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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