# Improving Passive Time Reversal Underwater Acoustic Communications Using Subarray Processing
## 1 Introduction  
Because of the unique characteristics of underwater acoustic (UWA) channels, achieving reliable high-speed wireless communications over underwater acoustic channels is still a challenging task. Typical UWA channel characteristics include very limited bandwidths, time-varying multipath propagation, double-selective channel fading, and strong background noise; furthermore, large-delay spread of the multipath leads to severe inter-symbol interference (ISI) in the received signal. Efficient mitigation of multipath propagation is one of the key design goals of most UWA communication receiver algorithms. To mitigate ISI and signal fading caused by multipath propagation, spatial diversity and equalizers are widely used in high-rate underwater acoustic communications [1; 2; 3]. Multichannel decision feedback equalization (MC-DFE) is one efficient way to deal with ISI. MC-DFE has been successfully applied to high-rate UWA communications over the past two decades in combination with a second-order digital phase-locked loop (DPLL) [1; 4]. Various adaptive algorithms are used to update the equalizer coefficients in the MC-DFE. However, for some acoustic channels withmultipath spreading over several tens of symbol intervals, the MC-DFE receiver for phase-coherent communication is extremely complex, especially for multichannel receivers containing a large number of elements. At the same time, the order of the adaptive filters, which is determined by the maximum multipath delay, increases with the signaling rate, and the performance of the system is limited because of the noise enhancement and the increased sensitivity of the adaptive algorithm [2]. To better explore the advantages of the multichannel receiver, a variety of methods were investigated to improve the performance of the single-carrier communication system, including the use of a multiple-beam domain equalizer and the subarray processing approach [5; 6; 7; 8]. Spatial precoming (beamforming) was proposed to reduce the total number of input channels (M) to a small number (\(P<M\)) for the following MC-DFE [5]. The performances of beamforming and multichannel equalization algorithms are compared comprehensively using the experimental data [6]. The results indicate that beam-domain processing can be used to improve the performance when the signal fades across the entire array. Empirical results have shown that partitioning an array with large numbers of elements into subarrays, independently processing the signals received on each subarray, and then combining the soft outputs of the processors for each subarray can lead to improved performance and reduced computational complexity [7]. Time reversal (TR) processing is a low-complexity solution for reliable high-rate underwater acoustic communications [2; 9; 10; 11; 12; 13; 14; 15]. The well-known benefits of TR processing include temporal and spatial focusing. TR is an effective way to shorten the channel and suppress ISI, and thus reduce the receiver complexity. However, the performance of TR processing alone is saturated because of ISI caused by imperfect focusing (\(q(t)\
eq\delta(t)\)) [2]. To eliminate with residual ISI, the passive TR is usually followed by an adaptive single-channel DFE, which is called TR-DFE [3]. TR-DFE can improve output signal-to-noise ratio (SNR) by approximately 13 dB compared to TR, as shown in [2; 9]. An adaptive spatial combination with different combination coefficients on each array sensor is proposed to enhance spatial focusing and thus improve the performance of the TR-DFE [10]. In this paper, we proposes a new receiver structure which combines passive TR processing of subarrays and a low-order adaptive multichannel DFE (TR-MC-DFE) to improve the performance of conventional passive TR. The entire array with \(M\) elements is divided into \(P\) subarrays, each of which contains \(K\) elements (\(M>P\)), and the signals received on each subarray are independently processed by TR alone.