干擾 (interference) 對無線通訊而言是一個很大的瓶頸。由於在分散式的資源分配 (distributed resource allocation)，使用者實際在實體層 (Physical layer) 所經歷的干擾是突發 (bursty) 的，意即干擾不一定一直出現。若能妥善利用如此的特性以設計系統，則能得到顯著的效能增益。為了探討此潛在增益，我們在本篇論文考慮兩使用者多輸入單輸出突發性干擾通道 (two-user multiple-input single-output (MISO) bursty interference channel)，其中我們假設使用者之間的干擾在每個時槽 (time slot) 只有一定的機率出現。基於突發性狀態 (burstiness state) 的資訊，每個傳輸端會依照此資訊採用不同的波束 (beamforming) 以及傳輸速率來進行通訊。在此設定下，我們的目標為將平均系統效能最大化，並針對以下兩種情況考慮波束設計：a) 傳輸端有完整通道資訊 (perfect channel state information (CSI))， 以及 b) 傳輸端只有通道統計資訊 (channel distribution information (CDI))。以上兩種最佳化問題 (optimization problem) 皆為非凸(nonconvex)，並且困難。為了解決此問題，我們使用了ㄧ系列的凸近似 (convex approximation)，例如半正定放寬 (semidefinite relaxation (SDR)) 以及一階近似 (first-order approximation)。我們可進一步利用我們的連續凸近似演算法 (successive convex approximation (SCA) algorithm) 來改善我們的近似。除此之外，我們也提出了此演算法之收斂分析。透過模擬結果，我們驗證了此演算法的確能得到接近最佳解 (near-optimal solution)。此外，我們的結果也指出若能妥善運用干擾通道的突發性特性 (burstiness)，我們的確可以得到一個顯著的效能增益。

Interference, a main bottleneck in modern wireless communication, may not be always present in many practical situations. In fact, due to the bursty nature of traffic in wireless networks, the corresponding interference is also bursty in general. Such burstiness, if properly exploited, can provide significant gain in performance. To investigate this potential gain, a two-user multiple-input single- output (MISO) bursty interference channel is considered in this work. It is assumed that interference between users is only present with a certain probability. Based on the knowledge of burstiness status, each transmitter adopts a different beamforming strategy and a different rate for communication. Under this setting, we aim to maximize the average system utility and consider the optimal beamforming design for two cases: a) when perfect channel state information (CSI) is assumed, and b) when only channel distribution information (CDI) is assumed at transmitter end. Both optimization problems are nonconvex and difficult to solve. To handle such difficulty, we apply a series of convex approximation techniques such as semidefinite relaxation (SDR) and first-order approximation. Furthermore, we improve the approximation accuracy of our approximation through solving the approximated problem successively, and propose a successive convex approximation (SCA) algorithm. The convergence analysis for the proposed SCA algorithm is also provided. The near-optimal performance of our proposed SCA algorithm is demonstrated by simulations. Our results demonstrate that significant performance gain can be achieved by exploiting the bursty nature of wireless interference network.

[1] A. B. Carleial, “Interference channels,” IEEE Trans. Inf. Theory, vol. 24, pp. 60 – 70, 1978.
[2] M. Karakayali, G. Foschini, and R. Valenzuela, “Network coordination for spectrally efficient
communications in cellular systems,” IEEE Trans. Wireless Commun., pp. 56 – 61, 2006.
[3] S. Venkatesan, A. Lozano, and R. Valenzuela, “Network MIMO : Overcoming intercell interference in indoor wireless systems,” Proc. IEEE ACSSC’07, pp. 83–87, 2007.
[4] 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 J. Sel. Areas Commun., vol. 28, pp. 1380 – 1408, 2010.
[5] E. Jorswieck, E. Larsson, and D. Danev, “Complete characterization of the Pareto boundary for the MISO interference channel,” Signal Processing, IEEE Transactions on, vol. 56, no. 10, pp. 5292–5296, Oct 2008.
[6] X. Shang, B. Chen, and H. Poor, “Multiuser MISO interference channels with single-user detection: Optimality of beamforming and the achievable rate region,” IEEE Trans. Inf. Theory, vol. 57, pp. 4255 – 4273, 2011.
[7] R. Mochaourab and E. Jorswieck, “Optimal beamforming in interference networks with perfect local channel information,” IEEE Trans. Signal Process., vol. 59, no. 3, pp. 1128–1141, March 2011.
[8] Y.-F. Liu, Y.-H. Dai, and Z.-Q. Luo, “Coordinated beamforming for MISO interference channel: Complexity analysis and efficient algorithms,” IEEE Trans. Signal Process., vol. 59, pp. 1142 – 1157, 2011.
