在本文中，我們考慮了多輸入單輸出（MISO）突發性干擾通道（bursty interference channel）的協調波束形成（coordinated beamforming）設計。在現實的情況下，分散式媒介控制機制或不同用戶的分散式網絡協議有助於網絡流量的突發性質。為了利用這種突發提供的潛在收益，需要將干擾狀態信息反饋給傳送端。實際上，在這種反饋中可能出現錯誤，此流量未知性導致波束成形設計問題。在這裡我們通過一個隱馬爾可夫模型（HMM）來模擬這種流量未知性。假設傳送端可以獲得完整的通道狀態信息（CSI）或不完整的信道狀態信息，我們的目標是在流量為知性下，使平均係統的效能最大化。由此產生的問題是高度非凸面性的。因此，我們應用一系列的凸優化近似（convex approximation）技術來處理非凸面問題。我們進一步提高了我們提出的連續凸面近似（SCA）演算法（HMM-SCA-1和HMM-SCA-2）的精確度。

在我們的模擬結果中，我們假設完整通道狀態信息在傳送端上，比較了窮舉法（ES）和我們提出的HMM-SCA-1實現的系統效用。我們證明了我們提出的演算法為所考慮的優化問題提供了一個低複雜度的近似最佳解。具體而言，HMM-SCA-1平均比ES算法快728倍。即使在流量未知的情況下，比起干擾的突發性根本沒有被利用（非突發SCA），我們提出的HMM-SCA-1仍然表現更好。對於假設傳送端只有不完整的通道狀態信息的情況下，模擬結果表明，我們提出的HMM-SCA-2比非突發SCA提高了41.4％。與假設通道有完整的通道狀態信息相比，我們可以看出，在不完整的通道狀態信息的其況下，效能的提升更為顯著。當考慮到通道估計誤差時，考慮突發性干擾通道對於實際的無線通信系統是至關重要的。

In this thesis, we consider coordinated beamforming design for a multiple-input single-output (MISO) bursty interference channel. In realistic scenarios, distributed medium access control mechanisms or the decentralized networking protocols across different users contributes to the bursty nature of network traffic. To exploit the potential gain provided by such burstiness, the interference state information needs to be fed back to the transmitters. In practice, errors may occur during such feedback, leading to uncertainties of user traffic in the beamforming design problem. Here, we model such traffic uncertainties via a hidden Markov model (HMM). Assuming that perfect channel state information (CSI) or imperfect CSI is available at transmitters, our goal is to maximize the average system utility subjected to average power constraints under traffic uncertainties. The resulting problem is highly non-convex. We hence apply a series of convex approximation techniques to handle the non-convex problem. We further improve the approximation accuracy by our proposed successive convex approximation (SCA) algorithms (\textbf{HMM-SCA-1} and \textbf{HMM-SCA-2}). In our simulation results, we compared the system utilities achieved by the exhaustive search (\textbf{ES}) method and our proposed \textbf{HMM-SCA-1} when perfect CSI is available at transmitters. We demonstrated that our proposed algorithm provide a low-complexity near-optimal solution for the considered optimization problem. Specifically, \textbf{HMM-SCA-1} is 728 times faster than the \textbf{ES} algorithm on average. Even under traffic uncertainties, our proposed \textbf{HMM-SCA-1} still performs better ($\bf 9.5\%$ improvement) compared with the case where the bursty nature of the interference is not exploited at all (\textbf{Non-bursty-SCA}). For the imperfect CSI case, the simulation showed that our proposed \textbf{HMM-SCA-2} provided a $41.4\%$ improvement over \textbf{Non-bursty-SCA}. Compared with the perfect CSI case, we can observed that the performance improvement is much more significant for the imperfect CSI case. Exploiting bursty traffic is hence critical for a practical wireless communication system when channel estimation errors are considered.

