From: Resource allocation for statistical QoS guarantees in MIMO cellular networks
Parameter | Description |
---|---|
L | Total number of MIMO links |
l | Link index |
i | DoF index |
d | DoF of MIMO link, i.e. d= min{n _{ t },n _{ r }} |
θ ^{l} | QoS of lth link |
ξ ^{k} | kth vector of DoFs of L links, i.e., ξ ^{1}=(1,…,1) |
and \(\boldsymbol {\xi ^{d^{L}}}=(d,\ldots,d)\) | |
δ ^{l}(t) | DoF of lth link at time t, i.e., δ ^{l}(t)=i∈{1,…,d} |
\(\boldsymbol {\widetilde {\delta }_{(t)}}\) | Vector of DoFs of all links, i.e., \(\boldsymbol {\widetilde {\delta }_{(t)}}=(\delta ^{1}(t),\dots,\delta ^{L}(t))\) ∈ |
{ξ ^{1},…,ξ ^{d} ^{L}} | |
\(\boldsymbol {\delta }_{i}^{-l}\) | DoF vector with lth link having i DoF, i.e., \(\boldsymbol {\delta }_{i}^{-l}=(\delta ^{1},\dots,\delta ^{l-1},\) |
i,δ ^{l+1},…,δ ^{L}) | |
\(\widetilde {\phi }^{l}(\boldsymbol {\widetilde {\delta }_{(t)}})\) | Instantaneous slot allocation for lth link |
\(\widetilde {\phi }^{l}(\boldsymbol {\widetilde {\delta }_{(t)}})\) | Updated slot allocation for lth link |
\({\pi _{i}^{l}}\) | Probability of lth MIMO link having i DoF |
\(\bar {\rho }^{l}\) | Average transmit SNR of lth MIMO link, i.e., \(P{\sigma _{\textit {ij}}^{l}}^{2}/{\sigma _{n}^{2}}\) |
α | Exponential moving average weight used in time-slot update |
υ ^{l} | Auxiliary function \({R_{i}^{l}}-\frac {{\log \pi _{i}^{l}}}{\theta ^{l}}\) |
\(\widetilde {E}_{C}^{l}(\theta ^{l})\) | Updated effective capacity for link l |
Ψ(t) | System utility function, i.e., \(\sum _{l} \log (1+\widetilde {E}_{C}^{l}(\theta ^{l}))\) |
0 | Vector of zeros |
ε | Halt condition |