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Table 1 Simplified coalition formation algorithm for two-way friendly jammer selection problem

From: Distributed coalitional game for friendly jammer selection in ultra-dense networks

Initialization

The coalitional structure is initialized as \(\Pi _{0}=\Omega =\mathbb {M}\cup \mathbb {K}\) and each player i’s history set h(i) is set empty.

Phase 1 : Qualification Confirmation

a Each SBS k measures the channel gain to the eavesdropper and MUEs, i.e., \(h_{k,e}^{n_{m}}\), \(h_{k,m}^{n_{m}}\), \(m\in \mathbb {M}\).

b MBS broadcasts the collected channel information to MUEs.

c Each player i calculates its potential partner list. For SBS k, \({\Psi _{k}} = \{ m|h_{k,e}^{{n_{m}}} / h_{k,m}^{{n_{m}}} > 1,m \in \mathbb {M}\}\), For MUE m, \({\Psi _{m}} = \{ k|h_{k,e}^{{n_{m}}} / h_{k,m}^{{n_{m}}} > 1,k \in \mathbb {K}\}\).

Phase 2 : Coalition Formation

Loop:

Given the current partition Π current (in the beginning, Π current =Π 0), for every player i in coalition SΠ current

a Update the utility in S, U current =u k (Π current ,S)

b For SBS, find the coalitions that contain the MUEs in Ψ i , S Ψ ={S |S Π current S,mΨ i ,mS } For MUE, find the SBSs who are still alone in Ψ i , S Ψ ={S |kΨ i ,kS ,|S |=1}

c Investigate the possible switching operation among S {}, according to the switching rule. Record the maximal utility U max and the corresponding coalition

d If U max >U current

Player i stores the current coalition S into history set h(i), and joins the new coalitionelse Player i stays in the current coalition and the coalition partition does not changeend

Until: No player deviate from its coalition.

Phase 3 : Friendly Jamming

The SBS in non-singleton coalition allocates α of the total power on its client MUE m’s subchannel n m to transmit the information as the jamming noise. MUE pays to its jammers according to (14) and (15).