This problem can be formulated as max p k, w k R s.t.
According to the system model, the considered RA problem can be formulated as max P, A, B R P, A, B s.t.
Mathematically, the optimization problem can be formulated as max ω ∈ [ 0, 1 ], N ∈ N + T = ( 1 − ω ) P I ( 1 − p ls ( ω, N ) ) (14) s.t.
From (25), the power allocation optimization problem can be formulated as max λ i ≥ 0 ∀ i C ̃ u (29) s.t. 1 T λ i = P i ′ ∀ i. (30).
Then, the objective function of maximizing the sum utility of all users under per-sector power constraints can be formulated as max U P c, S c = ∑ k = 1 K c U k R ̄ k ( t ).
Assuming that the minimum SNR required by the two transceivers is t, the optimization problem can be formulated as max w t, (38a) subject to ( SNR 1 ) lower ≥ t, ( SNR 2 ) lower ≥ t, P r ≤ P. (38b).
Specifically, subproblem n0 is formulated as max A n 0, B n 0 R n 0 P m − 1, A n 0, B n 0 s.t.
Specifically, subproblem n0 is formulated as max A n 0, B n 0, C n 0 R n 0 A n 0, B n 0 s.t.
Satisfying the QoS, the time-slot allocation problem to maximize the network throughput T SA is formulated as max 0 ≤ η ≤ 1 η T i + ( 1 − η ) T o OA subject to T ¯ h ≥ Ω h, T ¯ c ≥ Ω c = ε Ω h (28).
Concerning the joint RB and power allocation, the optimization problem is formulated as: max frac{frac{W}{G}{displaystyle {sum}_{g=1}^G{ log}_2left(1+{mathrm{SINR}_n^{gg,F}right)}}{{displaystyle {sum}_{g=1}^Gleft({p}_n^{g,F}+{p}_cright)}},forall n=1,dots, N,Gin left{1,2,dots, Qright} (7).
Thus, the classical QoS-constrained optimization problem is formulated as max p log 2 I + ∑ j = 1 M p j g j M ∏ i = 1 M I + ∑ j = 1, j ≠ i M p j g j, subject to : ∀ i, 0 ≤ p i ≤ p max ∀ i, p i g i I + ∑ j = 1, j ≠ i M p j g j ≥ γ Σ i = 1 M p i g i ≤ P R max (6).
