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Table 1 Notations

From: Adaptive mechanism design and game theoretic analysis of auction-driven dynamic spectrum access in cognitive radio networks

Symbol

Definition

T

Total transmission time of the frame

h i

Channel coefficient of secondary user i

The set of secondary users

b i

The bidding strategy of secondary user i

b i k

The k th bidding strategy of secondary user i

B i

The set of bidding strategy of secondary user i

K i

The cardinality of B i

u i

The utility reward to secondary user i

v i

The monetary efficiency function of secondary user i

C i

The channel capacity of secondary user i

ρ i

The transmit power of secondary user i

β i

The risk preference parameter of secondary user i

b ̂ i

The bidding strategy of winner i

θ i

The sensitive parameter of secondary user i

U i

The utility function of secondary user i

ω i

The ordered auction price parameter of secondary user i

i

The index of the winning secondary users i

bid i

The ordered (i th highest) bid of secondary user i

Ω

The set of parameterized auction mechanisms

M

The cardinality of Ω

ω 2 m

The m th element in Ω

r

The utility function of base station

p ik

The probability of the k th bidding strategy of secondary user i

p i

The probability distribution over B i

q m

The probability of m th auction mechanism

q

The probability distribution over Ω

g i

The expected utility of secondary user i

r ̄

The expected utility of the primary user

γb(t)

The reaction of the primary user

γ i s (t)

The reaction of i

λ b

The normalized parameter of the primary user

λ s

The normalized parameter of the secondary users

δ b

The stepsize of the primary user

δ s

The stepsize of the secondary users

d i

The distance from the primary user to secondary user i