## 1 Introduction  
It is well known that the underwater acoustic channel is one of the most intricate wireless communication channels, particularly under conditions of low signal-to-noise ratio (SNR) and pronounced Doppler effects. In order to address the challenges posed by low SNR and to achieve robust underwater acoustic communication, extensive research efforts have been undertaken [1, 2, 3, 4]. Among the various underwater acoustic communication technologies, Direct Sequence Spread Spectrum (DSSS) is a commonly employed communication technique due to its exceptional interference resistance and robustness against channel fading. DSSS expands the signal over a broader frequency band by utilizing noise-like pseudo-random spreading codes (SCs), enabling coherent demodulation systems to recover the signal through coherent despreading of energy [5]. Generally, the spreading gain is substantial (for instance, when the SC length is 511, the spreading gain reaches 27 dB) [6]. This gain facilitates the accurate decoding of received signals under noisy conditions while also providing a degree of confidentiality. However, the communication rate of DSSS is constrained by the narrow bandwidth of the underwater acoustic channel, resulting in a relatively low transmission speed [7, 8]. Furthermore, due to the time-varying nature of the marine environment, the Doppler shift within a single frame often exhibits variability, with longer transmission packets facing even more pronounced Doppler shifts. The time-varying Doppler shift can induce rapid fluctuations in the carrier phase, significantly diminishing the spreading gain during the coherent despreading process. In the context of time-varying Doppler shifts, the robustness of underwater spread spectrum communication is considerably compromised. Therefore, enhancing the communication rate of underwater spread spectrum communication and mitigating time-varying Doppler shifts are two critical research focal points in this field. To enhance the communication rate of spread spectrum communication, a Code Index Modulation-Spread Spectrum (CIM-SS) scheme has been proposed in the realm of terrestrial radio communication [9]. By introducing the spreading code domain and employing a new dimension to map information bits, the data rate is enhanced. This scheme preserves the advantages of spread spectrum modulation without increasing the system's computational complexity and is easy to implement. The study in [10] extended the CIM technology. Simulation results indicate that, compared to traditional DSSS systems, the proposed modulation scheme exhibits superior performance in terms of data rate, energy consumption, and complexity. To address the time-varying Doppler effect, which induces rapid carrier phase shifts and reduces spreading gain, Doppler estimation and compensation are generally required. In previous studies, the methods for Doppler estimation can be categorized as follows: (1) utilizing adjacent pseudo-random codes for time-domain correlation to compute Doppler factors; (2) employing Doppler-sensitive training sequences to conduct time-frequency two-dimensional search methods; (3) utilizing LFM signals to perform block estimation methods; (4) combining coding techniques with iterative estimation algorithms. Among these, the method of using adjacent pseudo-random codes for time-domain correlation to estimate Doppler factors can obtain Doppler estimates between adjacent symbols, but it requires adjacent symbols to have the same pseudo-random code, making it applicable only to DSSS processing with relatively low spectral efficiency [7; 11]. [PERSON] et al. designed an M-ary sequence spread spectrum (M-SS) communication method that incorporates several identical pseudo-random codes into the frame structure for Doppler estimation. Although it sacrifices some communication rate, the accuracy of Doppler estimation is significantly improved [12; 13].