Table 2 Summary of the DT-ACMO SG algorithm in MAS

1:

Generate Φ[0] randomly with the power constraint.

2:

For each instant of time, i=1, 2, …, compute

3:

,

4:

where \({\boldsymbol {r}}_{e}[i]={\boldsymbol {r}}_{MAS}[i] - \sum _{k=1}^{n_{r}}{\boldsymbol {\Phi }}^{\boldsymbol {\Delta }}_{{eq_{k}}_{MAS}}[i]{\boldsymbol {G}}_{{eq_{k}}_{MAS}}[i]\hat {\boldsymbol {s}}[i]\).

5:

Update \({\boldsymbol {\Phi }}^{\boldsymbol {\Delta }}_{{eq_{k}}_{MAS}}[i]\) by

6:

,

7:

Normalization: \({\boldsymbol {\Phi }}^{\boldsymbol {\Delta }}_{{eq_{k}}_{MAS}}[i] = \frac {{\sqrt {\mathrm {P}_{\mathrm {R}}}}{\boldsymbol {\Phi }}^{\boldsymbol {\Delta }}_{{eq_{k}}_{MAS}}[i]}{\sqrt {\sum _{k=1}^{n_{r}}{\text {Tr}} \left ({\boldsymbol {\Phi }} ^{\boldsymbol {\Delta }}_{{eq_{k}}_{MAS}}[i]\left ({\boldsymbol {\Phi }}^{\boldsymbol {\Delta }}_{{eq_{k}}_{MAS}}[i]\right)^{{H}}\right)}}\).