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We focus on how to jam UAVs network efficiently. The system model is described and the problem is formulated. Based on two properties and a theorem which helps to decide good location for a jammer, we present the Triangle method to find good locations for jammers. The Triangle method is easy to understand and has overall computational complexity of

Unmanned aerial vehicles (UAVs) are used for a wide range of missions [

Some defense strategies [

Different from these works, we do research on jamming UAVs network effectively. Some general jamming attack techniques for wireless networks are described in [

We state the problem of jamming UAVs network and give out the problem formulation.

We introduce Triangle method and GA (genetic algorithm) based method for the jamming of UAVs network. They perform significantly better than Random method.

We analyze the simulation result and show how to choose the UAVs jamming method. With fewer jammers, GA method should be chosen. However, when more jammers are available, Triangle method should be considered firstly.

The rest of the paper is organized as follows. The UAVs jamming problem is introduced formulated and analyzed in Section

We consider jamming the communication in a UAVs network as shown in Figure

UAVs system architecture.

The jamming power to signal power ratio at the receiver determines the degree to which jamming will be successful. For digital signals, the jammer’s goal is to raise this ratio to a level such that the BER is above a certain threshold. For analog voice signals, the goal is to reduce the articulation performance so that the signals are difficult to understand. The following JSR models at the receiver’s antenna are defined in [

Ground reflection propagation,

Nicholson,

where

We use the Nicholson JSR model (

When we put parameters of (

When formulating the UAVs jamming problem, the following notations are used.

All UAVs communicate with bidirectional communication links. UAV

The total jamming effect can be computed through adding jamming effect of all links and is denoted as

A term of

UAV

As shown in Figure

Jamming area.

When parameters are set as condition (

As shown in Figure _{1}. When UAV 1 is the sender and UAV 2 is the receiver, UAV 2’s jamming area includes all the points whose distance to UAV 2 is less than

When parameters are set as condition (_{good} for a jammer to disrupt both _{good}, communication between UAV

When the value of each parameter is set as condition (

Properties

For achieving better jamming effect, jammers should be placed to appropriate locations. We present Triangle method to search locations for jammers. The idea of Triangle method is simple. It divides all UAVs into groups. Each group has three UAVs. The algorithm for forming such groups is descripted in Algorithm

Consider the following:

for _{num},

for _{num},

Triangle method.

Steps from (12) to (15) find locations for UAV groups. The function

The group has three UAVs which usually form a triangle. (a) The function calculates the distances between each pair of two points; (b) it finds the two short sides; (c) it selects the point which connects the two short sides as the location for the group.

The group has two UAVs which usually form a line. (a) The function calculates the midpoint between each pair of two points; (b) it returns the midpoint as the location for the group.

The group has only one UAV. The function returns the location of the UAV as the location for the group.

The selecting process continues till all locations for groups are found. Function _{num}, then the first _{num} jammers are assigned the locations of

The Triangle method is based on following theorem.

When parameters are set as condition (

(1) There are 3 UAVs in the group. As shown in Figure _{3} is not less than Len_{1} and Len_{2}. So the jammer should be located at the point of UAV 1. When the values of parameters are set as condition (

(2) There are 2 UAVs in the group. As shown in Figure

(3) There is only 1 UAV in the group. The location of the UAV is selected as the location for the jammer. At this case,

In Algorithm

GAs are global optimization techniques that avoid many of the shortcomings that exist in classical local search techniques on difficult search spaces [

We propose a GA-based method to solve the UAV jamming problem, as shown in Algorithm

A solution of the jamming problem consists of

Consider the following:

generate an initial population (

while loop times

evaluate the fitness of each solution;

select promising solutions;

create new solutions incorporate into original population.

The procedure of evaluating the fitness (Step (3)) requires

The methods provided by this paper are used to jam the communication among 20, 30, 40, and 50 UAVs with 1

Simulation result.

20 UAVs

30 UAVs

40 UAVs

50 UAVs

60 UAVs

70 UAVs

We define a new metric to measure the performance of each jamming method.

The ratio of jammed links to total links (RJT) computed by

We can see easily from Figure

It is also clear that Triangle and GA methods give out better result than Random method. But there is an exception when 1 jammer is used to jam the communication network with 40 UAVs. All jammers are randomly placed in Random method. One of them happens to be assigned a good location. So the Random method performs better than the Triangle method as shown in Figure

Figure

It is also obvious that there is a threshold

In this paper, we focus on jamming UAVs network efficiently. Firstly, the system architecture is described and the jamming problem is formulated. We analyze the system’s two properties. Secondly, a theorem, which helps to decide locations for jammers, is proved. Based on this theorem, we introduce the Triangle method to solve the jamming problem. Triangle method divides all UAVs into groups. Each group has at most three UAVs. It finds the best location for jamming all UAVs in each group. The overall computational complexity of Triangle method is

The two methods besides a Random method are simulated in the scenario given in Section

More jammers yield higher performance.

At most cases, Triangle and GA methods are significantly better than Random method.

With a small number of jammers, GA method has better performance than Triangle method. However, with the number of jammers increasing, the performance of Triangle method is improved more than GA method. When the ratio of jammers’ number to UAVs’ number is higher than 1/5, Triangle method does better than GA method.

The overall computational complexity of Triangle method is

It should be noted that this paper just does the work of the first step. Here, we assume the topology of UAVs is fixed and does not change. The properties and theorem are deduced under condition (

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by the Academician Foundation of Chongqing (CSTC2011GGYS0001).