\( \overset{\sim }{\Phi} \)

Potential transmitters (the initial PPP) contending to access the spectrum

\( {\overset{\sim }{\Phi}}_{\mathrm{t}} \)

Concurrently transmitting nodes under CSMA protocol

x
_{
i
}

Location of a node and the node itself

P
_{
t
}

Transmitting power of each transmitter

\( {g}_i^j \)

Fading channel gain of the link between node x_{
i
}and node x_{
j
}

\( {F}_i^j \)

Virtual power emitted from node x_{
i
} to node x_{
j
}

P
_{0}

Power threshold for a node to sense another transmitting node

μ

Rayleigh fading factor

β

Path loss exponent

r
_{
e
}

Distance threshold for a node sensing another transmitting node

N(x_{
i
})

Neighborhood of node x_{
i
}

C
_{
i
}

Contention domain of node x_{
i
}, and the set of nodes coexisting with x_{
i
} in the domain

T

SINR threshold for a receiver can successfully decode

N

Average number of neighbor nodes for node x_{
i
}without fading

M

Average number of nodes in the shadow (Fig. 4) without fading

\( \overset{\sim }{N} \)

Average number of neighbor nodes for node x_{
i
} with fading

\( \overset{\sim }{M} \)

Average number of nodes that cannot be sensed by node x_{
i
} while can be sensed by x_{
j
} with fading

\( \overset{\sim }{P} \)

Average number of nodes that can be sensed both by x_{
i
} and x_{
j
} simultaneously

P_{retain}[i]

Probability of a node x_{
i
} being retained

P_{1}[i], P_{min}[i]

Probability of a node x_{
i
} having the lowest mark in its neighborhood set

P_{2}[i]

Probability of a node x_{
i
} having the second lowest mark in its neighborhood set

P_{2_retain}[i]

Probability of a node x_{
i
} with the second lowest mark in its neighborhood set being retained

\( {\overline{P}}_i\left[j\right] \)

Probability of node x_{
j
} having the lowest mark in C_{
i
}, and x_{
j
} not being retained

e_ps

Mean probability for a node successful reception

TC

Transmission capacity
