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Table 1 List of parameters

From: Exploiting prospect theory and risk-awareness to protect UAV-assisted network operation

Symbol

Description

ℜ

Network radius [m]

N, |N|

Set of all users, cardinality of the set

xi

User specific investment to UAV (%)

NUAV

Users transmitting via the UAV

NMBS

Users transmitting via the MBS

NN,|NN|

Set of normal users, cardinality of the set

NM,|NM|

Set of malicious users, cardinality of the set

WMBS

MBS bandwidth [Hz]

WUAV

UAV bandwidth [Hz]

γi

Signal to Interference plus noise ratio

\(P^{MBS}_{i}\)

Transmission power via MBS [W]

\(P^{UAV}_{i}\)

Transmission power via UAV [W]

xT

Aggregate users investment to UAV-based communication

hi

Channel gain

\(\mathscr {R}(x_{T})\)

Rate of return function

\(\overline {\mathscr {R}_{i}}(x_{T})\)

PT related rate of return

\(\mathscr {P}(x_{T})\)

UAV’s bandwidth probability of failure

ai,βi

Sensitivity parameters

κi,λi

Risk aversion parameters

\(\mathscr {F}_{i}(x_{T})\)

Effective rate of return

\(\mathscr {J}(x_{T})\)

User specific optimal non zero investment

Ri

User data rate [bps]

\(\mathscr {B}_{i}(\mathbf {x_{-i}})\)

User best response

\(\mathscr {X}_{i}\)

User power investment strategy set