## 1 Introduction  
Underwater acoustic communication networks [1, 2, 3] can facilitate the exchange of information among multiple types of observation equipment in diverse underwater locations. This technology has been extensively applied in marine resource exploitation, marine environment monitoring, and related fields [4, 5, 6]. As a result, this topic has emerged as a significant area of research. After extensive development, underwater acoustic communication technology has evolved to include a wide range of communication modes [7, 8, 9, 10, 11, 12], including single-carrier coherent phase shift keying (PSK), noncoherent multifrequency shift keying (MFSK), and random spread spectrum (PRSS). Each mode offers distinct advantages in terms of communication capability, reliability, and invisibility. However, the current underwater acoustic communication network typically relies on a single mode, which may not effectively adapt to complex and dynamic marine environments or the increasing diversity of applications. By dynamically selecting the optimal communication mode [13, 14, 15], an underwater network can maximize efficiency in various environments and application requirements. In a previous paper [14], a multimode underwater acoustic network was introduced, although it only demonstrated its capability for multimode transmission without analyzing its impact on network performance. In another paper [15], [PERSON] proposed a multimode network in which the communication regime is selected based on the channel delay and SNR. However, the choice of the communication regime is mainly determined by the marine environment and the point-to-point receiving SNR, focusing solely on the node's perspective rather than considering a multimode optimization scheme that maximizes the network's overall performance. Throughput serves as a crucial metric for evaluating the transmission performance of an underwater acoustic network. Therefore, this paper aims to analyze the throughput performance of a multimode underwater acoustic communication network and determine the optimal multimode solution. The extended propagation delay of the underwater acoustic channel gives rise to an ambiguous channel state (busy/idle) and uncertain signal arrival time. This complexity creates challenges when designing traditional protocols for underwater acoustic communication networks and significantly reduces network throughput performance. However, recent research [15; 16; 17; 18] has presented an alternative viewpoint. [PERSON] [16] proposed a novel method for analyzing throughput in networks with large propagation delays, which deviates from the traditional approach of suppressing such delays. Instead, it utilizes propagation delay as an advantage to achieve higher network throughput. Building upon this approach, [PERSON] [17] proposed a method for analyzing the upper limit of throughput performance in linear underwater acoustic networks. In [18], the authors focused on the physical layer and examined the throughput performance in a time-slotted UASN with guard time. [PERSON] [19] analyzed the throughput performance of network nodes with different packet sizes. The study of network performance heavily relies on the state of the physical layer transmission. However, these studies have oversimplified the physical layer of underwater acoustic communication by assuming that each node possesses identical transmission capability without accounting for the variations in channel characteristics and communication rates across different links. Furthermore, refs. [15; 16; 17; 18] utilized a traditional interference conflict model that assumes that conflicting signals cannot be successfully decoded when they overlap. In reality, multiple communication signals can overlap and be decoded successfully under certain conditions. This inconsistency with real-world scenarios leads to inaccurate limitations on network throughput performance. Scholars have studied the influence of underwater acoustic channels on network transmission.