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Table 1 Parameters used in dynamic-FAA

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