Particle filter based optimization scheme for trajectory design and resource allocation of UAV-enabled WPCN system

Abstract

For unmanned aerial vehicles (UAV)-enabled wireless powered communication network (WPCN) system, trajectory design and resource allocation are dominate strategies for maximizing the minimum uplink throughput of the UAV. However, this is a multi-constrained optimization problem with large-scale variables, which is difficult to obtain a global optimal solution. In this paper, a novel particle filter based optimization scheme for trajectory design and resource allocation of UAV-Enabled WPCN System is proposed. To solve the multi-constrained optimization problem, we transform the optimization process into a state estimation problem of the global optimal solution, and propose an improved particle filter based optimization algorithm. Combined with the block coordinate descent (BCD) technology, the objective function with large-scale variables can be effectively optimized. In practice, the large-scale variables are divided into several parts of small-scale variables to reduce the optimization dimension. Then the variables after dimensionality reduction are iteratively optimized by the proposed particle filter based optimization algorithm in turn. We demonstrate that the success rate of the optimization scheme for optimizing the objective function can be significantly improved. Simulation results have shown that the minimum uplink throughput of the proposed scheme outperformed other related schemes.

Introduction

With the popularity of unmanned aerial vehicles (UAV), it brings flexibility to relay communication and Long-distance wireless communication. Now, using UAV to relay communication with low transmission power nodes has become a hot research topic [1], [2], [3], [4]. In the age of Internet of Things (IoT), everything is connected, and information transmission is a matter of some urgency. However, for ground information nodes (GINs) in IoT, the information transmission is usually carried out in the form of wireless information transmission (WIT) [5], [6]. Its energy is limited, and its information transmission power is low, so the distance of its information transmission is finite [7], [8], [9], [10]. UAV is a flexible deployment platform, and it has become a convenient and efficient way to use UAV for relay communication [11], [12], [13], or collect information of the GINs in the IoT [14], [15], [16].

The GINs in IoT are usually energy-limited, and so they are unable to supplement energy by themselves, which need to be supplied externally. It is very inconvenient for GINs, since they are far away from the power source equipment. However, with the emergence of wireless power transfer (WPT) technology [17], [18], [19], such a problem can be effectively solved. With WPT technology, the GINs in IoT can charge themselves by receiving some special energy signals, which effectively extend the usage time of GINs. At present, UAV has been widely deployed in the wireless powered communication network (WPCN) system, which is composed of WPT technology and WIT technology. The GINs in IoT can be efficiently charged, and the information of the GINs also can be efficiently collected. It is convinced that the usage time of the GINs in IoT network can be significantly improved.

For UAV-enabled WPCN system, trajectory design and resource allocation are the key issues to determine the charging and collecting efficiency for GINs. However, the trajectory design of UAV is a non-convex function, and it is hard to find a global optimal solution. At present, there are many related researches on UAV-enabled WPCN system, but the objective of these works is different. The objective of some works focus on maximizing the minimum energy harvested by GINs [20], [21], [22], [23], [24] or minimizing the energy consumed by UAV [25]. But another more works focus on maximizing the minimum uplink throughput of the UAV [26], [27], [28], [29], [30], [31], [32].

In the UAV-enabled WPCN system, UAV charge GINs through downlink, and GINs transmit information through uplink. The minimum uplink throughput not only related to channel fading in wireless networks, but also related to the transmit power of GINs. Trajectory designs and resource allocation for UAV are the dominate strategies for maximizing the minimum uplink throughput of the UAV at present. In [26], a WPCN system model with a single UAV serving multiple GINs is considered, and a trajectory design strategy for UAV successive-hover-and-fly (SHF) is proposed. The minimum uplink throughput of the UAV is maximized by joint trajectory designs and the wireless resource allocation optimization. However, the minimum uplink throughput of the UAV is limited by the number of UAVs. The authors in [27] considered a WPCN system model in which two UAVs serve multiple GINs, where the minimum uplink throughput of the UAVs is maximized by jointly optimizing the trajectories designs, transmission power, and resource allocations. Although the number of UAVs in the scheme has been increased to two, but it still has to serve multiple GINs, and the minimum uplink throughput of the UAVs still have chance to improve it. In [28], [29], [30], a WPCN system model with two UAVs and two GINs is considered. In the system model, the UAV charges the two GINs through downlink, and the GINs transmit information to the corresponding UAV through downlink. The minimum uplink throughput of the UAVs is maximized by jointly optimizing the trajectories designs and the resource allocation. In [28], two GINs transmit information to the corresponding UAV simultaneously, which will cause interference and result in a decrease in the minimum uplink throughput of UAVs. In [29], [30], two UAVs charge two GINs in an alternate way through downlink and two GNs also alternately transmits their information to the corresponding UAV, which can effectively reduce the interference when the time allocation is optimized.

