1. CoBRA: Cooperative Beamforming-Based Resource Allocation for Self-Healing in SON-Based Indoor Mobile Communication System Kisong Lee, Student Member, IEEE, Howon Lee, Member, IEEE, Yong-Up Jang, Member, IEEE, and Dong- Ho Cho, Senior Member, IEEE

2. agenda Abstract I. INTRODUCTION II. SYSTEM MODEL AND PROBLEM FORMULATION III. COOPERATIVE BEAMFORMING-BASED RESOURCE ALLOCATION (COBRA) ALGORITHM IV. SIMULATION RESULTS AND DISCUSSION V. CONCLUSION

3. Abstract This paper focuses on self-healing, in order to resolve the problem of unexpected network faults and improve network throughput simultaneously. To deal with this problem, we propose a healing channel selection and a cooperative beamforming-based iterative resource allocation algorithms.

4. Abstract We utilize the cooperative beamforming in the healing channel based on phase pre-adjustment, and this cooperative beamforming can be performed without power cooperation between distributed nodes. Moreover, we derive the sub-optimality and convergence of the proposed algorithm in weak interference condition by using contraction mapping.

5. I. INTRODUCTION

6. Previous studies on self-healing have concentrated on accurate detection, diagnosis, and fast escape from failure [5]-[7], not on methods for repairing failures. The concept of healing channels (HC) was proposed, which are subchannels that normal base stations use to support users in faulty cells.

7. EPA-FHC an algorithm for managing network failure directly was proposed, but this algorithm just considered simple equal power allocation and a fixed set of healing channels (EPA-FHC). As a result, network failure could be managed but network throughput was degraded severely.

8. CRA a collaborative resource allocation (CRA) algorithm was proposed, in which normal femtocell base stations allocate power on HCs cooperatively to serve users in faulty femtocells. The CRA algorithm solves network failure more effectively, compared with the EPA-FHC algorithm. In order to improve the network throughput here, we can exploit a beamforming transmission strategy based on the cooperation of distributed nodes

9. Users in faulty indoor cells can find the pilot of the MBS, and they can be supported from that MBS. However, the users in faulty indoor cells cannot be served reliably by the MBS because power from the MBS can be attenuated by the outer wall of indoor cells and it can be also weak when indoor cells are placed in the edge of a macrocell. Moreover, the hundreds of indoor cells can be installed in the range of the macrocell. Thus, we propose a cooperative beamforming- based resourceallocation (CoBRA) algorithm.

10. The CoBRA algorithm consists of the following two steps: i) to support users in faulty indoor cells, we use an adaptive mechanism to find the set of HCs, and ii) we perform a cooperative beamforming-based iterative resource allocation to maximize network throughput. Also, we prove that the CoBRA algorithm converges to a unique fixed point in weak interference condition by using contraction mapping.

11. In particular, when the number of HCs is 10, the CoBRA algorithm improves the average cell capacity by 5% and user fairness by 10% with the same complexity compared with the CRA algorithm.

12. II. SYSTEM MODEL AND PROBLEM FORMULATION

13. We focus on self-healing in centralized SON- based indoor mobile communication system [14], where multiple IBSs are connected to a centralized unit called as operation and management (OAM), as shown in Fig. 1.

14. Fig. 1.

15. assume the following. i) There are N subchannels that are independent of each other; each subchannel is used by only one user in an IBS but users in other IBSs can access the same subchannel. ii) Perfect instantaneous channel quality information is acquired at IBSs and channel quality does not vary during the transmission time of one packet.

16. iii) Interference from an MBS is considered as additive white Gaussian noise (AWGN). The interference from the MBS is dominated by path loss, so the fast-fading effect on each subchannel is negligible. iv) Users in indoor cells are stationary or move slowly. v) Users whose service is unusually disconnected find the preamble or pilot of neighbor indoor cells, in which case they can obtain information about the HC and be served continuously by normal indoor cells. vi) IBSs can share transmission data used for cooperation through the OAM.

19. Data rate

20. Objective function

21. III. COOPERATIVE BEAMFORMING- BASED RESOURCE ALLOCATION (COBRA) ALGORITHM

22. The problem (1) is a constrained non-convex optimization problem, so finding an optimal solution is non-deterministic polynomial-time (NP) hard [15]. To reduce complexity, we propose a two-step resource allocation algorithm that consists of (a) the selection of HCs, and (b) the cooperative beamforming- based iterative resource allocation.

23. A. Healing Channel Selection To reduce the complexity, we propose an algorithm that finds the set of HCs adaptively. The goal when choosing the set of HCs is to minimize the throughput degradation of normal indoor cells while maximizing the throughput of faulty indoor cells. To achieve this goal, the OAM finds the set of HCs using the following procedures.

24. A. Healing Channel Selection

27. B. Cooperative Beamforming-based Iterative Resource Allocation We now propose a resource allocation algorithm that comprises both subchannel allocation and power allocation. In the subchannel allocation, normal IBSs allocate NCs to their own users according to (2) and allocate HCs to the user who receives the largest beamforming gain in faulty indoor cells according to (3). The objective function of problem (1) can be maximized by this subchannel allocation.

