Robust resource allocation in future wireless networks

Robust Resource Allocation in Future Wireless Networks

Volumn , Issue , 2017, Pages 1-245

  Parsaeefard, Saeedeh ^a   Sharafat, Ahmad Reza ^b   Mokari, Nader ^b  

^a Research Institute for Communications and Information Technology ^*  (Iran)

^b TARBIAT MODARES UNIVERSITY   (Iran)

Author keywords

Cognitive radio networks; Distributed resource allocation; Ergodic resource allocation; Heterogonous wireless networks; Homogenous wireless networks; Next generation wireless; Robust optimization theory; Wireless networks; Worst case robust optimization

Indexed keywords

COGNITIVE RADIO; OPTIMIZATION; RESOURCE ALLOCATION; SITE SELECTION;

COGNITIVE RADIO NETWORK; DISTRIBUTED RESOURCE ALLOCATION; ERGODICS; ROBUST OPTIMIZATION; ROBUST OPTIMIZATION THEORY;

WIRELESS NETWORKS;

EID: 85034778110     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-319-50389-9     Document Type: Book

References (336)

1. C. Liang, F. Yu, X. Zhang, Information-centric network function virtualization over 5G mobile wireless networks.IEEE Netw. 29(3), 68-74 (2015)
2. E. Hossain, M. Hasan, 5G cellular: key enabling technologies and research challenges. IEEE Instrum. Meas. Mag. 18(3), 11-21 (2015)
3. S. Sun, M. Kadoch, L. Gong, B. Rong, Integrating network function virtualization with SDR and SDN for 4G/5G networks. IEEE Netw. 29(3), 54-59 (2015)
4. N. Zhang, N. Cheng, A. Gamage, K. Zhang, J. Mark, X. Shen, Cloud assisted HetNets toward 5G wireless networks. IEEE Commun. Mag. 53(6), 59-65 (2015)
5. M. Peng, Y. Li, Z. Zhao, C. Wang, System architecture and key technologies for 5G heterogeneous cloud radio access networks. IEEE Netw. 29(2), 6-14 (2015)
6. M. Chiang, P. Hande, T. Lan, C.W. Tan, Power control in wireless cellular networks. Found. Trends Netw. 2(4), 381-533 (2008)
7. Z. Han, K.J.R. Liu, Resource Allocation for Wireless Neworks: Basics, Techniques, and Applications (Cambridge University Press, New York, 2008)
8. S. Stanczak, M. Wiczanowski, H. Boche, Resource Allocation in Wireless Networks: Theory and Algorithms (Springer, Berlin, 2006)
9. R.D. Yates, A framework for uplink power control in cellular radio systems. IEEE J. Sel. Areas Commun. 17(7), 1341-1347 (1995)
10. S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, 2004)
11. M. Chiang, Geometric programming for communication systems. Found. Trends Commun. Inf. Theory 2(1/2), 1-154 (2005)
12. G. Xu, Global optimization of signomial geometric programming problems. Eur. J. Oper. Res. 233(3), 500-510 (2014)
13. D.T. Ngo, S. Khakurel, T. Le-Ngoc, Joint subchannel assignment and power allocation for OFDMA femtocell networks. IEEE Trans. Wirel. Commun. 13(1), 342-355 (2014)
14. T. Wang, L. Vandendorpe, Iterative resource allocation for maximizing weighted sum min-rate in downlink cellular OFDMA systems. IEEE Trans. Signal Process. 59(1), 223-234 (2011)
15. J. Papandriopoulos, J.S. Evans, SCALE: a low-complexity distributed protocol for spectrum balancing in multiuser DSL networks. IEEE Trans. Inf. Theory 55(8), 3711-3724 (2009)
16. A. Ben-Tal, A. Nemirovski, Robust solutions to uncertain programs. Oper. Res. Lett. 25, 1-13 (1999)
17. A.B. Gershman, N.D. Sidiropoulos, Space-Time Processing for MIMO Communications (Wiley, New York, 2005)
