and Bk= = P4 : {tk},{f}},{Pk} max (8.8a) s.t. (8.6c)-(8.6g) (8.8b) Furthermore, ({,, {N } } ) satisfies the following equations for Nk=NK = and Bk= = (8.9) Please refer to [92] for the detailed proof. Based on the above Lemma, P3 can be solved iteratively. At each iteration, the objective function becomes a convex one with giving Nk and Bk in (8.8a), then the auxiliary value of Nk and Bk will be updated according to Section 8.3.3. 8.3.3 Proposed Solution to P4 with given (2kg,Bk) To summarize, for given (2kg Bk), a complete version of P4 is illustrated at the top of next page. Where = simplicity. It is easy to verify that, for given and at each iteration, P4 is a convex optimization problem and can be solved by standard method such as interior-point algo- rithm. The optimized variable, once computed from the optimization problem, will be used to update and TO for the input of next iteration. Furthermore, the conver- gence of this iterative algorithm can be guaranteed by concave-convex procedure (CCCP). 8.4 Numerical Results Notice that for SCA algorithm, it is vital to select an appropriate initial value. The initial point used for iterative algorithm should be feasible for the optimization problem. We will discuss more details in the simulation part. 8.3.4 Update (Ak, Bk) In this part, we give descriptions for updating the auxiliary variables Nk and Bk. Notice that in Lemma 1, the optimal solution Pk, tx, and fk should also satisfy the following system conditions: (8.10) (8.11) Similarly, according to [92], we define functions for notational brevity. Specifically, let - 1, j E {1,2, K}. The optimal solution for Nk and Bk can be obtained by solving T(Nk, = [T, T2, ,T2K] = 0. We can apply iterative method to update the auxiliary variables. Specifically, (8.12) (8.13) Ek(Pk) where O(i) is the largest 0 that satisfies (1 - q is the Jacobian matrix of T, l E {1,2,...}, O E (0,1), and ZE (0,1). This update is also available in our prior study [173]. To summarize, we list the detailed algorithm in Algorithm 8.1. Algori