28. B. Cooperative Beamforming-based Iterative Resource Allocation

29. KKT Conditions 在數學中，卡羅需 - 庫恩 - 塔克條件（英文原 名： Karush-Kuhn-Tucker Conditions 常見別名： Kuhn-Tucker ， KKT 條件， Karush-Kuhn-Tucker 最優化條件， Karush-Kuhn-Tucker 條件， Kuhn-Tucker 最優化條件， Kuhn-Tucker 條件） 是在滿足一些有規則的條件下，一個非線 性規劃（ Nonlinear Programming ）問題能有 最優化解法的一個必要和充分條件。這是 一個廣義化拉格朗日乘數的成果。

30. B. Cooperative Beamforming-based Iterative Resource Allocation

34. the normal IBS m can determine the amount of power that should be allocated to HC n in order to achieve the objective of the optimization problem (1) by iterative updates

35. Theorem 1

36. Proof

40. equal power allocation(EPA) The overall process that all normal IBSs allocate power is as follows. At first, all normal IBSs use equal power allocation on all subchannels. Normal IBS 1 updates its power allocation according to (10) and (11) by fixing the power allocation of other IBSs as the equal power allocation. Next, based on the changed power allocation of normal IBS 1, normal IBS 2 also updates its power allocation by fixing the power allocation of other IBSs. In this step, the changed power allocation of normal IBS 1 affects the power allocation of normal IBS 2. For example, in the case of NCs, the power allocation of normal IBS 1 changes the inverse SINR value of the subchannel in normal IBS 2, thereby affecting the power allocation of normal IBS 2. In the case of HCs, the power allocation of normal IBS 1 also changes the SINR value of HC n in normal IBS 2. If the SINR of HC n was larger than that of HC n in the preceding iteration, normal IBS 2 judges that other normal IBSs transmit enough power on HC n to serve the user reliably in faulty indoor cells. So, normal IBS 2 reduces the power that it allocates to HC n. Otherwise, normal IBS 2 increases the power that it allocates to HC n. but the capacity of normal indoor cells falls severely.

41. CoBRA Our cooperative allocation of power to HCs among normal IBSs prevents this undesirable situation from occurring. The procedure by which normal IBSs allocate power continues in order iteratively until the power allocations of all the normal IBSs converge. The steps in the CoBRA algorithm are presented in Algorithm 1.

43. computational complexity The CoBRA algorithm performs HC selection only once, and carries out subchannel allocation and power allocation iteratively. The computational complexities for selecting HCs and subchannel allocation are O((N^2)*S) and O(N*S), respectively, while solving water- filling algorithm for power allocation has a complexity, O(MN log2 N). Thus, the computational complexity of the CoBRA algorithm is O((N^2)*S + IN(S + M log2 N)).

44. computational complexity Consequently, the computational complexity of exhaustive search for finding the global optimal solution is O(2^N*S^(NM)*e^(NM)). This indicates that the CoBRA algorithm reduces the computational complexity remarkably, compared with the algorithm for finding global optimal solution.

45. IV. SIMULATION RESULTS AND DISCUSSION

46. assumption we assumed that there were four indoor cells and one of them was disabled. The radius of the indoor cells was 10 m and the distance between IBSs was 20 m. In each indoor cell, 10 users were distributed uniformly. The carrier frequency and bandwidth of the spectrum were 2.3 GHz and 10 MHz, respectively. In addition, there were 32 subchannels, each of which experienced frequency flat Rayleigh fading based on the Jakes fading model independently. The path-loss model for a macrocell was a modified Okumura-Hata model [18] and the pathloss model for an indoor cell was a modified COST 231 multiwall model without the effect of floor attenuation [19]. The maximum transmission power for the IBS and MBS were 15 dBm and 43 dBm, respectively [14][20]. And, the thermal noise density was −174 dBm/Hz.

47. Fig. 1.

48. Compared algorithms

49. PERFORMANCE COMPARISON BETWEEN OPTIMAL SOLUTION AND COBRA

55. V. CONCLUSION

56. CONCLUSION In this paper, we addressed self-healing issue, which is one of the most important functionalities in SON, to solve abrupt failure of network components in real time. To deal with this problem, we formulated the joint optimization problem and proposed a CoBRA algorithm. In the CoBRA algorithm, each normal IBS determined the set of HCs adaptively and performed an iterative resource allocation with cooperative beamforming to serve users in a faulty indoor cell as well as users in normal indoor cells efficiently. In addition, we showed that the CoBRA algorithm converges to a unique fixed point in high SINR regions, where the interference is weak, by using contraction mapping. Through simulation results, we have shown that the CoBRA algorithm serves users in both faulty and normal indoor cells very well. As a result, the CoBRA algorithm improves user fairness with little degradation of system capacity compared with the other algorithms.