|
\( \overset{\sim }{\Phi} \)
|
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
|
|
Pretain[i]
|
Probability of a node x
i
being retained
|
|
P1[i], Pmin[i]
|
Probability of a node x
i
having the lowest mark in its neighborhood set
|
|
P2[i]
|
Probability of a node x
i
having the second lowest mark in its neighborhood set
|
|
P2_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
|
