Table 1 Notations used in our work

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