18. A. Ben-Tal, A. Nemirovski, Selected topics in robust convex optimization. Math. Program. 112(1), 125-158 (2007)
19. D. Bertsimas, D. Pachamanovab, M. Sim, Robust linear optimization under general norms. Oper. Res. Lett. 4(32), 510-516 (2004)
20. G. Calafiore, M. Campi, Uncertain convex programs: randomized solutions and confidence levels. Math. Program. A (102), 25-46 (2005)
21. C.A. Floudas, P.M. Pardalos (eds.), Encyclopedia of Optimization (Kluwer, Dordrecht, 2001)
22. Z.-Q. Luo, S. Zhang, Dynamic spectrum management: complexity and duality. IEEE J. Sel. Top. Sign. Proces. 2(1), 57-72 (2008)
23. C.W. Tan, S. Friedland, S.H. Low, Spectrum management in multiuser cognitive wireless networks: optimality and algorithm. IEEE J. Sel. Areas Commun. 29(2), 421-430 (2011)
24. C.W. Tan, M. Chiang, R. Srikant, Maximizing sum rate and minimizing MSE on multiuser downlink: optimality, fast algorithms and equivalence via max-min SINR. IEEE Trans. Signal Process. 59(12), 6127-6143 (2011)
25. C.W. Tan, S. Friedland, S.H. Low, Nonnegative matrix inequalities and their application to nonconvex power control optimization. SIAM J. Matrix Anal. Appl. 32(3), 1030-1055 (2011)
26. G. Scutari, D.P. Palomar, S. Barbarossa, Optimal linear precoding strategies for wideband noncooperative systems based on game theory- Part I: Nash equilibria. IEEE Trans. Signal Process. 56(3), 1230-1249 (2008)
27. J. Wang, G. Scutari, D.P. Palomar, Robust MIMO cognitive radio via game theory. IEEE Trans. Signal Process. 59(3), 1183-1201 (2011)
28. Y. Su, M. van der Schaar, A new perspective on multi-user power control games in interference channels. IEEE Trans. Wirel. Commun. 8(6), 2910-2919 (2009)
29. Z. Han, Z. Ji, K. Liu, Non-cooperative resource competition game by virtual referee in multicell OFDMA networks. IEEE J. Sel. Areas Commun. 25(6), 1079-1090 (2007)
30. D.P. Palomar, Y.C. Eldar, Convex Optimization in Signal Processing and Communications (Cambridge University Press, Cambridge, 2010)
31. S. Sorooshyari, Z. Gajic, Autonomous dynamic power control for wireless networks: user-centric and network-centric consideration. IEEE Trans. Wirel. Commun. 7(3), 1004-1015 (2008)
32. M. Haddad, S. Elayoubi, E. Altman, Z. Altman, A hybrid approach for radio resource management in heterogeneous cognitive networks. IEEE J. Sel. Areas Commun. 29(4), 831-842 (2011)
33. D. Niyato, E. Hossain, Competitive pricing for spectrum sharing in cognitive radio networks: dynamic game, inefficiency of Nash equilibrium, and collusion. IEEE J. Sel. Areas Commun. 26(1), 192-202 (2008)
34. D.P. Palomar, M. Chiang, A tutorial on decomposition methods for network utility maximization. IEEE J. Sel. Areas Commun. 24(8), 1439-1451 (2006)
35. F. Wang, M. Krunz, S. Cui, Price-based spectrum management in cognitive radio networks. IEEE J. Sel. Top. Sign. Proces. 2(1), 74-87 (2008)
36. D. Niyato, E. Hossain, A cooperative game framework for bandwidth allocation in 4G heterogeneous wireless networks, in Proceedings of IEEE International Conference on Communications (ICC), vol. 9 (2006), pp. 4357-4362
37. R. Kaewpuang, D. Niyato, P. Wang, E. Hossain, A framework for cooperative resource management in mobile cloud computing. IEEE J. Sel. Areas Commun. 31(12), 2685-2700 (2013)
