# Table 1 Table of symbols

Symbol Meaning Equation number
(.)1,(.)2 Model I and Model II, respectively
σ 2 The noise power
|hp| The magnitude of the primary user’s channel
|hs| The magnitude of the secondary user’s channel
R p The transmission rate of the primary user (1)
p p The transmission power of the primary user
L a The rate of transmission of an active primary user
R s,i The capacity of the secondary user when
the primary user is active(idle), i.e., i = 1(i = 0) (2),(3)
$P s , i ( m )$ The power of the secondary user when transmitting m packets while
the primary user is active(idle), i.e., i = 1(i = 0)
n The maximum number of packets the secondary user can transmit
when the primary user is idle
a The maximum number of packets the secondary user can transmit
when the primary user is active
$P inst max$ The maximum instantaneous power of the secondary user (4)
rp(t) The number of packets admitted to the primary user’s queue at time slot t (6),(7)
θ The probability that the primary user is active in model I
b The probability that the primary user is active given
it was idle in the previous time slot in model II
h The probability that the primary user is idle given
it was active in the previous time slot in model II
rs(t) The number of packets admitted to the secondary user’s queue at time slot t (8)
α The probability that the secondary user has new packets to transmit
1−P d Probability of missed detection of an active primary user as idle
P fa Probability of sensing an idle primary user as active
γ(t) The outcome of the sensing process at time slot t
As(t) The number of packets transmitted by the secondary user in time slot t (9)
Qs(t) The queue state of the secondary user in time slot t (10)
M(t) The capacity of the secondary user
K The maximum length if the secondary user’s queue
F(t) A feedback signal to be sent to the transmitters
g kij(m),(g kuij(m)) The probability of transmitting m packets when
the system is at state k,i,j(k,u,i,j) (11),(34)
λk i j,l s q,(λk u i j,l v s q) The transition probability from state {k i j}({k u i j}) to {l s q}({l v s q}) (19),(42)
$C s ( 1 ) ( C s , l ( 2 ) )$ The probability that the sensing outcome is s in model I(II) (17),(41)
C i,l,m The probability of receiving a feedback signal l
given sensing outcome i and transmission rate m (18)
Λ The transition probability matrix
π kij (π kuij ) The steady state probability of being at state {k i j}({k u i j}) (29)
$P ̄$ The average power consumption of the secondary user per packet (30),(43)
L(t) The discretized probability of the primary user being idle at slot t (31)
(.)| Δ Discretization by step size Δ
$D ̄$ The average packet delay of the secondary user (44),(45)
The probability of packet loss (46),(47)
ζ p The probability of collision of the primary user’s packets (48),(??)
$( . ̂ )$ Retransmission scenario
(.)p Transmission using power control