# Table 1 Summary of key variables

Variable Description
Key variables for no-reporting-error scenario
$P j ℋ 0$ ($P j ℋ 1$) Probability that channel j is available (or not available)
$P d ij$($P f ij$) Probability of detection (false alarm) experienced by SU i for channel j
$P d j$ ($P f j$) Probability of detection (false alarm) for channel j under SDCSS
εij, γij Detection threshold, signal-to-noise ratio of the PU’s signal
τij, τ Sensing time at SU i on channel j, total sensing time
N0, f s Noise power, sampling frequency
a j , b j Parameters of a-out-of-b rule for channel j
N, M Total number of SUs, total number of channels
$S j U$, $S U$ Set of SUs that sense channel j, set of all N SUs
$S i$,$S$ Set of assigned channels for SU i, set of all M channels
$Φ l k$ Particular set k of l SUs
$Ψ k 0 l 0$ Set l0 of k0 actually available channels
$Θ k 1 l 1$, $Ω k 2 l 2$ Set l1 of k1 available channels (which are indicated by sensing outcomes),
Set l2 of k2 misdetected channels (which are indicated by sensing outcomes)
$NT$ Normalized throughput per one channel
$T p ne$, $T j 2 ne$ Conditional throughput: for one particular realization of sensing outcomes corresponding to two sets $Θ k 1 l 1$ and $Ω k 2 l 2$, for a particular channel j2
n j , k e Number of SUs who select channel j to access, $k e =∣ Θ k 1 l 1 ⋃ Ω k 2 l 2 ∣$
T, TR Cycle time, total reporting time
TS, $T ¯ S$ Time for transmission of packet, time for successful RTS/CTS transmission
$T I i , j$ ($T ¯ I j$) i th duration between two consecutive RTS/CTS transmission on channel j (its average value)
TC, $T ¯ cont j$ Duration of collision, average contention time on channel j
PD Propagation delay
PS, ACK Lengths of packet and acknowledgment, respectively
SIFS, DIFS Lengths of short time interframe space and distributed interframe space, respectively
RTS, CTS Lengths of request-to-send and clear-to-send, respectively
p, $P C j$ Transmission probability, probability of a generic slot corresponding to collision
$P S j$, $P I j$ Probabilities of a generic slot corresponding to successful transmission, idle slot
$N c j$($N ¯ c j$) Number of collisions before the first successful RTS/CTS exchange (its average value)
$f X N c$, $f X I$ PMFs of $N c j$, $T I i , j$
Key variables as considering reporting errors
$P e i 1 i 2$ Probability of reporting errors between SUs i1 and i2
$P d i 1 i 2 j$ ($P f i 1 i 2 j$) Probabilities of detection (false alarm) experienced by SU i1 on channel j with the sensing result received from SU i2
$Θ k 1 , j 3 l 1$ l1th set of k1 SUs whose sensing outcomes indicate that channel j3 is vacant
$Ω k 2 , j 4 l 2$ l2th set of k2 SUs whose sensing outcomes indicate that channel j4 is vacant due to misdetection
$Φ k 3 , j 3 l 3$ l3th set of k3 SUs in $Θ k 1 , j 3 l 1$ who correctly report their sensing information on channel j3 to SU i4
$Λ k 4 , j 3 l 4$ l4th set of k4 SUs in $S j 3 U ∖ Θ k 1 , j 3 l 1$ who incorrectly report their sensing information on channel j3 to SU i4
$Ξ k 5 , j 4 l 5$ l5th set of k5 SUs in $Ω k 2 , j 4 l 2$ who correctly report their sensing information on channel j4 to SU i9
$Γ k 6 , j 4 l 6$ l6th set of k6 SUs in $S j 4 U ∖ Ω k 2 , j 4 l 2$ who incorrectly report their sensing information on channel j4 to SU i9
$S 1 , i a$, $S 2 , i a$ Sets of actually available channels and available due to sensing and/or reporting errors, respectively
$Ŝ 1 a$, $Ŝ 2 a$ $Ŝ 1 a = ⋃ i ∈ S U S 1 , i a$, $Ŝ 2 a = ⋃ i ∈ S U S 2 , i a$
$S i a$, $Ŝ a$ $S i a = S 1 , i a ⋃ S 2 , i a$, $Ŝ a = Ŝ 1 a ⋃ Ŝ 2 a$
$k e i$, kmax $k e i =∣ S i a ∣$, $k max =∣ Ŝ a ∣$
$Ψ j a$, Ψa Set of SUs whose SDCSS outcomes indicate that channel j is available, $Ψ a = ⋃ j ∈ Ŝ a Ψ j a$
N j , Nmax $N j =∣ Ψ j a ∣$, Nmax=Ψa
$T p re$, $T j 2 re$ Conditional throughput for one particular realization of sensing outcomes and for a particular channel j2, respectively