38. E. Altman, T. Jimenez, N. Vicuna, R. Marquez, Coordination games over collision channels, in 6th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks and Workshops (WiOPT) (2008), pp. 523-527
39. L. Song, D. Niyato, Z. Han, E. Hossain, Game-theoretic resource allocation methods for device-to-device communication. IEEE Trans. Wirel. Commun. 21(3), 136-144 (2014)
40. W. Zame, J. Xu, M. van der Schaar, Cooperative multi-agent learning and coordination for cognitive radio networks. IEEE J. Sel. Areas Commun. 32(3), 464-477 (2014)
41. CVX Research, CVX: Matlab software for disciplined convex programming, version 2.0 (2012). http://cvxr.com/cvx
42. M. Chiang, C.W. Tan, D. Palomar, D. O’Neill, D. Julian, Power control by geometric programming. IEEE Trans. Wirel. Commun. 6(7), 2640-2651 (2007)
43. S. Boyd, S.J. Kim, L. Vandenberghe, A. Hassibi, A tutorial on geometric programming. Optim. Eng. 8(1), 67-127 (2007)
44. J.-S. Pang, G. Scutari, D. Palomar, F. Facchinei, Design of cognitive radio systems under temperature-interference constraints: a variational inequality approach. IEEE Trans. Signal Process. 58(6), 3251-3271 (2010)
45. F. Facchinei, J.S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problem (Springer, New York, 2003)
46. G. Scutari, D.P. Palomar, F. Facchinei, J.-S. Pang, Convex optimization, game theory, and variational inequality theory in multiuser communication systems. IEEE Signal Process. Mag. 27(1), 35-49 (2010)
47. D. Fudenberg, J. Tirole, Game Theory (MIT, Cambridge, 1991)
48. B.R. Marks, G.P. Wright, A general inner approximation algorithm for nonconvex mathematical programs. Oper. Res. 26(4), 681-683 (1978)
49. M. Avriel, A. Williams, Complementary geometric programming. SIAM J. Appl. Math. 19(1), 125-141 (1970)
50. D. Nguyen, T. Le-Ngoc, Sum-rate maximization in the multicell MIMO multiple-access channel with interference coordination. IEEE Trans. Wirel. Commun. 13(1), 36-48 (2014)
51. H. Al-Shatri, T. Weber, Achieving the maximum sum rate using D.C. programming in cellular networks. IEEE Trans. Signal Process. 60(3), 1331-1341 (2012)
52. D.P. Bertsekas, J. Tsitsiklis, Parallel and distributed computation: numerical methods, Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, 2003
53. L. El-Ghaoui, F. Oustry, H. Lebret, Robust solutions to uncertain semidefinite programs. SIAM J. Optim. 9, 33-52 (1998)
54. A. MacKenzie, S. Wicker, Game theory and the design of self-configuring, adaptive wireless networks. IEEE Commun. Mag. 39(39), 126-131 (2001)
55. E. Altman, T. Boulogne, R. El-Azouzi, T. Jimenez, L. Wynter, A survey on networking games in telecommunications. Comput. Oper. Res. 33(2), 286-311 (2006)
56. G. Scutari, D.P. Palomar, S. Barbarossa, Optimal linear precoding strategies for wideband noncooperative systems based on game theory - Part II: algorithms. IEEE Trans. Signal Process. 56(3), 1250-1267 (2008)
57. A.J.G. Anandkumar, A. Anandkumar, S. Lambotharan, J. Chambers, Robust rate maximization game under bounded channel uncertainty. IEEE Trans. Veh. Technol. 60(9), 4471-4486 (2011)
58. P. Setoodeh, S. Haykin, Robust transmit power control for cognitive radio. Proc. IEEE 97(5), 915-939 (2009)
