###### Abstract  
In mobile underwater acoustic (UWA) communications, the Doppler effect causes severe signal distortion, which leads to carrier frequency shift and compresses/broadens the signal length. This situation has a more severe impact on communication performance in the case of low signal-to-noise ratio and variable-speed movement. This paper proposes a non-data-aided Doppler estimation method for _M_-ary spread spectrum UWA communication systems in mobile scenarios. The receiver uses the spread spectrum codes dedicated to transmitting signals with different frequency offsets as local reference signals. Correlation operations are performed symbol by symbol with the received signal. The decoding and Doppler estimation of the present symbol are achieved by searching the correlation maximum in the code domain and frequency domain. The length of the current symbol is corrected for the next symbol synchronization using the estimated Doppler coefficient. To optimize the process of Doppler estimation and symbol synchronization, a heuristic search method is used. By adjusting the Doppler factor search step size, setting the threshold value, and using the Doppler factor estimation of the previous symbol, the search range can be significantly reduced and the computational complexity decreased. The Fisher-Yates shuffle algorithm is used to traverse the search range to ensure reliability of the results. Simulation results show that enlarging the frequency-domain search step size in some degree does not affect the decoding accuracy. On 15 May 2021, a shallow-water mobile UWA spread spectrum communication experiment was conducted in Weihai, China. The horizontal distance between the transmitter and the receiver is 3.7-4.0 km, and the communication rate is 41.96 bits per second. The transmitting ship moves at a speed of 0-3 m/s, and the bit error rate (BER) is lower than 1e\(-\)3, which is better than that of the sliding correlation despreading method with average Doppler compensation. M _-ary spread spectrum; Doppler estimation; heuristic search; symbol synchronization; mobile underwater acoustic communication_  
[PERSON] 1,2,3,*, 1,  
signal length [6; 7]. Some researchers estimate Doppler based on the time-domain broadening/compression caused by the Doppler effect [8; 9], which has a strong anti-noise ability. However, only the average Doppler of data block is obtained by the block estimation. For the autonomous undersea vehicle/unmanned undersea vehicle (AUV/UUV) that needs to realize reliable UWA communication while moving at a non-uniform velocity, the constant-velocity assumption is no longer applicable [10; 11; 12; 13; 14]. In this application scenario, to ensure the communication's robustness, Doppler estimation needs to be performed periodically [15]. Carrier frequency variation and synchronization error accumulation must be considered in the receiving process [16]. The research into mobile UWA communication mainly focuses on the Doppler estimation and equalization algorithm. Single carrier multiple phase shift keying (SC-MPSK) [17] and orthogonal frequency division multiplexing (OFDM) [18; 19] are generally studied. Both have a weak anti-Doppler capability. Accurate symbol synchronization and channel equalization are the keys to achieving high-quality SC-MPSK communication; OFDM needs to conduct Doppler estimation and compensation with different accuracy step by step [20; 21]. Considering the specific application limitations of AUV, we need to achieve reliable communication performance with the smallest hardware overhead possible. The spread spectrum does not have the problem of a high peak-to-average ratio in the OFDM and is not limited by the inter-symbol interference, as the SC-MPSK is. Without much demand on the communication rate, we believe that the spread spectrum technique is an appropriate choice.