An efficient scheduling policy must determine the proper set of links for which there exists a power and rate allocation that meets power constraints and SINR requirements.
The first phase establishes that for a given set of links, there exists a power and rate allocation that satisfies the SINR requirements imposed by some MCSs under a set of power constraints.
Given minimum utility requirements, and, the arbitrator should be able to determine if this pair is feasible, that is, whether there exists a power pricing pair that leads to a unique NE that fulfills these requirements simultaneously.
The power vector found by (14) does not consider the power constraints (5) or (6), and they are taken into account once there exists a power vector defined by (4) such that p ∈ R + + | K |, which corresponds to a feasible target allocation where no power constraints are imposed.
For a unicast transmission scenario, a directed communication link l ij is established from node i to node j if there exists a power level P ∈ [ 0, P max ( i ) ], under which the SNR level measured at the receiver of node j exceeds a prescribed threshold level γ(j); i.e., G ij P η ≥ γ ( j ) (1).
Let F denote the feasible utility region, where for each point U = (U1,…,U L ) in F, there exists a power vector p such that U l = U l (γ l (p)) for all l ∈ L. The feasible utility region F is nonconvex, and in general, finding the globally optimal solution to (2) in F is challenging.
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These rate targets must be feasible, which means there must exist a feasible power allocation such that the per-user rate target is satisfied and the per-antenna power constraints not being violated.
For this case, it is obvious that there must exist a smaller power P S1′ satisfying C S1=C S2, which can obtain the same data rate of SU, however, with less interference to PU and lower transmit power of SU.
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