From: Joint power and rate scheduling for cognitive multi-access networks with imperfect sensing
Symbol | Meaning | Equation number |
---|---|---|
(.)^{1},(.)^{2} | Model I and Model II, respectively | |
σ ^{2} | The noise power | |
|h_{p}| | The magnitude of the primary user’s channel | |
|h_{s}| | 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) | |
${P}_{\mathrm{s},i}^{(m)}$ | 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 | ||
${P}_{{\text{inst}}_{\text{max}}}$ | The maximum instantaneous power of the secondary user | (4) |
r_{p}(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 | ||
r_{s}(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 | |
A_{s}(t) | The number of packets transmitted by the secondary user in time slot t | (9) |
Q_{s}(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) | |
λ_{k i j,l s q},(λ_{k 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) |
$\stackrel{\u0304}{P}$ | 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 | |
$\stackrel{\u0304}{D}$ | 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),(??) |
$(\widehat{.})$ | Retransmission scenario | |
(.)^{p} | Transmission using power control |