[9] R. Zakhour and D. Gesbert, “Coordination on the MISO interference channel using the virtual SINR framework,” Proc. Int. ITG Workshop Smart Antennas, Berlin, Germany, pp. 1–7, Feb 2009.
[10] R. Zhang and S. Cui, “Cooperative interference management with MISO beamforming,” IEEE Trans. Signal Process., vol. 58, pp. 5450–5458, 2010.
[11] D. A. Schmidt, C. Shi, R. A. Berry, M. L. Honig, and W. Utschick, “Distributed resource al- location schemes: Pricing algorithms for power control and beamformer design in interference networks,” IEEE Signal Process. Mag, vol. 26, pp. 53–63, 2009.
[12] J. Lindblom, E. Karipidis, and E. Larsson, “Outage rate regions for the MISO IFC,” in 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers, Nov 2009, pp. 1120–1124.
[13] E.Bjornson,R.Zakhour,D.Gesbert,andB.Ottersten,“Cooperative multicell precoding : Rate-region characterization and distributed strategies with instantaneous and statistical CSI,” IEEE Trans. Signal Process., vol. 58, pp. 4298–4310, 2010.
[14] S. V. Hanly and D. N. C. Tse, “Multiaccess fading channels– part II: Delay-limited capacities,” IEEE Trans. Inf. Theory, vol. 44, no. 7, pp. 2816–2831, Nov. 1998.
[15] S. Kandukuri and S. Boyd, “Optimal power control in interference-limited fading wireless channels with outage-probability specifications,” IEEE Trans. Wireless Commun., vol. 1, no. 1, pp. 46–55, Jan 2002.
[16] S. Ghosh, B. Rao, and J. Zeidler, “Outage-efficient strategies for multiuser MIMO networks with channel distribution information,” IEEE Trans. Signal Process., vol. 58, no. 12, pp. 6312–6324, Dec 2010.
[17] W.-C. Li, T.-H. Chang, C. Lin, and C.-Y. Chi, “Coordinated beamforming for multiuser MISO interference channel under rate outage constraints,” IEEE Trans. Signal Process., vol. 61, no. 5, pp. 1087–1103, March 2013.
[18] I.-H. Wang, C. Suh, S. Diggavi, and P. Viswanath, “Bursty interference channel with feedback,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), pp. 21–25, 2013.
[19] N. Khude, V. Prabhakaran, and P. Viswanath, “Harnessing bursty interference,” in Proc. IEEE Inf. Theory Workshop (ITW 2009), Volos, Greece, Jun 2009.
[20] N. Khude, V. Prabhakaran, and P. Viswanath, “Opportunistic interference management,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), pp. 2076 – 2080, 2009.
[21] Z.-Q. Luo and T.-H. Chang, SDP relaxation of homogeneous quadratic optimization: Approximation bounds and applications.
[22] J. Mo and J. Walrand, “Fair end-to-end window-based congestion control,” IEEE/ACM Trans. Netw., vol. 8, pp. 556–567, 2000.
[23] Z.-Q. Luo, W.-K. Ma, A. M.-C. So, Y. Ye, and S. Zhang, “Semidefinite relaxation of quadratic optimization problems,” IEEE Trans. Signal Process. Mag, vol. 27, no. 3, pp. 20 –34, May 2010.
[24] M.Grant and S.Boyd,“CVX:Matlab software for disciplined convex programming,version2.1,” 2015, http://cvxr.com/cvx.
[25] Y. Huang and D. Palomar, “Rank-constrained separable semidefinite programming with applications to optimal beamforming,” IEEE Trans. Signal Process., vol. 58, no. 2, pp. 664–678, Feb 2010.
[26] J. G. Proakis and M. Salehi, Digital Communications, 5th ed. McGraw-Hill, 2007.
[27] E. Karipidis, A. Grundinger, J. Lindblom, and E. G. Larsson, “Pareto-optimal beamforming for the miso interference channel with partial CSI,” 2009 3rd IEEE International Workshop on Com- putational Advances in Multi-Sensor Adaptive Processing, 2009.
[28] B. R. Marks and G. P. Wright, “Technical note—a general inner approximation algorithm for nonconvex mathematical programs,” Operations Research, vol. 26, no. 4, pp. 681–683, 1978.
[29] D. P. Bertsekas, A. Nedi ́c, and A. E. Ozdaglar, Convex Analysis and Optimization. Cambridge, Massachusetts: Athena Scientific, 2003.
[30] R. A. Gamboa and B. Middleton, Taylor’s Formula with Remainder, Grenoble, France, April 8-9, 2002.