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However, we can obtain its optimal solution easily by using the bisection search technique since the throughput function is quite smooth [35].
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The outer loop is used for the bisection search of β, and the inner loop is used to solve f(P t))=β for a given β.
A second level of iterations is used for the bisection search of λ c in each base station until the total power constraint is satisfied.
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.
Thus, to satisfy the average power constraint (23b), the bisection search method can also be used to find the optimal β∗.
Since the total power consumption is monotonic in λ, the bisection search described in the Appendix can be used to find λ.
The bisection search procedure can be applied to solve (40).
Similar to the solution of (40), (43) is solved by the bisection search procedure.
The specific steps of the bisection search method is provided in Algorithm 1.
Combining the bisection search and the uplink-downlink SINR duality, a distributed algorithm is proposed in[20].
In this paper, the bisection search method is employed to reduce the computing time of searching the optimal solution.
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