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Table 1 Explanation of adopted symbols

From: Power minimization of cooperative beamforming networks with spectrum sharing

Symbol Explanation
y j Received signal at the jth node
h i j Channel coefficient from ith to jth node
P ij Transmitting power per bandwidth from the ith node to the
  jth node
x i Transmitting signal at the ith node
W Transmission bandwidth
N o Spectral density height of thermal noise
n j Thermal noise
λ ij Rate parameter of exponential distribution
d ij Distance between the ith and jth nodes
R d Direct transmission data rate
γ d Transmitting SINR of direct transmission
h d Channel coefficient of direct transmission
R c Data rate of PR
$R_{p{s_{k}}}\phantom {\dot {i}\!}$ Data rate of the link of PT-SR k
R MRC Data rate of MRC
γ p Ratio between the transmission signal power over the noise
  variance for PU
$h_{p{s_{k}}}\phantom {\dot {i}\!}$ Channel coefficient of the link PT-SR k
$\gamma _{{s_{k}}d}\phantom {\dot {i}\!}$ Ratio between the transmission signal power over the noise
  variance between ST k and PR
$h_{{s_{k}}d}\phantom {\dot {i}\!}$ Channel coefficient of the link ST k -PR
$R_{{su}_{k}}\phantom {\dot {i}\!}$ Data rate of the kth SU
$\gamma _{{su}_{k}}\phantom {\dot {i}\!}$ Ratio between the transmission signal power over the noise
  variance for the kth SU
$h_{{su}_{k}}\phantom {\dot {i}\!}$ Channel coefficient of the link ST-SR
R N Cooperative network throughput
T Time for the 1st and 2nd phase transmission
t k Time for the third phase transmission
P p Transmitting power of PT
P d Transmitting power of non-cooperative scheme
$P_{{s_{k}}d}\phantom {\dot {i}\!}$ Transmitting power of the ST k
${P_{s{u_{k}}}}\phantom {\dot {i}\!}$ Transmitting power of the third phase
w k Beamforming weight of the ST k
P OV Circuit power
P SR Overheads of cooperative beamforming
P TR Overheads of message sharing
P c Circuit power
M Number of cooperative SUs
b RD Number of bits per symbol for cooperative beamforming
b SR Number of bits per symbol for message sharing
ρ Amplifier efficiency
N TR Number of symbols of training period
N RD Number of symbols of cooperative beamforming
P b Power consumption per throughput
β k Time allocation ratio of the kth SU
Q p QoS of PU
Q s QoS of SU
$P_{\mathrm {d}}^{\text {out}}$ Outage probability of direct transmission
$C_{\text {d}}^{\text {out}}$ Outage capacity of direct transmission
Csuout Outage capacity of SU
ε Outage probability threshold
$C_{\text {cb}}^{{\text {out}}}$ Outage capacity of cooperative beamforming
η Energy efficiency
θ 1 SNR threshold for decoding
θ 2 SNR of the worst link between ST k and PR
d p Distance between PT and PR
${d_{{s_{k}}d}}\phantom {\dot {i}\!}$ Distance between PT and PR
d su Distance between ST and SR
${d_{p{s_{k}}}}\phantom {\dot {i}\!}$ Distance between PT and ST
P max Maximum transmitting power
γ d Ratio between the direct transmission signal power over the
  noise variance
ζ Network energy consumption for unit bit of throughput
L s Number of SUs
v Moving speed of users