In the following, we will substitute the power prices with their inverse to ease the analysis with regard to the power allocation and utility.
(50) Like case 1, we substituted the power variable by its optimal value to get a new problem without power parameter.
The framework of energy-efficient location-based service and mobile cloud convergence was proposed by Choi et al. [10], which substituted the power-intensive sensors for decreasing the power dissipation.
Hence, the power variable in (43) can be eliminated by substituting the optimal power allocation found in (48).
To solve ( {p}_n^{ast }(t) ), substituting the rate-power function Eq. (2) into Eq. (18), then differentiating with respect to the transmit power p n (t) (decision variable), we will obtain: {p}_n^{ast }(t)=frac{Q_n(t)+{Z}_n(t)}{2mathit{ln}2cdot pV}-frac{1}{h_n(t)}forall n,kern0.5em t (19).
Substituting the beamforming transmitter power allocation matrix into (10), we have the capacity for beamforming, CBF, given by C BF = E log ∣ I N R + ( A 2 H w + A 1 Σ μ ) Σ Q, BF ( A 2 H w + A 1 Σ μ ) H σ 2 ∣, (28).
By substituting into the power constraint, we have (5).
end{aligned} (6) We substitute the formal power series (hat{mathcal {B}}_{q 1/k_{2}}(F T,m,epsilon))) with the acceleration of (psi _{k_{1}}^{mathfrak{d}_{p}}) for each (0le plevarsigma-1) and study the resulting equation for each p. The role of the acceleration operator is being played by q-Laplace transform of an adequate order.
From this fig, the maximum power can be seen to be <6.5 W while, by using Eq. (3) and substituting the appropriate values, the maximum power under identical operating conditions but without shading is 30.1 W.
By substituting the vector of optimal transmit power ( {mathbf{P}}^=left{{p}_1^(t),{p}_2^(t),cdots, {p}_N^(t)right} ) into the interference power constraint inequality in (6), we can obtain: sum limits_{iin mathcal{N}}{p}_i^(t){G}_{left i,bright)}le {varpi}_{mathrm{PBS}}.
