# Design of an Underwater Acoustic Waveform and Integrated System for Communication and Detection
## 1 Introduction
Due to CPM's constant envelope and superior spectral efficiency, as well as LFM's large time-bandwidth product, LFM-CPM has also attracted the attention of many researchers. [PERSON] proposed a modified three-section integrated waveform based on linear frequency modulation and continuous phase modulation (LFM-CPM) [27]. The modified waveform shows significant improvement in bit error rate (BER) performance under strong interference conditions. In the dual-functional radar communication system proposed by [PERSON], the CPM-LFM signal is adopted to enhance both the radar's range resolution and the bit error rate [28]. However, due to the characteristics of underwater acoustic signals, such as slow transmission speed, narrow bandwidths, and significant signal attenuation, the integration of underwater acoustic communication and detection presents even greater challenges. Whether the aforementioned waveforms and systems for radar-communication integration are applicable to underwater acoustics still requires extensive exploration. In this paper, the CPM-LFM waveform is studied for underwater acoustic sonar-communication integration. The minimum Euclidean distance, bit error rate (BER), and ambiguity function [29] of the shared waveform are derived and analyzed to test the waveform's communication and detection performance. Underwater acoustic channels exhibit characteristics such as multi-path effects and significant propagation delays. Due to variations in seabed topography and sound velocity, precise estimation of propagation delays is challenging. These factors will impact the timing synchronization and frequency offset in underwater acoustic communication, resulting in a decline in its performance. Additionally, the underwater movement of AUVs can cause significant Doppler effects, further affecting the reliability of underwater acoustic communication. To address these challenges, an integrated underwater communication and detection system has been proposed. An information frame structure with symbol suffixes (SSs) is introduced to reduces the side lobe amplitude of the range ambiguity function and improve communication performance with two-step frequency and phase estimation and correction. The main contributions of this paper are summarized as follows:  
1. A shared waveform that integrates continuous phase modulation (CPM) with linear frequency modulation (LFM) is proposed for underwater acoustic communication and detection application, and its performance in communication and detection under an additive white Gaussian noise (AWGN) channel is derived. 2. A system model for integrated underwater communication and detection is proposed. The system's transmission module and the communication information processing flow in the reception module are well designed. Specifically, this paper presents an information frame structure that features symbol suffixes (SSs). The introduction of SSs effectively reduces the side lobe amplitude of the range ambiguity function, improving ranging performance, and employs repeated symbols for enhanced two-step frequency and phase estimation and correction, thereby boosting communication performance. 3. Simulation analysis is conducted to verify the feasibility of the proposed communication and detection waveform, as well as the system. The subsequent arrangement of the article is as follows. In Section 2, the mathematical model of the shared waveform and its characteristics in the time-frequency domain are presented. Under an AWGN channel, the bit error rate performance of the shared waveform in communication applications and the ambiguity function performance in detection applications are derived. Section 3 presents the models for the transmitter and receiver of the integrated acoustic communication and detection system. The focus is on the information processing of the communication system at the receiver. A symbol suffix (SS) frame structure is proposed, which utilizes preamble codes and repeated data blocks for precise frequency and phase offset estimation.