# Accurate Sybil Attack Detection Based on Fine-Grained Physical Channel Information
## 3 Preliminaries
### Sybil Attack Models  
In the wireless network, most clients have a fixed position. The Sybil attacker may for the identity of normal clients, such as IP addresses, MAC addresses or public keys. We present generalized Sybil attack models in Figure 1. We assume that there are four clients A, B, C, D in the indoor wireless network, which are located at \([30^{\circ},150^{\circ},60^{\circ},120^{\circ}]\) of the witnessing AP 1. Client A and client B are located in a 3-m radius of the circle. Similarly, client C and client D are located in a 2-m radius of the circle. AP 1 is the centre of these circles. It receives service requests from those clients in a period of time.  
In Figure 1a, we assume Client A is a Sybil client, which is located \(30^{\circ}\) of AP 1 and steals the identity of Client B. When Client A forged Client B's ID as node \(B^{\prime}\), Client A sent massive data to AP 1. AP 1 thinks the data are from Client B and exchanges massages with it. This is a spoofing attack, and node \(B^{\prime}\) is the Sybil node. Spoofing attacks may also occur at different radians of the same angle above the radius. Unlike Figure 1a, Client A, Client D is located in the same degree \(30^{\circ}\). Figure 1b shows that Client A forges the identity information of Client D and appears as node D'. Therefore, the information exchanged between Client D and AP 1 can be tapped by node D'.  
As shown in Figure 1c, it is also assumed that Client A is a Sybil client. Client A claims that it has multiple identities such as node \(A^{\prime}\), node \(A^{\prime\prime}\), node \(A^{\prime\prime\prime}\), and so on, which can consume the resources of witnessing AP 1 by sending massive high-rate service requests. Clients B, C, D will fail to access the network especially when the number of Sybil nodes is large enough. This is the typical generalized Sybil attack. Simultaneously, those nodes forged by Client A are Sybil nodes.  
The attack's Sybil nodes and part of normal clients may distribute in a small range. If Sybil nodes \(A^{\prime}\), \(A^{\prime\prime}\), \(A^{\prime\prime\prime}\) forged by Client A gather together in Figure 1c, they are distributed in a tiny space around Client C, so we need to detect attackers from a dynamic perspective. In general, this situation happens rarely. However, when the attacker tries to move its position to change the character of the channel, the above situation still cannot be captured.  
Therefore, according to the core principle of attack, the Sybil nodes forged by the attacker come from the same physical device, and they must appear or disappear simultaneously. Attack clients  
Figure 1: Sybil attack models. (**a**) Attack for different angles; (**b**) attack for the same angles; (**c**) a large number of Sybil nodes.  
have the same physical layer characteristics, such as the same angle and the same distance from the AP. Therefore, whether we can accurately detect a client's AoA will be the key to identifying Sybil attacks. As we know, in the radar system, the MUSIC algorithm [43] can detect the AoA by using the phase difference between the antennas. Therefore, the receiver uses three antennas. At the same time, we combine the MUSIC algorithm with MIMO technology to detect each user's AoA.