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 |