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Table 1 Notations used in our work

From: Enhancing energy efficiency for cellular-assisted vehicular networks by online learning-based mmWave beam selection

Notations Description
L The number of non-overlapping sectors of the mmSBS
\({\mathcal{M}}^{l}\) The set of virtual beams of the l-th sector
\(M^{l}\) The number of virtual beams of the l-th sector
\(\aleph^{l}\) The set of transmission power levels of the l-th sector
\(N^{l}\) The number of transmission power levels of the l-th sector
n The maximum number of RF chains
\(g_{t}^{l}\) The set of vehicle groups of the l-th sector of each time slice t
\(G_{t}^{l}\) The number of vehicle groups of the l-th sector of each time slice t
\({\text{\rm O}}_{{G_{t}^{l} }}\) The D-dimensional vector set of group context
\(o_{t,i}^{l}\) The group context of each incoming vehicle group \(g_{t,i}^{l}\) of each time slice t
\({\mathcal{B}}{\text{\rm P}}_{t}^{l}\) The set of chosen beam-power pairs in each time slice t of the l-th sector
\(b_{t,j}^{l}\) The chosen beam in each time slice t of the l-th sector
\(p_{t,j}^{l}\) The chosen transmission power level in each time slice t of the l-th sector
\(r_{{\left\langle {b_{t,j}^{l} ,p_{t,j}^{l} } \right\rangle }} \left( {o_{t,i}^{l} } \right)\) The amount of data of the vehicle group with the context \(o_{t,i}^{l}\) successfully receives via the chosen beam-power pair \(\left\langle {b_{t,j}^{l} ,p_{t,j}^{l} } \right\rangle\)
\(e_{{\left\langle {b_{t,j}^{l} ,p_{t,j}^{l} } \right\rangle }} \left( {o_{t,i}^{l} } \right)\) The energy efficiency of the vehicle group with the context \(o_{t,i}^{l}\) gets the beam-power pair \(\left\langle {b_{t,j}^{l} ,p_{t,j}^{l} } \right\rangle\) during the time slice t
\(\tilde{e}_{{\left\langle {b_{t,j}^{l} ,p_{t,j}^{l} } \right\rangle }} \left( {o_{t,i}^{l} } \right)\) The expected performance of energy efficiency
\({\mathcal{B}}{\text{\rm P}}_{t}^{l*} \left( {{\text{\rm O}}_{{G_{t}^{l} }} } \right)\) The optimal subset of beam-power pairs in the time slice t of the l-th sector
\({\mathcal{B}}{\text{\rm P}}_{{{\text{G}}{\mathcal{H}}_{t}^{l} }}^{ue} \left( t \right)\) The set of under-explored beam-power pairs of the set of subspaces of the l-th sector
\(u^{l} \left( t \right)\) The number of under-explored beam-power pairs of the set of subspaces of the l-th sector
\({\mathcal{B}}{\text{\rm P}}_{{{\text{G}}{\mathcal{H}}}}^{ue} \left( t \right)\) The set of under-explored beam-power pairs of the set of subspaces of the mmSBS
\({\mathcal{B}}{\text{\rm P}}_{{{\text{G}}{\mathcal{H}}}}^{ve} \left( t \right)\) The set of beam-power pairs to be used of the set of subspaces of the mmSBS