# Optimal Deployment of Vector Sensor Nodes in Underwater Acoustic Sensor Networks
## 1 Introduction  
Underwater acoustic sensor networks (UWASNs) are widely used in several applications such as target detection and tracking, ocean pollution monitoring, and various ocean data collection techniques [1; 2; 3; 4]. The effectiveness of a UWASN can be evaluated in terms of the connectivity among the sensor nodes deployed in a targeted area, as well as the coverage rate. It is hard to precisely deploy numerous sensor nodes in underwater environments, and these nodes are also very expensive. Therefore, in terms of efficiency, it is important to minimize the number of nodes deployed in a targeted area. Several approaches have been proposed to determine the optimal positions of sensor nodes in UWASNs [5; 6; 7]. However, most attempts have assumed that the communication performance of every node deployed at the target underwater area is the same without considering variations in the ocean environment. Acoustic waves propagating through underwater channels undergo multiple interactions with the ocean boundaries such as the sea surface and seabed, which cause severe time delays, resulting in inter-symbol interference (ISI) [8]. ISI causes issues related to communication demodulation. In addition, underwater communication is characterized by a time-varying channel, which produces large Doppler spreading and a short coherence time [9; 10; 11]. In addition, marineorganisms such as barnacles and algae might build up on a transducer as time goes on, which can block the communication signals, causing data corruption. For these reasons, underwater acoustic modems should be energy-efficient and resistant to biofouling [12]. Recently, [PERSON] and [PERSON] [13] suggested a new algorithm to maximize communication coverage using a limited number of sensor nodes in shallow water areas. For this, we implemented a communication performance surface (PS) in our algorithm. The communication PS is a geospatial map displaying the communication performance information of the targeted area. The PS was obtained based on channel impulse responses predicted by a BELLHOP model [14] for grid points in the targeted area. The BELLHOP model is a highly efficient acoustic ray-tracing model for predicting acoustic pressure fields in ocean environments. Based on the PS, a virtual force-particle swarm optimization (VFPSO) algorithm was used to determine the optimal positions of the sensor nodes. We assumed that each sensor node was a vertical line array composed of vertically separated receiver elements to improve the communication performance. The array processing techniques can be used to enhance the communication performance by alleviating the effect of ISI [15; 16]. However, such a large-scale array system degrades the spatial efficiency in a UWASN. In recent years, the propagation properties of acoustic vector quantities such as acceleration or acoustic particle velocity have been studied [17; 18; 19]. Vector sensors have been applied in several areas, including target detection and tracking, noise reduction, and acoustic communication [20; 21; 22; 23; 24]. A vector sensor measures the three directional components of the vector quantities, and accordingly, a diversity gain can be achieved even when a single-vector sensor is used. In this paper, a vector sensor measuring the particle velocity is used as a sensor node of a UWASN, with the aim of improving the communication performance and the spatial efficiency. The outputs of the vector sensor are considered to be the outputs of a single-input multiple-output (SIMO) communication system [22; 23; 24]. The optimal algorithm proposed in our previous paper [13] is then applied to obtain the optimal deployment scheme for the single-vector sensor nodes. This paper is organized as follows. Section 2 provides a short summary of previous research and describes the algorithm to calculate the communication PS of the single-vector sensor nodes.