Table 1 Description of modeling variables

N

Number of channels to be sensed

P _d

Probability of detection of I3S scheme

P _f

Probability of false alarm of I3S scheme

P _m

Probability of miss detection of I3S scheme

r(t)

Received signal

s(t)

Transmitted signal

n(t)

Additive white gaussian noise (AWGN)

h

Amplitude gain of the channel

H ₀

Indicates absence of PU

H ₁

Indicates presence of PU

E

Received energy at output of energy detector

γ

Instantaneous SNR

m

time bandwidth product

P _d,E

Probability of detection for bi-threshold energy detector

P _f,E

Probability of false alarm for bi-threshold energy detector

P _d,C

Probability of detection for cyclostationary detector

P _f,C

Probability of false alarm for cyclostationary detector

P _d,EC

Probability of detection for combined energy and cyclostationary detector

P _f,EC

Probability of false alarm for combined energy and cyclostationary detector

P _d,M

Probability of detection for matched filter

P _f,M

Probability of false alarm for matched filter

P

Probability that channels are sensed by cyclostationary detector

P _r

Probability that channel would sensed by combined energy and cyclostationary detector

1−P _r

Probability that channel would sensed by matched filter

$\overline{T}$

Mean detection time of I3S scheme

$\overline{T_{\text{EC}}}$

Mean detection time of combined energy and cyclostationary detector

$\overline{T_{\mathrm{M}}}$

Mean detection time of matched filter

$\overline{T_{\mathrm{E}}}$

Mean detection time of energy detector

$\overline{T_{\mathrm{C}}}$

Mean detection time of cyclostationary detector