## 1 Introduction  
Multipath spreads and Doppler effects make UWA channels some of the most challenging wireless communication environments [1, 2]. The large multipath spreads cause severe ISI, degrading the quality of communication signal. In addition, the slow speed of sound propagation makes Doppler effects significant even for relatively slowly moving platforms [3], resulting in decoding errors. In an effort to improve the performance of UWA communication, the received signal requires channel equalization processing and Doppler compensation.  
TRM has temporal and spatial focusing capability. The temporal compression recombines the multipath signal and mitigates ISI, while the spatial focusing improves the signal-to-noise ratio (SNR) and reduce the influence of channel degradation. The capability of TRM makes it widely used in UWA communication [4, 5, 6, 7, 8, 9]. However, there are still some residual ISI after TRM processing. Subsequently TRM combined with a single-channel decision feedback equalizer (DFE) was put forward to eliminate the residual ISI and achieves nearly optimal performance in theory [2; 10; 11; 12]. The traditional TRM approach described above consists of a vertical receiving array, which complicates the communication device. In this paper, we use single element TRM, which consists of a single sound pressure sensor. Although the single element TRM sacrifices the spatial focusing gain of the array, it can still achieve temporal focusing and channel equalization by recombining the multipath channel structure [13; 14; 15]. During UWA communication, if there is relative motion between the transmitter and receiver, the communication signals will experience a Doppler compression or dilation [1], which will cause errors in decoding. Therefore, it is necessary to compensate Doppler. In [16; 17; 18], a phase-locked loop is used to estimate the Doppler coefficient. In [19; 20], researchers estimate the Doppler coefficient by interleaving transmitting signal with preambles, such as training symbols or pseudo-noise (PN) sequences. References [21; 22] estimated the Doppler coefficient by measuring the length variation of the signal, which is called a block Doppler estimation algorithm. After obtaining the Doppler coefficient, those approaches remove the Doppler effects by resampling the received signal. In this paper, we propose a real-time symbol-based Doppler compensation (SBDC) method for pattern time delay shift coding (PDS) communication scheme [15; 23; 24; 25]. The proposed method does not need to calculate the Doppler coefficient and resample the received signal, moreover, it can compensate Doppler in real-time.  
In view of significant multipath and Doppler effects in UWA channels, this paper proposes a new UWA communication method using single element TRM combined with SBDC (TRM-SBDC) based on the PDS communication scheme. The proposed method can not only suppress ISI resulting from multipath spreads, but also overcome the Doppler effects induced by relative motion between the transmitter and receiver. The results of the simulations with real sounding channels and the UWA communication experiments conducted in the Songhua River in Harbin (China) verify the feasibility and robustness of the proposed method.