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Table 1 List of key abbreviations

From: Modeling and analysis of random dense CSMA networks

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