Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 5178136, 7 pages

http://dx.doi.org/10.1155/2016/5178136

## Research on Maritime Radio Wave Multipath Propagation Based on Stochastic Ray Method

^{1}College of Information Science & Technology, Hainan University, 58 Renmin Avenue, Haikou, Hainan 570228, China^{2}FITM, City University of Macau, Choi Kai Yan Building, Taipa, Macau

Received 24 January 2016; Revised 8 May 2016; Accepted 22 May 2016

Academic Editor: Yuri Vladimirovich Mikhlin

Copyright © 2016 Han Wang and Wencai Du. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Multipath effect in vessel communication is caused by a combination of reflections from the sea surface and vessels. This paper proposes employing stochastic ray method to analyze maritime multipath propagation properties. The paper begins by modeling maritime propagation environment of radio waves as random lattice grid, by utilizing maximum entropy principle to calculate the probability of stochastic ray undergoing* k* time(s) reflection(s), and by using stochastic process to produce the basic random variables. Then, the paper constructs the multipath channel characteristic parameters, including amplitude gain, time delay, and impulse response, based on the basic random variables. Finally, the paper carries out a digital simulation in two-dimensional specific fishery fleet model environment. The statistical properties of parameters, including amplitude response, probability delay distribution, and power delay profiles, are obtained. Using these parameters, the paper calculates the root-mean-squared (rms) delay spread value with the amount of 9.64 *μ*s. It is a good reference for the research of maritime wireless transmission rate of the vessels. It contributes to a better understanding of the causes and effects of multipath effect in vessel communication.

#### 1. Introduction

As we know that about 70% of the Earth surface is covered by the ocean waters and over 90% of the world’s goods are transported by merchant fleet over sea. Maritime communication plays an important role in many marine activities, such as offshore oil exploitation, maritime transportation, and marine fishery. The current maritime communication systems mainly include signal sideband (SSB) short-wave radio system, VHF radiotelephone, coast cellular mobile communication network, and maritime satellite communication network. Maritime VHF radio telephone is mainly used for ship-to-shore and ship-to-ship voice communication scenario. The transmission distance of the maritime VHF radio is limited to 20 nautical miles. Another drawback of the maritime VHF radio is its lack of support of data services. Maritime satellite communication systems [1, 2], such as the Inmarsat-F system and Fleet-Broadband maritime data service, are suitable for ocean sea ship communications. However, the satellite communication system is relatively expensive, due to the high cost of the terminal equipment and high maintenance and upgrade costs. Although the service fee is high, the data transmission rate is far from the user requirements. Consequently, maritime communications which can deliver voice and higher data transmission rates are hot topic in current and future research.

Generally, the approaches to modeling wireless channel propagation can be divided into two categories: statistical measurement and electromagnetic field prediction. The former is a mainstream channel modeling methodology, which includes parametric statistical modeling method and physical propagation modeling method. The latter is an approach, which includes ray method, finite difference time domain method, and moment method. Maritime communication channel modeling based on statistical measurements of empirical models has been widely studied. The majority of scholars have utilized measurement and estimation data to predict a particular path loss in mobile channel modeling over sea [3–8]. In [8], authors have extended the ITU-R P.1546-5 as a radio over sea propagation model for investigating the path loss curve.

However, the analysis of large-scale fading in vessel communication environment or ship to shore communication environment cannot reflect the multipath channel characteristics, where multipath effect should be considered. The vast majority of small-scale multipath analyses are based on field measurements [9–12]. Measurements are carried out in different sea areas, but the conclusions have regional limitations. The finite difference time domain method is also adopted in maritime channel modeling [7, 13]. However, this method has high calculation costs and requires well-defined communication environment.

The paper will contribute to technique in modeling wireless channel propagation in the sea. The sea surface reflections and other ships reflections are considered in exploring the multipath rms delay spread in fishery fleet communication environment by employing the stochastic ray method to measure maritime wireless radio multipath propagation properties, by utilizing lattice grid to describe the maritime fishery fleet propagation scenario and using Brownian bridge process to construct the basic statistical properties of random variables and by numerical simulation to obtain the rms delay spread value. This study provides stochastic ray channel modeling method that can effectively evaluate the maritime multipath propagation channel.

The rest of this paper is organized as follows: Section 2 describes the stochastic ray theory and its probability distribution. Maritime random radio wave propagation multipath statistical characteristics are given in Section 3. The simulation and analysis are presented in Section 4. Finally, the conclusion is presented in Section 5.

#### 2. Stochastic Ray Theory and Its Probability Distribution

In the analysis of wireless channel propagation, the multipath effect under the unknown environment should be taken into consideration. Due to the complexity and sensitivity of the wireless propagation environment and the requirements of a stochastic channel model, no-wave approach is utilized in the practical electromagnetic engineering [14]. In [15, 16], the propagation environment is modeled as a random distribution of point scatters. Stochastic ray method is used to analyze the propagation process. Researches [14–17] show that stochastic ray method is an effective method to study the characteristics of urban wireless multipath propagation channel.

##### 2.1. Stochastic Bridge Process

The process where a number of rays emitted from the source after a multihop random walk reach the destination is called beam multipath diffusion process. The formal mathematical definition of this process is given with Definition 1.

*Definition 1. *For all , if the trajectory of stochastic process passing through two fixed points , , where , the process is called stochastic bridge process, denoted by . It can be formulated aswhere is a stochastic process with the starting point at the source point.

##### 2.2. Random Lattice Channel

The authors in [14] proposed an idea for modeling of the urban propagation environment as a random lattice. The percolation theory was exploited in the domain of channel modeling for the first time. Consider a finite array (see Figure 1) made of square sites with side of unit length. The status (occupied or empty) of a cell is independent of the status of all other cells in the lattice and assume that empty probability is and the occupancy probability is . Given a very large lattice randomly occupied with probability , percolation theory deals with the quantitative analysis of groups of neighboring empty sites (clusters): form, average size, number, and so forth. For modest values of (say, near zero) the average dimension of clusters is small, while for near unity the lattice looks like a single cluster with sporadic holes. As grows, the dimension of the empty clusters grows as well. Clearly, for , the whole lattice is empty. There exists a threshold level at which the lattice appearance suddenly changes: for a single empty cluster that spans the whole lattice forms, while for all empty clusters are of finite size. Near the percolating threshold the characteristics of the -lattice change qualitatively; the system exhibits a phase transition. There exists an average distance among the closed clusters in the site percolation with given , denoted by , where is the cell side length of lattice.