# On Performance Analysis of Protective Jamming Schemes in Wireless Sensor Networks
## 1 Introduction  
Cyber Physical Social Sensing (CPSS) has emerged as a promising paradigm to enable the interactions between humans and the physical environment [1; 2; 3; 4]. As a key component of CPSS systems, wireless sensor networks (WSNs) play an important role in sensing, collecting and transmitting confidential information [5; 6]. However, WSNs are also susceptible to various malicious attacks due to the vulnerability of sensor nodes [7]. _Eavesdropping_ attack, as one of typical malicious attacks in WSNs has attracted considerable attention recently. It is difficult to detect eavesdropping behaviours since _malicious_ nodes (also called eavesdroppers) passively wiretap the confidential information without disclosure of their existence.  
Encryption has been typically used to protect the confidential communications in wireless networks. For example, Cellular Message Encryption Algorithm has been used in cellular networks [8] and KASUMI has been used in 3G networks [9] while wireless local area networks (WLANs) have adopted Wired Equivalent Privacy (WEP) [10], Wi-Fi Protected Access (WPA) and Wi-Fi Protected Access II (WPA2) [11]. However, the traditional cryptographic methods may not be feasible to WSNs due to the following constraints: (1) the limited battery power of sensor nodes; (2) the inferior computational capability of sensor nodes and (3) the difficulty of managing distributed sensor nodes in a centralized way, which is however necessary for many encryption algorithms [12].  
In this paper, we propose a novel anti-eavesdropping mechanism to protect confidential communications in WSNs. In particular, we deploy a small number of _friendly jammers_ in WSNs, which can generate sufficient interference to prevent eavesdroppers from snooping legitimate communications. We name such schemes as Friendly-Jamming (Fri-Jam) schemes. Recently, [13; 14; 15; 16; 17] also proposed a similar approach named _Protective jamming_ (Pro-Jam) to prohibit the eavesdropping attacks in RFID-like networks. However, Pro-Jam is mainly designed for the environment with a fence at the boundary of the network, where jammers are placed outside the fence. This assumption is impractical to WSNs since eavesdroppers can appear at any location in WSNs. Besides, most of the study on Pro-Jam scheme have been focused on the power assignment in a specific scenario. To the best of our knowledge, _there is a lack of performance analysis on friendly-jamming schemes_.  
In this paper, we establish a general analytical model to evaluate the performance of Fri-Jam schemes. The primary contributions of this paper can be summarized as follows.  
* In particular, we propose a general theoretical model to quantify the eavesdropping risk (measured by the eavesdropping probability) and evaluate the impact of Fri-Jam schemes on the legitimate communications (measured by the transmission probability).
* We consider three types of Fri-Jam schemes: random placement of jammers (named FJ-Ran scheme), regular placement of jammers (named FJ-Reg scheme) and FJ-Reg scheme with power control (named FJ-PC scheme).
* We compare the eavesdropping probability of WSNs without jammers with that with friendly jammers (FJ-Ran, FJ-Reg and FJ-PC schemes). We find that all of three Fri-Jam schemes can effectively reduce the eavesdropping probability in contrast to no-jamming scenarios.
* Our results also show that the appropriate placement of friendly jammers in WSNs can significantly reduce the eavesdropping probability whilst there is no significant impairment on legitimate communications. Besides, to adjust emitting power of jammers properly can mitigate the eavesdropping risk while has no significant impairment to the legitimate transmission.  
The rest of this paper is organized as follows. We summarize the related works in Section 2. Section 3 introduces the models used in this paper. We then analyze the eavesdropping probability of different Fri-Jam schemes in Section 4. We next show the results in Section 5. Finally, Section 6 concludes this paper.