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Table 1 Symbols and parameters for mathematical formulations

From: A new fair-efficient spectrum allocation scheme for the LTE and WiFi coexistence platform

Parameters Explanations
\({\mathcal{A}}_{\mathcal{D}}\) The totally allocated spectrum resource for the \(\mathcal{D}\)
\({\mathcal{A}}_{\mathcal{D}}^{\mathfrak{B}}\) The \(\mathcal{D}\)’s LTE spectrum amount
\({\mathcal{A}}_{\mathcal{D}}^{\mathcal{W}}\) The \(\mathcal{D}\)’s WiFi spectrum amount
\(\mathfrak{B}\) The LTE base station
\({\mathbb{B}}_{\mathcal{W}}\) The \(\mathcal{W}\)’s IoT devices generated BESs
\({\mathbb{D}}\) The set of IoT devices
\({\mathcal{D}}_{1\le j\le n}\) The jth IoT device
\({\mathbb{G}}_{\mathfrak{B}}\) The second phase bargaining game
\({\mathbb{G}}_{\mathcal{W}}^{\mathfrak{B}}\) The first phase bargaining game
\({\mathbb{G}}_{\mathcal{W}}\) The third phase bargaining game
\({\mathcal{J}}_{\mathcal{D}}\) The \(\mathcal{D}\)’s strategy in the \({\mathbb{G}}_{\mathcal{W}}\)
\({\mathfrak{M}}_{\mathfrak{B}}^{t}\) Total sum of \({\mathcal{T}}_{\mathcal{D}}\) where \(\mathcal{D}\in {\mathbb{Q}}_{\mathfrak{B}}\)
\({\mathfrak{M}}_{\mathcal{W}}^{t}\) Total sum of \({\mathcal{T}}_{\mathcal{D}}\) where \(\mathcal{D}{\in {\mathbb{B}}}_{\mathcal{W}}\)
\({\mathcal{R}}_{\mathfrak{B}}\) The \(\mathfrak{B}\)’s part of the \({\mathcal{S}}_{\mathfrak{B}}\)
\({\mathcal{R}}_{\mathcal{W}}\) The \(\mathcal{W}\)’s part of the \({\mathcal{S}}_{\mathfrak{B}}\)
\({\Upsilon}_{\mathcal{D}}\) The \(\mathcal{D}\)’s strategy to share the \({\mathcal{R}}_{\mathfrak{B}}\) in the \({\mathbb{G}}_{\mathfrak{B}}\)
\({\mathcal{S}}_{\mathfrak{B}}\) The licensed spectrum band of \(\mathfrak{B}\)
\({\mathcal{S}}_{\mathcal{W}}\) The unlicensed spectrum band of \(\mathcal{W}\)
\({\mathcal{T}}_{\mathcal{D}}\) The \(\mathcal{D}\)’s maximum spectrum requirement
\({\mathfrak{U}}_{\mathfrak{B}}\left(\cdot \right)\) The \(\mathfrak{B}\)’s utility function in the \({\mathbb{G}}_{\mathcal{W}}^{\mathfrak{B}}\)
\({\mathfrak{U}}_{\mathcal{W}}\left(\cdot \right)\) The \(\mathcal{W}\)’s utility function in the \({\mathbb{G}}_{\mathcal{W}}^{\mathfrak{B}}\)
\({U}_{\mathcal{D}}\left(\cdot \right)\) The \(\mathcal{D}\)’s utility function in the \({\mathbb{G}}_{\mathcal{W}}^{\mathfrak{B}}\) game
\({\mathcal{U}}_{\mathcal{D}}^{BES}\left(\cdot \right)\) The \(\mathcal{D}\)’s utility function of BES in the \({\mathbb{G}}_{\mathcal{W}}\)
\({\mathcal{U}}_{\mathcal{D}}^{QPS}\left(\cdot \right)\) The \(\mathcal{D}\)’s utility function of QPS in the \({\mathbb{G}}_{\mathcal{W}}\)
\({\mathbb{Q}}_{\mathfrak{B}}\) All IoT devices, which generate QPSs
\({\mathbb{Q}}_{\mathcal{W}}\) The \(\mathcal{W}\)’s IoT devices generated QPSs
\({\mathbb{W}}\) The set of WiFi access points
\({\mathcal{W}}_{1\le i\le m}\) The ith WiFi access point