Virtual Space-Time DiversityTurbo Equalization Using Cluster Sparse Proportional Recursive Least Squares Algorithm for Underwater Acoustic Communications  
[PERSON]  
1 GNSS Research Center, Wuhan University, Wuhan 430072, China; [EMAIL_ADDRESS]  
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2 Electronic Information School, Wuhan University, Wuhan 430072, China; [EMAIL_ADDRESS]  
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3 School of Computer Science, Wuhan University, Wuhan 430079, China; [EMAIL_ADDRESS]  
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1 GNSS Research Center, Wuhan University, Wuhan 430072, China;  
UWA communication technology the foundation for the implementation of tightly coupled UCNDISs. The performance of underwater acoustic communication is extremely affected by time-varying transmission channels [5]. Owing to its abominable propagation characteristics, such as a low speed of the acoustic signal, large attenuation and significant multipath interference, the UWA channel can be seen as one of the most challenging elements [6]. The Doppler effect and multipath propagation caused by boundary reflection are the fundamental factors causing channel distortion, for which the acoustic signal experiences time and frequency selectivity [7; 8; 9]. One of the most widely utilized approaches to mediate harsh inter-symbol interference (ISI) due to channel aberration is the use of a decision-feedback equalizer (DFE) with a digital phase locked loop (DPLL) embedded in it [10]. Traditional time-domain equalizers cannot satisfy the requirements of precise information, especially in high-speed UWA communications of shallow water nowadays. Turbo equalization has been considered as an efficient technology to make significant improvements in bit error rate (BER) manifestation under complicated UWA environments [11; 12]. Turbo equalization is derived from turbo decoders by employing a maximum a posteriori (MAP) equalizer as a replacement of one stand-alone MAP decoder in typical decoder processing [13; 14]. In order to realize computational complexity in large time-delay channels, a soft-input soft-output (SISO) equalizer is introduced into the iteration structure based on the minimum mean squared error (MMSE) criterion [15; 16; 17], least symbol error rate (LSER) criterion [18; 19] and so on. In some scenarios of high SNR, the adaptive equalizers based on the LSER criterion achieve better BER performance than the MMSE. The chief drawback of traditional DFEs is the error propagation of the feedback filter when extensive, inaccurate hard-decision symbols occur. A usually efficient method is the exploitation of a soft-decision feedback equalizer instead of a hard-decision one [15]. Another neoteric method is the bidirectional structure of an equalizer, which accomplishes the target of eliminating error propagation through a normal SISO equalizer and a time-reversed one using the virtual time reversal mirror (VTRM) technique [18; 20; 21]. The TRM technology with a simple structure provides noise suppression for communication systems equipped with single or multiple receiving transducers. Fractionally spaced equalizers (FSEs) have been applied in normal one-iteration channel equalization successfully for years and can achieve channel diversity gain by increasing the baseband sampling frequency to several times the symbol rate [22]. The several branches are regarded as independently identical distributions when the FS order is low enough. However, the FSE has seldom been employed for turbo equalization in current works, and researchers have exhibited more interest in multiple receivers to achieve space diversity [23; 24; 25]. Turbo equalization applied to UWA communications is classified into two categories depending on whether channel estimation is carried out or not. The channel-estimation-based turbo equalization (CE-TEQ) has to compute the equalizer coefficients, which involve a large-dimension matrix inversion, particularly in the long-time delay-spread channel [25; 26]. Moreover, because the UWA channel is time-varying, repetitive channel estimation would be an encumbrance to computation.