USING MPD
For a narrowband signal whose bandwidth is much less than its central frequency, the Doppler effect can be assumed to be a frequency shift. However, for UWA signals, this assumption does not hold because the signal bandwidth is comparable to the central frequency. As a result, transmitted signals over UWA channels, in the 500 Hz to 20 kHz medium-to-high frequency band, will undergo Doppler scalings as well as multipath distortions. The (noiseless) output signal x(t) of such a wideband channel can be modeled as a linear combination of time-shifted and Doppler-scaled versions of the input signal s(t), weighted by the WSF [6, 9], Ts ηmax √ X (τ, η) η s(η(t − τ )) dη dτ. (1) x(t) =
Using ray theory, the (noiseless) output signal of a sparse wideband UWA channel can be represented by [10] N √ ai ηi s(ηi (t − τi )) , (3) x(t) =
0
ηmin
Here, τ and η > 0 are the time delay and Doppler-scale parameters, respectively, and the WSF, X (τ, η), represents the strength of scatterers in the ocean. Due to the physical properties of realistic UWA environments, we assume that X (τ, η) is supported in τ ∈ [0, Ts ] and η ∈ [ηmin , ηmax ], where Ts is the time delay spread of the channel and η ∈ [ηmin , ηmax ] represents the range of possible scale changes. By geometrically sampling the scaling factors of the transmitted signal s(t) using its Mellin transform Ms (β), then it is possible to represent the physical characteristics of the channel in a discrete way and with a minimum number of parameters without loosing significant information. Any signal localized in the time-frequency domain can be shown to also be localized in the Mellin domain [6]. Assuming that s(t) is timefrequency bounded, then we can assume that its Mellin transform Ms (β) is bounded within β ∈ [−β0 /2, β0 /2]. Using the Mellin transform, the scaling factors in (1) are geometrically sampled as η = η0m where m is an integer and η0 = e1/β0 . The time-delay is uniformly sampled for each given scaling factor η0m as τ = n/(η0m W ) for the nth time-delay, where W is the bandwidth of s(t). The resulting discrete time-scale representation of the channel is given by [6] x(t) =
(m) M1 N m=M0 n=0
m
Ψn,m η02 s(η0m t − n/W ),
(2)
where M0 = ln(ηmin )/ ln(η0 ), M1 = ln(ηmax )/ ln(η0 ), N (m) = η0m W Ts , and Ψn,m is a smoothed version of the WSF. It can be shown, under certain assumptions, that the M1 (N (m) + 1) decomposition in (2) can result in M = m=M 0 independent time-scale paths [6]. From (2), it can be seen that estimating the UWA channel corresponds to estimating the WSF coefficients over the specified channel spread. For ˆ = (S T S)−1 S T x, example, an estimate of the coefficients, Ψ can be obtained using the least squares error estimation method, where S is a matrix whose columns consist of timeshift and scale-changed versions of the transmitted signal s(t), and x is the sampled received signal vector.
