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Table 1 Summary of key variables

From: Joint cooperative spectrum sensing and MAC protocol design for multi-channel cognitive radio networks

Variable Description
Key variables for no-reporting-error scenario  
P j 0 ( P j 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