[1] A. Carleial, “Interference channels,” IEEE Transactions on Information Theory, vol. 24, no. 1, pp. 60–70, 1978.
[2] M. K. Karakayali, G. J. Foschini, and R. A. Valenzuela, “Network coordination for spectrally efficient communications in cellular systems,” IEEE Wireless Communications, vol. 13, no. 4, pp. 56–61, 2006.
[3] D. Gesbert, S. Hanly, H. Huang, S. Shamai Shitz, O. Simeone, and W. Yu, “Multi-Cell MIMO Cooperative Networks: A New Look at Interference,” IEEE Journal on Selected Areas in Communications, vol. 28, no. 9, pp. 1380–1408, Dec. 2010.
[4] W.-C. Li, T.-H. Chang, C. Lin, and C.-Y. Chi, “Coordinated Beamforming for Multiuser MISO Interference Channel Under Rate Outage Constraints,” IEEE Transactions on Signal Processing, vol. 61, no. 5, pp. 1087–1103, Mar. 2013.
[5] C. Lin, C.-J. Lu, and W.-H. Chen, “Outage-Constrained Coordinated Beamforming With Opportunistic Interference Cancellation,” IEEE Transactions on Signal Processing, vol. 62, no. 16, pp. 4311–4326, Aug. 2014.
[6] E. Jorswieck, E. Larsson, and D. Danev, “Complete Characterization of the Pareto Boundary for the MISO Interference Channel,” IEEE Transactions on Signal Processing, vol. 56, no. 10, pp. 5292–5296, Oct. 2008.
[7] X. Shang, B. Chen, and H. V. Poor, “Multiuser MISO Interference Channels With Single-User Detection: Optimality of Beamforming and the Achievable Rate Region,” IEEE Transactions on Information Theory, vol. 57, no. 7, pp. 4255–4273, Jul. 2011.
[8] R. Mochaourab and E. A. Jorswieck, “Optimal Beamforming in Interference Networks with Perfect Local Channel Information,” IEEE Transactions on Signal Processing, vol. 59, no. 3, pp. 1128–1141, Mar. 2011.
[9] H. Dahrouj and W. Yu, “Coordinated beamforming for the multicell multi-antenna wireless system,” IEEE Transactions on Wireless Communications, vol. 9, no. 5, pp. 1748–1759, May 2010.
[10] L. Venturino, N. Prasad, and X. Wang, “Coordinated linear beamforming in downlink multi-cell wireless networks,” IEEE Transactions on Wireless Communications, vol. 9, no. 4, pp. 1451–
1461, Apr. 2010.
[11] N. Khude, V. Prabhakaran, and P. Viswanath, “Harnessing bursty interference,” in IEEE Information Theory Workshop on Networking and Information Theory, 2009., pp. 13–16.
[12] I.-H. Wang, C. Suh, S. Diggavi, and P. Viswanath, “Bursty interference channel with feedback,” in 2013 IEEE International Symposium on Information Theory Proceedings (ISIT)., pp. 21–25.
[13] I.-H. Wang and S. Diggavi, “Interference channels with bursty traffic and delayed feedback,” in 2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC)., pp. 205–209.
[14] S. Mishra, I.-H. Wang, and S. Diggavi, “Harnessing bursty interference in multicarrier systems with output feedback,” IEEE Transactions on Information Theory, 2017.
[15] H.-C. Tsao and C. Lin, “Utility Maximization for MISO Bursty Interference Channel,” Master’s thesis, National Tsing Hua University, of the R.O.C., 2016.
[16] D. Treeumnuk and D. C. Popescu, “Using hidden Markov models to enable performance awareness and noise variance estimation for energy detection in cognitive radio,” in Annual Conference on Information Sciences and Systems (CISS), 2012 46th., pp. 1–5.
[17] Q. Lv, Z. Mei, Y. Qiao, Y. Zhong, and Z. Lei, “Hidden markov model based user mobility analysis in LTE network,” in International Symposium on Wireless Personal Multimedia Communications (WPMC), 2014, pp. 379–384.
[18] M. B. Shenouda and T. N. Davidson, “Outage-based designs for multi-user transceivers,” in IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2009, pp. 2389–
2392.
[19] K.-Y. Wang, T.-H. Chang, W.-K. Ma, and C.-Y. Chi, “A semidefinite relaxation based conservative approach to robust transmit beamforming with probabilistic SINR constraints,” in Signal Processing Conference, 2010 18th European, pp. 407–411.
[20] K.-Y.Wang, T.-H. Chang,W.-K. Ma, A. M.-C. So, and C.-Y. Chi, “Probabilistic SINR constrained robust transmit beamforming: A bernstein-type inequality based conservative approach,” in IEEE
International Conference on Acoustics Speech and Signal Processing (ICASSP), 2011, pp. 3080–3083
[21] M. B. Shenouda and T. N. Davidson, “Convex conic formulations of robust downlink precoder designs with quality of service constraints,” IEEE Journal of Selected Topics in Signal Processing, vol. 1, no. 4, pp. 714–724, 2007.
[22] G. Zheng, K.-K. Wong, and T.-S. Ng, “Robust linear mimo in the downlink: A worst-case optimization with ellipsoidal uncertainty regions,” EURASIP Journal on Advances in Signal Processing, vol. 2008, p. 154, 2008.
[23] C. Shen, T.-H. Chang, K.-Y. Wang, Z. Qiu, and C.-Y. Chi, “Distributed robust multicell coordinated beamforming with imperfect CSI: An admm approach,” IEEE Transactions on signal processing, vol. 60, no. 6, pp. 2988–3003, 2012.
[24] Q. Li, Q. Zhang, and J. Qin, “Robust beamforming for cognitive multi-antenna relay networks with bounded channel uncertainties,” IEEE Transactions on Communications, vol. 62, no. 2, pp. 478–487, 2014.
[25] J. Mo and J. Walrand, “Fair end-to-end window-based congestion control,” IEEE/ACM Transactions on Networking (ToN), vol. 8, no. 5, pp. 556–567, 2000.
[26] Z.-Q. Luo and T.-H. Chang, SDP relaxation of homogeneous quadratic optimization: Approximation bounds and applications.
[27] M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming, version 2.1,” 2015, http://cvxr.com/cvx.
[28] Y. Huang and D. P. Palomar, “Rank-constrained separable semidefinite programming with applications to optimal beamforming,” IEEE Transactions on Signal Processing, vol. 58, no. 2, pp. 664–678, 2010.
[29] A. Beck, A. Ben-Tal, and L. Tetruashvili, “A sequential parametric convex approximation method with applications to nonconvex truss topology design problems,” Journal of Global Optimization, vol. 47, no. 1, pp. 29–51, 2010.
[30] D. P. Bertsekas, A. Nedi, A. E. Ozdaglar et al., “Convex analysis and optimization,” 2003.
[31] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge university press, 2004.
[32] J. Sturm, “Sedumi version 1.05,” McMaster University, 1998.