In above described optimization schemes, the minimum uplink throughput of UAVs is maximized by joint designing the trajectories, optimizing the resource allocation of downlink and uplink, and the transmission power of the GINs. However, the trajectory design is a non-convex function, and it is hard to obtain a global optimal solution. The mainstream ways are using some technologies to convert the non-convex objective functions into a convex function, such as the Successive Convex Approximation (SCA) technology. Then the convex optimization technologies can be used to solve it. However, this kind of methods can only obtain a local optimal solution in general [26], [27], [28], [29], [30]. In order to obtain the global optimal solution of the UAV trajectory design, some researches use heuristic algorithms to search the global optimal solution. The authors in [31] proposed an improved Genetic Algorithm (GA) based optimization scheme for UAV successive hover-and-fly (SHF), where a single UAV serves multiple GINs. A global optimal solution can be obtained after iterative optimization. With the same system, the authors in [32] proposed a Particle Swarm Optimization (PSO) based optimization scheme to search for a global optimal solution. For GA, PSO or other heuristic algorithms, there is no requirement for the objective function to be convex. However, the optimization problem in this paper is a multi-constrained optimization problem with a large-scale variable, the optimization of GA and PSO are not good enough, and they are easy to trap into local extreme points.

For GA, it is easy converges to a local optimal solution prematurely, and prone to occur some irregular and inaccurate problems during the encoding. For PSO, the performance of the optimization deeply relies on the parameter settings. Since the parameter settings depend on experience, it will increases the complexity and difficulty of the optimization. Thus, when dealing with high-dimensional complex optimization problems, these two algorithms may converge prematurely and trap into a local optimal solution. There is an urgency to find a non-parametric optimization algorithm, which can deal with the high-dimensional complex optimization problems. Particle filter (PF) algorithm can provide such an opportunity. Contrary to GA and PSO, PF has non-parametric characteristics and is currently widely applied in the field of target tracking [33], [34], [35], localization and navigation [36], [37]. In recent literatures, PF algorithm is utilized to estimate the state of the system. It is a method used to solve the filtering problem of nonlinear and non-Gaussian systems [38], [39], [40], [41]. The state of the system is updated iteratively according to some random samples in the state space of the system, so that the optimal estimation of the system state can be achieved. However, PF is not designed for optimization problems. The optimization problem needs to be converted to the optimal estimation of the system, so that PF can be applied to search the global optimal solution [42]. For high-dimensional complex optimization problems, the Block Coordinate Descent (BCD) is an effective technology, which can reduce the dimension of the optimization variables. Thereby efficiency and success rate of the optimization can be improved. BCD technology is currently widely applied in high-dimensional complex optimization problems [43], [44], [45], [46] to improve the efficiency of the optimization scheme.

For the multi-constrained optimization problem with a large-scale variable, the SCA based schemes [26], [27], [28], [29], [30], [43], [44], [45], [46] maximize the minimum uplink throughput by using the SCA technology to convert non-convex objective function to convex function. Then CVX technology or other standard optimization technologies combining with the BCD technology can be utilized to solve the convex function. It is effective, but only a local optimal solution can be obtained. The minimum uplink throughput still have the chance to be improved. For GA-based schemes [31] and the PSO-based schemes [32], it is difficult to deal with the multi-constrained optimization problems with a large-scale variable, and prone to converge to the local optimal solution prematurely. There is an urgency to find an effective optimization scheme to solve the multi-constrained optimization problem with a large-scale variable.

In this paper, we propose a particle filter based optimization scheme to search a global optimal solution for the multi-constrained optimization problem. In order to maximize the minimum uplink throughput of the UAV in WPCN system, we joint optimize the trajectory of two UAVs, the transmission power of two GINs and the time allocation of energy transmission and information transmission. Since the objective function is a multi-constrained optimization problem with large-scale variables, we transform the optimization problem into a state estimation problem of the global optimal solution, and propose an improved particle filter based optimization algorithm with large-scale particles. Combining with the Block Coordinate Descent (BCD) technology, the large-scale variables is divided into several small-scale variables to reduce the dimension of the optimization problem. Then the global optimal solution can be obtained by optimizing each small-scale variables with the proposed particle filter based optimization algorithm in turn. Simulation results are performed to verify the effectiveness of our method. The main contribution of this paper are organized as follows:

• We formulate the object function of maximizing the minimum uplink throughput, and propose a particle filter based optimization algorithm to search a global optimal solution. In order to solve such multi-objective and multi-constraint problem, we transform the optimization problem into a state estimation problem of the global optimal solution, and propose an improved particle filter based optimization algorithm. We also introduce the crossover and mutation operations of GA to enrich the diversity of sampled particles and avoid the degeneracy of particles as iterations increase.

• In order to improve the efficiency and success rate of optimization, a optimization scheme combining with BCD technology and the proposed particle filter based optimization algorithm is proposed to iteratively optimize the objective function. Based on the BCD technology, we decompose the large-scale variables of the objective function to reduce the dimension of the optimized variables, and then iteratively optimize the decomposed variables to improve the success rate of the particle filter based optimization algorithm.

• We conduct some simulation experiments to demonstrate the performance of the proposed scheme.

The content of this paper is organized as follows: The system model and problem formulation are presented in Section 2, the particle filter based optimization algorithm is proposed in Section 3, an optimization scheme combining with BCD technology and the proposed particle filter based optimization algorithm is proposed in Section 4, the simulation experiments is demonstrated in Section 5 to verify the performance of our scheme. We draw a conclusion of this paper in Section 6.