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i=1
where N is the number of propagation ray paths, and ai , τi and ηi are the attenuation factor, time delay and scale change parameters associated with the ith ray. When the source is moving at a constant speed v, the Doppler scale of the ith ray satisfies ηi = 1/[1−(v/c) cos(θi )], where θi is the declination angle of the ith ray and c is the sound speed in the medium [10]. We note that the ray theory based signal representation in (3) can be shown to be a special case of the time-scale system characterization in (1), with the WSF given by N ai δ(τ − τi )δ(η − ηi ), (4) X (τ, η) = Xray (τ, η) = i=1
where δ(·) is the Dirac delta function. Note that the WSF in (4) still corresponds to a wideband time-varying channel; it however characterizes a sparse wideband channel as its spreading unction is highly-localized in the time-scale plane. Due to the channel-sparse assumption, the MPD can be used to determine the time-scale features associated with the channel. The MPD is an iterative algorithm which expands a signal into a weighted linear combination of elementary functions (or atoms) chosen from a complete dictionary [11]. The resulting L−1expansion of a finite energy signal is given by x(t) = i=0 αi gi (t) + pL (t), where gi (t) is the basis function selected at the ith iteration, αi is the corresponding expansion coefficient, and pL (t) is the residual signal after L MPD iterations. To best fit the UWA model with matched time-scale transformations, the dictionary atoms are designed to match the channel propagating nature by selecting them to be time-delayed and Doppler scaled versions of the transmitted signal s(t) as in (3). We can thus choose them using the wideband ambiguity function (WAF) of the transmitted signal [10,12]. Using the MPD, the ith atom in the dictionary √ will correspond to gi (t) = ηi s(ηi (t−τi )), ηi = 0. Thus, the extracted UWA channel features are simply the MPD parameters (αi , ηi , τi ), i = 0, · · · , L − 1, resulting in highlylocalized and sparse signal characterizations. 4. ALGORITHM VALIDATION USING KAM08 DATA The KAM08 experiment was conducted in shallow water off the western coast of Kauai, Hawaii, in June 2008 [13]. The transmitter was submerged at a depth varying from 20 m to 50 m and towed at a 3 knots (about 1.54 m/s) constant speed. For the analyzed transmission, the source-receiver separation was about 1,500 m and the towing ship was moving towards the fixed receiver. The transmitted signal was sampled at 50 kHz. It consisted of a linear frequency-modulated (LFM) chirp with 8 kHz bandwidth, 16 kHz central frequency, and 100 ms duration, followed by a 100 ms silent interval and eight 276 ms OFDM words with a 20 ms cyclic prefix. The
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Fig. 2. Estimated WSF of the UWA channel.
Fig. 1. Spectrogram of the received LFM and OFDM signals, transmitted by a moving source over an UWA channel.
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4.1. WSF Approach Using the WSF representation for the received OFDM signal, we estimated the channel WSF coefficients as shown in Fig. 2. For the experimental received OFDM signal, the channel time delay spread was Ts ≈ 0.0253 s and the signal bandwidth was W ≈ 10 kHz. From the data Mellin transform, η0 = 1.0001. The possible speed ranged from v = 0 m/s to v = 2 m/s, resulting in ηmin = 1/[1 − (v/c)] = 1 (with v = 0 and c = 1, 500 m/s) and ηmax = 1.00134. The corresponding discrete scale changes in (2) ranged from M0 = 0 to M1 = 13. For this experimental data set, since η0 is close to 1, the number of time shifts is approximately the same for all the different scale factors so that N (m) = η0m W Ts ≈ 253. Thus, the time-delay and Doppler-scale spread are both very large, and the total of possible independent time-scale Mnumber 1 (N (m) + 1) ≈ 3, 542. Once we sampaths is M = m=M 0 ple over the WSF parameters and their approximate bounds, the WSF is estimated using the least squares error estimation approach. Using the estimated WSF and the transmitted OFDM signal s(t) (that was also made available), we can recover the received signal using (2). The recovered signal x ˆ(t) is shown in Fig. 3 superimposed with the received signal x(t). The recovered signal matches the original experimental data very well, with a recovery 9.8%. The recovery error of = error is defined as = |x(t) − x ˆ(t)|2 dt/( |x(t)|2 dt). 4.2. MPD Approach Figure 4 shows the WAF of the received OFDM signal together with the channel time-scale features extracted after 130 MPD iterations (shown as crosses, with scale represented as
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2048 OFDM carrier ranged over 12-20 kHz. The spectrogram of the received signal is depicted in Fig. 1. Instead of the single transmitted LFM chirp, multiple LFM chirps are shown from about 25 ms to 125 ms (represented by sloped lines in the time-frequency plane); this is due to the time-scale effect of the channel in Equation (2).
