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Table 1 List of key abbreviations
| 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 |
