Channel Assignment Technique

We present a discrete-time interference-aware DCA technique to reduce channel conflicts for a given network topology. We let Nv denote the neighbors of node v ∈ V,

Nv = {u ∈ V|evu ∈ E} . (2.1)

We also define δv, v ∈ V, as the degree of node v, i.e., the cardinality |Nv| of the neighboring set.

In the event of a channel conflict with one or more neighbors, we assume an AP can determine which channels are available to switch to so that it is no longer in conflict with its neighbors. An available channel is one that is in the set of usable channels but not in any of the interference sets of the AP’s neighbors. An interference set includes all channels that overlap with the assigned channel based on a channel separation constant. For an AP, v ∈ V, on channel cv ∈ C, the AP’s

interference set denoted Ivconsists of adjacent channels, i.e.,

Iv = {max(cv − ∆, 1), . . . , cv− 1, cv, cv+ 1, . . . , min(cv+ ∆, |C|)}, (2.2)

where ∆ is the channel separation constant. For example, for a separation value of 2, a channel cv

will overlap with channels cv − 2, cv − 1, cv + 1 and cv + 2. For all examined test cases, we used

a channel separation constant ∆ = 2. The set of channels an AP v can freely switch to, denoted Lv, is thus the set difference of usable channels and the union of the interference sets of all its

neighbors, i.e.,

Lv = C \

[

u∈Nv

Iu , u, v ∈ V. (2.3)

its interference set, i.e.,

Dv = {u ∈ Nv : cu ∈ Iv}. (2.4)

Since we can count how many times a given channel appears in an interference set, we can build a histogram ∀c ∈ C to find the least interfering channel.

Without loss of generality, we follow the following procedure to assign a new channel to a certain node v, albeit pinball attacks apply to other DCA algorithms. If Lv is non-empty, i.e., Lv 6= ∅, then

v is assigned any channel drawn randomly from Lv. Otherwise, v is assigned the least interfering

channelaccording to the histogram. Graph coloring is generally NP-hard. Therefore, we do not attempt to obtain a state of minimum conflict. Instead, we adopt a greedy graph coloring approach to channel assignment as described in Algorithm 1.

Before randomly assigning channels to any node, the nodes are sorted in decreasing order accord- ing to their node degrees, thereby giving priority to the hub nodes with the higher degrees. Let vsorteddenote the ordered sequence of nodes.

Algorithm 1 CA based on Greedy Graph Coloring

1: procedure CHANNELASSIGNMENT(vsorted, C)

2: for v in vsorteddo

3: Find: Lv, Nvand Iv.

4: Update: Channel Histogram.

5: if Lv 6= ∅ then

6: Assign v a channel cv = c, c ∈ Lv, drawn randomly.

7: else

8: Choose cvas the least interfering channel.

9: end if

10: end for

11: end procedure

non-interfering channel or a least interfering channel. At any time stage, the system may trigger this algorithm to resolve a conflict. Based on this algorithm, no channel switching would occur unless it resolves or reduces the network interference as in the DCA protocol applied in the Cisco Radio Resource Management (RRM) system [1]. In the RRM system, the wireless controller collects information from all the APs to estimate the interference and noise levels experienced by each channel, and makes channel switching decisions accordingly.

Figure 2.1: Step 1: Initial channel assignments, the network has 3 conflicts. Step 2: After an AP switches from channel 9 to 2, the network has 1 conflict. Step 3: After an AP switches from channel 7 to 10, the network is conflict-free.

2 11 9 4 2 7 10 7 2 11 2 4 2 7 10 7 3 2 11 2 4 2 7 10 10 3 (a) (b) (c)

Figure 2.2: Step 1: System starts with 3 conflicts. Step 2: Attacker jams its victim node with jamming channel 3 and the system switched the node using channel 9 to the non-interfering channel 2. However, due to the jammer the new frequency is now suffering interference. Step 3: The system is not only unable to resolve conflicts in 3 steps, but also three nodes may not find any vacant non-interfering channels, resulting in perpetual switching among other nodes as well.

boring nodes assigned adjacent frequencies interfere. While the generation of the interference map (hence, the underlying topology) depends on the physical distances between the nodes, the chan- nel attenuation, and the used power levels, only the emerging adjacency structure and the actual channel assignment are relevant to the occurrence of conflicts and to channel switching decisions2_.

For example, in DCA protocols, channel switching occurs when the interference levels exceed certain thresholds – and the topology already specifies which nodes interfere at levels that warrant switching. In turn, the adjacency structure and the channel assignment information are sufficient for optimal policy design by an attacker aiming to increase the number of conflicts and induce a cascading channel switching behavior. Therefore, we henceforth use the distance in hops as our distance measure.