59. G. Scutari, F. Facchinei, J.-S. Pang, L. Lampariello, Equilibrium selection in power control games on the interference channel, in INFOCOM (2012), pp. 675-683
60. X. Zhang, D.P. Palomar, B. Ottersten, Statistically robust design of linear MIMO transceivers. IEEE Trans. Signal Process. 56(8), 3678-3689 (2008)
61. S. Zhou, G.B. Giannakis, Optimal transmitter eigen-beamforming and space-time block coding based on channel mean feedback. IEEE Trans. Signal Process. 50(10), 599-613 (2002)
62. G. Zheng, K.-K. Wong, B. Ottersten, Robust cognitive beamforming with bounded channel uncertainties. IEEE Trans. Signal Process. 57(12), 4871-4881 (2009)
63. G. Zheng, S. Ma, K.-K. Wong, T.-S. Ng, Robust beamforming in cognitive radio. IEEE Trans. Wirel. Commun. 9(2), 570-576 (2010)
64. L. Zhang, Y.-C. Liang, Y. Xin, H.V. Poor, Robust cognitive beamforming with partial channel state information. IEEE Trans. Wirel. Commun. 8(8), 4143-4153 (2009)
65. K. Yang, J. Huang, Y. Wu, X. Wang, M. Chiang, Distributed robust optimization - Part I: framework and example. J. Optim. Eng. 15(1), 35-67 (2014)
66. C.W. Tan, D. Palomar, M. Chiang, Energy robustness tradeoff in cellular network power control. IEEE/ACM Trans. Netw. 17(3), 912-925 (2009)
67. N. Bambos, C. Chen, G.J. Pottie, Channel access algorithms with active link protection for wireless communication networks with power control. IEEE/ACM Trans. Netw. 8(5), 583-597 (2000)
68. B. Dimitris, M. Sim, The price of robustness. Oper. Res. 52(1), 35-53 (2004)
69. A. Nemirovski, A. Shapiro, Convex approximations of chance constrained programs. SIAM J. Optim. 17(4), 969-996 (2006)
70. S. Parsaeefard, A.R. Sharafat, Robust worst-case interference control in underlay cognitive radio networks. IEEE Trans. Veh. Technol. 61(8), 3731-3745 (2012)
71. Y. Wu, K. Yang, J. Huang, X. Wang, M. Chiang, Distributed robust optimization - Part II: wireless power control, http://personal.ie.cuhk.edu.hk/~jwhuang/publication/DRO2.pdf.
72. Y. Su, M. van der Schaar, Linearly coupled communication games. IEEE Trans. Commun. 59(9), 2543-2553 (2011)
73. Y. Su, M. van der Schaar, Structural solutions for additively coupled sum constrained games. IEEE Trans. Commun. 60(12), 3779-3796 (2012)
74. J.L. Massey, An introduction to contemporary cryptology. Proc. IEEE 76(5), 533-549 (1988)
75. L. Dong, Z. Han, A.P. Petropulu, H.V. Poor, Improving wireless physical layer security via cooperating relays. IEEE Trans. Signal Process. 58(3), 1875-1888 (2010)
76. Y. Liang, H.V. Poor, S.S. Shamai, Information theoretic security. Found. Trends Commun. Inf. Theory 5(45), 355-580 (2009)
77. F. Renna, N. Laurenti, H. Poor, Physical-layer secrecy for OFDM transmissions over fading channels. IEEE Trans. Inf. Forensics Secur. 7(4), 1354-1367 (2012)
78. A. Mukherjee, A. Swindlehurst, Jamming games in the MIMO wiretap channel with an active eavesdropper. IEEE Trans. Signal Process. 61(1), 82-91 (2013)
79. Y. Liang, A. Somekh-Baruch, H. Poor, S. Shamai, S. Verdu, Capacity of cognitive interference channels with and without secrecy. IEEE Trans. Inf. Theory 55(2), 604-619 (2009)
80. Y. Wu, K. Liu, An information secrecy game in cognitive radio networks. IEEE Trans. Inf. Forensics Secur. 6(3), 831-842 (2011)
