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Notice that the bisection method can be used to calculate numerically the optimum power allocation (13).
Given a lower and upper bound for each possible solution, a standard root finding method (e.g. bisection method) can be applied.
The optimum δ ∗, obtained using simple iterative techniques such as bisection method, can be used to find the optimum values (P_{T}^) and (P_{R}^).
As ηEE is strictly quasi-concave on PMU, the bisection method can be used to find the optimal ηEE and the corresponding PMU (denoted PMU_o p t).
If not impossible, it is very hard to find the closed-form for the optimal relay position (d ∗) from Eq. (71); however, simple iterative techniques such as bisection method can be used to find the optimum position of the relay, d ∗.
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Due to the monotonicity of f(P t)), the bisection search method can be used to find P t), satisfying f(P t))=β for a given β at each slot t.
A more robust method can be formulated as a combination of a line search algorithm and the bisection method.
Notice that the bisection method can also be used in this case to compute the optimum code allocation, n k ℓ.
Methods can be copied.
This algorithm relies on the waterfilling and bisection methods that can be implemented very efficiently (see e.g.[40]).[40]
Thus, to satisfy the average power constraint (23b), the bisection search method can also be used to find the optimal β∗.
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