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Fig. 3. Recovered signal using WSF and received signal. the inverse of velocity). Figure 5 shows a zoomed region of Fig. 4 around 0.049 s. Each propagated ray family can be seen as a high energy area in the WAF [10]. The relatively sparse multipath-scale profile obtained using the MPD is represented by crosses in Fig. 6. The solid line represents the multipath profile obtained using an approach proposed in [10]. Using the MPD, the recovery of the received OFDM signal, rˆ(t), can be computed directly from the functions used in the MPD signal decomposition. The reconstruction error after the first M = 130 MPD iterations was ε = 14.9%. Note that the higher error was expected as this approach assumed that the WSF of the channel is in the form of (4). 5. CONCLUSION We investigated two approaches for estimating wideband underwater acoustic channels for use in communication applications with a stationary receiver and a moving transmitter. The first method considers all possible wideband spreading function representations for the channel through a discretization process for implementation. The second method assumes a sparse channel representation and only estimates time shifts and Doppler scales corresponding to a fixed number of rays using the MPD. Both methods were successfully validated using OFDM communication data from the KAM08 experiment. Our approach demonstrated that, indeed, underwater acoustic channels using medium range frequencies result in different arrivals with different Doppler scales. Therefore,
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Fig. 6. Multipath profile using MPD approach (crosses).
channels with Doppler spread,” in IEEE DSP Workshop, Marco Island, FL, 2009, pp. 138–143.
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[6] Y. Jiang and A. Papandreou-Suppappola, “Discrete time-frequency models of generalized dispersive systems,” IEEE Trans. on Signal Processing, vol. 3, pp. 349–352, May 2006.
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Fig. 5. Zoomed region of the WAF in Fig. 4, around 0.049 s. time-scale diversity could be exploited if the receiver is properly designed, a subject now under investigation. Acknowledgments We would like to thank C. Ioana (GIPSAlab/DIS) and K. Tu (ASU) for fruitful discussions. 6. REFERENCES [1] W. Li and J. C. Preisig, “Estimation of rapidly timevarying sparse channels,” IEEE Journal of Oceanic Engineering, vol. 32, pp. 927–939, October 2007. [2] M. Stojanovic, “Low complexity OFDM detector for underwater acoustic channels,” in Proc. IEEE Oceans, Boston, MA, Sept. 2006, pp. 1–6. [3] K. Tu, D. Fertonani, T. M. Duman, M. Stojanovic, J. G. Proakis, and P. Hursky, “Mitigation of intercarrier interference for OFDM over time-varying underwater acoustic channels,” IEEE J. Oceanic Eng., submitted, 2009. [4] B. Li, S. Zhou, M. Stojanovic, L. Freitag, and P. Willett, “Multicarrier communication over underwater acoustic channels with nonuniform Doppler shifts,” IEEE Journal of Oceanic Eng., vol. 33, pp. 198–209, April 2008. [5] S. Mason, C. Berger, S. Zhou, K. Ball, L. Freitag, and P. Willett, “An OFDM design for underwater acoustic
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[7] S. Rickard, Time-frequency and Time-scale Representations of Doubly Spread Channels, Ph.D. thesis, Princeton, 2003. [8] N. F. Josso, J. Zhang, A. Papandreou-Suppappola, C. Ioana, J. I. Mars, C. Gervaise, and Y. Stephan, “On the characterization of time-scale underwater acoustic signals using matching pursuit decomposition,” in Proc. IEEE Oceans, October 2009. [9] A. Papandreou-Suppappola, C. Ioana, and J. Zhang, “Time-varying wideband channel modeling and applications,” in Wireless Communications over Rapidly TimeVarying Channels, F. Hlawatsch and G. Matz, Eds. Academic Press, 2009. [10] N. F. Josso, C. Ioana, J. I. Mars, C. Gervaise, and Y. Stephan, “On the consideration of motion effects in the computation of impulse response for underwater acoustics inversion,” The Journal of the Acoustical Society of America, in print, 2009. [11] S. G. Mallat and Z. Zhang, “Matching pursuits with time-frequency dictionaries,” IEEE Transactions on Signal Processing, vol. 41, pp. 3397–3415, Dec. 1993. [12] N. F. Josso, C. Ioana, C. Gervaise, Y. Stephan, and J. I. Mars, “Motion effect modeling in multipath configuration using warping based lag-Doppler filtering,” in IEEE ICASSP, Taiwan, 2009, pp. 2301–2304. [13] W. S. Hodgkiss, H. C. Song, M. Badiey, A. Song, and M. Siderius, “Kauai Acomms MURI 2008 (KAM08) experiment,” Trip Report, July 2008.