81. S. Parsaeefard, T. Le-Ngoc, Improving wireless secrecy rate via full-duplex relay-assisted protocols. IEEE Trans. Inf. Forensics Secur. 10(10), 2095-2107 (2015)
82. G. Zheng, I. Krikidis, J. Li, A. Petropulu, B. Ottersten, Improving physical layer secrecy using full-duplex jamming receivers. IEEE Trans. Signal Process. 61(20), 4962-4974 (2013)
83. P.-H. Lin, S.-H. Lai, S.-C. Lin, H.-J. Su, On secrecy rate of the generalized artificial-noise assisted secure beamforming for wiretap channels. IEEE J. Sel. Areas Commun. 31(9), 1728-1740(2013)
84. D. Ng, E.S. Lo, R. Schober, Secure resource allocation and scheduling for OFDMA decode-and-forward relay networks. IEEE Trans. Wirel. Commun. 10(10), 3528-3540 (2011)
85. W. Saad, X. Zhou, B. Maham, T. Basar, H. Poor, Tree formation with physical layer security considerations in wireless multi-hop networks. IEEE Trans. Wirel. Commun. 11(11), 3980-3991 (2012)
86. H. Sakran, M. Shokair, O. Nasr, S. El-Rabaie, A. El-Azm, Proposed relay selection scheme for physical layer security in cognitive radio networks. IET Commun. 6(16), 2676-2687 (2012)
87. Z. Han, N. Marina, M. Debbah, A. Hjorungnes, Physical layer security game: how to date a girl with her boyfriend on the same table, in Proceedings of International Conference on Game Theory for Networks (2009), pp. 287-294
88. J. Yue, B. Yang, X. Guan, Fairness-guaranteed pricing and power allocation with a friendly jammer against eavesdropping, in Proceedings of International Conference on Wireless Communications Signal Processing (WCSP) (2012), pp. 1-6
89. A. Alvarado, G. Scutari, J.-S. Pang, A new decomposition method for multiuser DC-programming and its applications. IEEE Trans. Signal Process. 62(11), 2984-2998 (2014)
90. N. Mokari, S. Parsaeefard, H. Saeedi, P. Azmi, Cooperative secure resource allocation in cognitive radio networks with guaranteed secrecy rate for primary users. IEEE Trans. Wirel. Commun. 13(2), 1058-1073 (2014)
91. Q. Zhang, X. Huang, Q. Li, J. Qin, Cooperative jamming aided robust secure transmission for wireless information and power transfer in MISO channels. IEEE Trans. Commun. 63(3), 906-915 (2015)
92. W. Liu, X. Zhou, S. Durrani, P. Popovski, Secure communication with a wireless-powered friendly jammer. IEEE Trans. Wirel. Commun. 15(1), 401-4015 (2016)
93. C. Wang, H.-M. Wang, X. gen Xia, C. Liu, Uncoordinated jammer selection for securing SIMOME wiretap channels: a stochastic geometry approach. IEEE Trans. Wirel. Commun. 14(5), 2596-2612(2015)
94. Z. Chu, M. Johnston, S. Le Goff, Alternating optimization for MIMO secrecy channel with a cooperative jammer, in Proceedings of IEEE 81st Vehicular Technology Conference (VTC Spring) (2015), pp. 1-5
95. X. Chen, C. Yuen, Z. Zhang, Exploiting large-scale MIMO techniques for physical layer security with imperfect channel state information, in Proceedings of IEEE Global Communications Conference (GLOBECOM) (2014), pp. 1648-1635
96. T. Riihonen, S. Werner, R. Wichman, Hybrid full-duplex/half-duplex relaying with transmit power adaptation. IEEE Trans. Wirel. Commun. 10(9), 3074-3085 (2011)
97. S. Parsaeefard, T. Le-Ngoc, Secrecy rate with friendly full-duplex relay, in Proceedings of IEEE Wireless Communications and Networking Conference (WCNC) (2015)
