Technical noteDistributed compressed sensing estimation of underwater acoustic OFDM channel
Introduction
With rapidly increasing requirement on efficient acquisition and transmission of underwater observation information associated with ocean environmental monitoring, underwater project engineering and sea bottom resource exploitation tasks, there is an urgent need for R&D of high data rate underwater acoustic communication systems [1]. Unfortunately, compared with wireless channel, underwater acoustic channel is much more complicated due to the strictly limited bandwidth, extensive multi-path spread, Doppler shift and background noise. Design and implementation of high data rate underwater acoustic communication pose a considerable challenge [2] to the research community.
OFDM has recently emerged as a promising alternative to single-carrier systems for underwater acoustic communication because of its robustness to long delay spreads and frequency selectivity [3], [4], [5]. As well, OFDM provides high data rate for underwater acoustic communication which can be used for underwater acoustic speech or photo communication occasions. However, underwater OFDM systems are sensitive to Doppler shifting and phase noise [6], which will destroy the orthogonality of OFDM subcarriers, and pose difficulties in channel estimation and coherence detection [7].
Various channel estimation methods developed based on the assumption of the rich multi-path channel model, have been summarized in the literature [8]. Qiao et al. [9] pose an iterative Lease Square (LS) channel estimation algorithm for MIMO OFDM systems, the algorithm can greatly improve estimation accuracy, and the low-pass filtering in time domain reduces AWGN and ICI significantly. Jeong and Lee [10] pose a low complexity channel tracking for adaptive MMSE channel Estimation in OFDM system, the experimental result shows that the proposed channel parameter estimator tracks channel condition reliably in various channel conditions without significant increase in computational complexity. Morelli and Mengali [11] pose a maximum likelihood estimator (MLE) for OFDM system. However, the algorithms mentioned above require larger number of pilots or preambles to guarantee the estimated channel accuracy, which, unfortunately, will reduce the bandwidth efficiency and increase a high computation overhead. Meanwhile, there will exist significant estimated noise in non-zeros taps.
The underwater acoustic channels are considered to be sparse both in time and frequency domain, i.e., the delay-Doppler spread function has a limited number of nonzero elements [12]. The compressed sensing (CS) methods have been widely used for channel estimation to exploit the channel sparsity [13], [14], [15], [16]. Wu and Tong [13] propose the Non-uniform norm constraint LMS algorithm for sparse underwater acoustic channel estimation. Singh et al. [14] investigate the compressed sensing algorithms for estimation of OFDM channel. By adopting the compressed sensing methods, the length of training sequence can be significantly cut to improve efficiency, and the estimation noise at non-zero taps can be effectively suppressed [17].
While the UWA channels typically consists of sparse multipath arrivals, the multipath structure of adjacent OFDM symbols appears similar sparse structure because the delay of multipath arrivals tend to exhibit much slower variation than the corresponding magnitude does [18]. It means that UWA channels of several continuous symbols can be modeled as sparse sets with common support. Baron et al. [19] study three joint sparsity models (JSMs): JSM1 has sparse common component, JSM2 has common sparse supports and JSM3 has non-sparse common component. Underwater acoustic OFDM channels among adjacent symbols can be described as a JSM2 type model. Based on the basic concept of CS, Distributed compressed sensing (DCS) is proposed to exploit the joint sparseness contained among different sparse signals so as to achieve further performance enhancement. The temporal, spatial correlation among multiple sparse targets have been employed for DCS sparse recovery in wireless networks [20].
In this paper, a temporal joint sparse recovery approach is proposed to exploit the sparse correlation among adjacent OFDM symbols to improve the performance of OFDM channel estimation. By converting the problem of OFDM channel estimation into reconstruction of joint sparse signals with common support, a joint sparse model under the framework of DCS is adopted to derive a joint sparse recovery OFDM channel estimation algorithm. The performance of the proposed method is quantitatively evaluated with the experimental bit error rate (BER) of an UWA OFDM communication system. Finally, underwater OFDM communication experimental results obtained in Xiamen harbor are provided to demonstrate the effectiveness of the proposed method in improving the performance of underwater acoustic OFDM communication, compared to the classic channel estimation methods.
The rest of this paper is organized as follows. In Section 2, the model of OFDM and distributed compressed sensing are derived. The experimental performance analysis and comparison are provided in Section 3. Some conclusions are made in Section 4.
Section snippets
Transmitting model
We consider an OFDM baseband system with K equally spaced subcarriers at frequencieswhere is the K subcarrier separation, therefore, the entire signal bandwidth is , and each OFDM symbol lasts . The K subcarriers can be allocated as either data symbols or pilot symbols, depending on the packet structure. Define the K subcarrier symbols of i-th OFDM symbol as :
The transmitted time-domain discrete signal OFDM symbol can be expressed as:
Setup of at-sea experiment
The experimental field data was collected from a shallow water acoustic channel with slight wind condition at Wuyuan Bay, Xiamen, China. The depth of the experiment area is about 10 m. The OFDM signal was transmitted from a transducer, at a depth of 2 m. The transmitted signal was received by two receivers submerged at the depth of 2 m and 6 m respectively. The transmitting transducer was suspended under a pier and the receivers are mounted at the rear of one anchored ship, with a distance of 1000 m
Conclusion
While the sparsity contained in UWA channels have been popularly employed to improve the performance of channel estimation by CS methods, for UWA channels of adjacent symbols, similar delay pattern of multipath arrivals provides attractable possibility for further performance enhancement under the framework of DCS. In this paper, we investigated the joint estimation of underwater acoustic OFDM channels by modeling the channels of continuous OFDM systems as sparse set with common support. By
Acknowledgement
The authors are grateful for the funding of the National Nature Science Foundation of China (No. 11274259 and No. 11574258) in support of the present research.
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