cus on the solution to this problem. 14.4.2.2 Problem Solution In the sequel, we propose an iteration algorithm to find the global optimal solution of the problem (14.37). Before that, we need the following properties about Nm. Property 14.2 Given Nm,Nm decreases monotonically with Pm. Proof: It is easy to infer that fo( in (14.36) decreases monotonically with Pm. Then, Em increases monotonically with Pm. Finally, Nm decreases monotonically with Pm. Property 14.3 Given Pm' (14.37) is a concave function with respect to Nm. Proof: See Ref. [34]. Based on Property 14.2 and 14.3, we propose an iterative algorithm to find the optimal solution for problem (14.37). Given Pm' the optimal values of Nm m that maximizes (14.37) can be found via bisection method. By searching Nm, the optimal and minimum value of Pm can be obtained by (14.36). Thereby, we can obtain the optimal resource allocation to maximize the communication SE in (14.37). The details of the algorithm are provided in Algorithm 14.1. 14.5 Simulations Results Algorithm 14.1: The iterative algorithm for optimal resource allocation. Input: cm, B, Tth, A, N m < 1, Nh = Bmax/B, and the accuracy requirement of the bisection method V 1: Set Pm= pmax 2: Nm= 3: while Em>1 - cm or > pmax do while (INh Nm/>>v) N* = Nk a(-nm) O then N m Nm N* =N Nm=Nm N m = Nm break end if end while Obtain Pm by solving to minimize transmission power 19: end while 20: m=Pm Output: Optimal resource allocation N * * and Pm. 14.4.3 Optimal Control Convergence Rate Once we obtain the maximum communication SE in (14.34), the communication reliability (1 - Em) can be obtained accordingly. Then, we can obtain the optimal control convergence rate PM to minimize control cost by solving the following equation: Pr{amn=1}=1-Em=C (14.38) Thereby, we can obtain an optimal overall system performance. Simulations Results In this section, we provide simulation results to demonstrate the performance of the method that was explained earlier in Section 14.4, where the system models are the same as shown 14