98. S. Parsaeefard, T. Le-Ngoc, Full-duplex relay with jamming protocol for improving physical-layer security, in Proceedings of IEEE 25 th International Symposium on Personal, Indoor and Mobile Radio Communications - (PIMRC) (2014)
99. A. Mukherjee, A. Swindlehurst, A full-duplex active eavesdropper in MIMO wiretap channels: construction and countermeasures, in Conference Record of the Forty Fifth Asilomar Conference on Signals, Systems and Computers (ASILOMAR) (2011), pp. 265-269
100. G. Chen, Y. Gong, P. Xiao, J. Chambers, Physical layer network security in the Full-duplex relay system. IEEE Trans. Inf. Forensics Secur. 10(3), 574-583 (2015)
101. G. Scutari, D.P. Palomar, S. Barbarossa, Cognitive MIMO radio: a competitive optimality design based on subspace projections. IEEE Signal Process. Mag. 2(6), 815-826 (2008)
102. A.P. Iserte, D.P. Palomar, A.I.P. Neira, M.A. Lagunas, A robust MAXIMIN approach for MIMO communications with imperfect channel state information based on convex optimization. IEEE Trans. Signal Process. 46(1), 346-360 (2006)
103. G. Scutari, D.P. Palomar, J.-S. Pang, F. Facchinei, Flexible design of cognitive radio wireless systems: from game theory to variational inequality theory. IEEE Signal Process. Mag. 26(5), 107-123 (2009)
104. A. Goldsmith, S.A. Jafar, I. Marie, S. Srinivasa, Breaking spectrum gridlock with cognitive radios: an information theoretic perspective. Proc. IEEE 97(5), 894-914 (2009)
105. I.F. Akyildiz, W.Y. Lee, M.C. Vuran, S. Mohanty, Next generation dynamic spectrum access cognitive radio wireless networks: a survey. Comput. Netw. 50(13), 2127-2159 (2006)
106. S. Haykin, Cognitive radio: brain-empowered wireless communications. IEEE J. Sel. Areas Commun. 23(2), 201-220 (2005)
107. Q. Zhao, B. Sadler, A survey of dynamic spectrum access. IEEE Signal Process. Mag. 24(3), 79-89 (2007)
108. B. Wang, K. Liu, Advances in cognitive radio networks: a survey. IEEE J. Sel. Top. Sign. Proces. 5(1), 5-23 (2011)
109. D.I. Kim, L.B. Le, E. Hossain, Joint rate and power allocation for cognitive radios in dynamic spectrum access environment. IEEE Trans. Wirel. Commun. 7(12), 5517-5527 (2008)
110. C.W. Tan, D. Palomar, M. Chiang, Energy robustness tradeoff in cellular network power control. IEEE/ACM Trans. Netw. 17(3), 912-925 (2009)
111. S. Parsaeefard, A.R. Sharafat, Robust distributed power control in cognitive radio networks. IEEE Trans. Mob. Comput. 12(4), 609-620 (2013)
112. S. Parsaeefard, A.R. Sharafat, Robust worst-case interference control in underlay cognitive radio networks. IEEE Trans. Veh. Technol. 61(8), 3731-3745 (2012)
113. N. Gatsis, A.G. Marques, G.B. Giannakis, Power control for cooperative dynamic spectrum access networks with diverse QoS constraints. IEEE Trans. Commun. 58(3), 933-944 (2010)
114. C.U. Saraydar, N.B. Mandayam, D.J. Goodman, Efficient power control via pricing in wireless data networks. IEEE Trans. Commun. 50(2), 291-303 (2002)
115. M.W.S. Stanczak, H. Boche, Resource Allocation in Wireless Networks: Theory and Algorithms (Springer, Berlin, 2006)
116. M. Chiang, P. Hande, T. Lan, C.W. Tan, Power control in wireless cellular networks. Found. Trends Netw. 2(4), 381-533 (2008)
117. L.B. Le, E. Hossain, Resource allocation for spectrum underlay in cognitive wireless networks. IEEE Trans. Wirel. Commun. 7(12), 5306-5315 (2008)
118. M. Chiang, C.W. Tan, D. Palomar, D. O’Neill, D. Julian, Power control by geometric programming. IEEE Trans. Wirel. Commun. 6(7), 2640-2651 (2007)
119. M. Chiang, Geometric programming for communication systems. Found. Trends Commun. Inf. Theory 2(1/2), 1-154 (2006)
120. A. Ben-Tal, A. Nemirovski, Selected topics in robust convex optimization. Math. Program. 1(1), 125-158 (2007)
121. K. Yang, J. Huang, Y. Wu, X. Wang, M. Chiang, Distributed robust optimization, Part I: framework and example. Springer J. Optim. Eng. 15(1), 35-67 (2014)
122. S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, 2004)
123. B. Dimitris, D. Pachamanovab, M. Sim, Robust linear optimization under general norms. Oper. Res. Lett. 4(32), 510-516 (2004)
124. I. CVX Research, CVX: Matlab software for disciplined convex programming, version 2.0. http://cvxr.com/cvx, Aug (2012)
125. R.D. Yates, A framework for uplink power control in cellular radio systems. IEEE J. Sel. Areas Commun. 17(7), 1341-1347 (1995)
126. D.P. Bertsekas, J. Tsitsikklis, Parallel and Distributed Computation: Numerical Methods (Prentice Hall, Englewood Cliffs, 1999)
127. Y. Xing, C.N. Mathur, M.A. Haleem, R. Chandramouli, K.P. Subbalakshmi, Dynamic spectrum access with QoS and interference temperature constraints. IEEE Trans. Mob. Comput. 6(4), 423-433(2007)
128. B. Dimitris, M. Sim, The price of robustness. Oper. Res. 52(1), 35-53 (2004)
129. D.G. Cacuci, Sensitivity and Uncertainty Analysis (Chapman and Hall/CRC, Boca Raton, 2003)
130. D.P. Palomar, M. Chiang, A tutorial on decomposition methods for network utility maximization. IEEE J. Sel. Areas Commun. 24(8), 1439-1451 (2006)
131. Z.-Q. Luo, S. Zhang, Dynamic spectrum management: Complexity and duality. IEEE J. Sel. Areas Commun. 2(1), 57-73 (2008)
132. W. Yu, R. Lui, Dual methods for nonconvex spectrum optimization of multicarrier systems. IEEE Trans. Commun. 54(7), 1310-1322 (2006)
133. K. Son, B.C. Jung, S. Chong, D.K. Sung, Opportunistic underlay transmission in multi-carrier cognitive radio systems, in Proceeding of IEEE WCNC, Budapest, April 2009, pp. 1-6
134. K. Son, B.C. Jung, S. Chong, D.K. Sung, Power allocation for OFDM-based cognitive radio systems under outage constraints, in Proceedings of IEEE ICC, Cape Town, May 2010, pp. 1-5
135. N. Mokari, S. Parsaeefard, P. Azmi, H. Saeedi, Robust ergodic uplink resource allocation in underlay OFDMA cognitive radio networks. IEEE Trans. Mob. Comput. 15(2), 419-431 (2015)
136. N. Mokari, S. Parsaeefard, H. Saeedi, P. Azmi, E. Hossain, Secure robust ergodic uplink resource allocation in relay-assisted cognitive radio networks. IEEE Trans. Signal Process. 63(2), 291-304 (2015)
137. N. Mokari, S. Parsaeefard, H. Saeedi, P. Azmi, Cooperative secure resource allocation in cognitive radio networks with guaranteed secrecy rate for primary users. IEEE Trans. Wirel. Commun. 13(2), 1058-1073 (2014)
138. S. Parsaeefard, A. Sharafat, M. Rasti, Robust probabilistic distributed power allocation by chance constraint approach, in Proceedings of IEEE 21st International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), Sept 2010, pp. 2162-2167
139. M. Hasan, E. Hossain, D.I. Kim, Resource allocation under channel uncertainties for relay-aided device-to-device communication underlaying LTE-A cellular networks. IEEE Trans. Wirel. Commun. 13(4), 2322-2338 (2014)
140. S. Mallick, R. Devarajan, R. Loodaricheh, V. Bhargava, Robust resource optimization for cooperative cognitive radio networks with imperfect CSI. IEEE Trans. Wirel. Commun. 14(2), 907-920 (2015)
141. Y. Zhang, X. Wang, G. Giannakis, S. Hu, Distributed robust resource allocation for renewable powered wireless cellular networks, in Proceedings of IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom), May 2015, pp. 210-214
142. D. Fudenberg, J. Tirole, Game Theory (MIT Press, Cambridge, MA, 1991)
143. D.P. Palomar, Y.C. Eldar, Convex Optimization in Signal Processing and Communications (Cambridge University Press, Cambridge, 2010)
144. G. Scutari, D.P. Palomar, S. Barbarossa, Optimal linear precoding strategies for wideband noncooperative systems based on game theory- Part I: nash equilibria. IEEE Trans. Signal Process. 56(3), 1230-1249 (2008)
145. G. Scutari, D.P. Palomar, S. Barbarossa, Optimal linear precoding strategies for wideband noncooperative systems based on game theory-Part II: algorithms. IEEE Trans. Signal Process. 56(3), 1250-1267 (2008)
146. A.J.G. Anandkumar, A. Anandkumar, S. Lambotharan, J. Chambers, Robust rate maximization game under bounded channel uncertainty. IEEE Trans. Veh. Technol. 60(9), 4471-4486 (2011)
147. J. Wang, G. Scutari, D.P. Palomar, Robust MIMO cognitive radio via game theory. IEEE Trans. Signal Process. 59(3), 1183-1201 (2011)
148. P. Setoodeh, S. Haykin, Robust transmit power control for cognitive radio. Proc. IEEE 97(5), 915-939(2009)
149. B. Wang, Y. Wu, K.R. Liu, Game theory for cognitive radio networks: an overview. Comput. Netw. 54(14), 2537-2561 (2010)
150. A. Mukherjee, S. Fakoorian, J. Huang, A. Swindlehurst, Principles of physical layer security in multiuser wireless networks: a survey. IEEE Commun. Surv. Tutor. 16(3), 1550-1573 (2014). Third quarter
151. K. Akkarajitsakul, E. Hossain, D. Niyato, D.I. Kim, Game theoretic approaches for multiple access in wireless networks: a survey. IEEE Commun. Surv. Tutor. 13(3), 372-395 (2011). Third quarter
152. S. Buzzi, H. Poor, D. Saturnino, Noncooperative waveform adaptation games in multiuser wireless communications. IEEE Signal Process. Mag. 26(5), 64-76 (2009)
153. R. Trestian, O. Ormond, G.-M. Muntean, Game theory-based network selection: solutions and challenges. IEEE Commun. Surv. Tutor. 14(4), 1212-1231 (2012), Fourth quarter
154. D. Yang, X. Fang, G. Xue, Game theory in cooperative communications. IEEE Wirel. Commun. 19(2), 44-49 (2012)
155. Y. Xu, J. Wang, Q. Wu, Z. Du, L. Shen, A. Anpalagan, A game-theoretic perspective on selforganizing optimization for cognitive small cells. IEEE Commun. Mag. 53(7), 100-108 (2015)
156. B. Ma, M.H. Cheung, V. Wong, J. Huang, Hybrid overlay/underlay cognitive femtocell networks: a game theoretic approach. IEEE Trans. Wirel. Commun. 14(6), 3259-3270 (2015)
157. J. Wei, K. Yang, G. Zhang, Z. Hu, Pricing-based power allocation in wireless network virtualization: a game approach, in Proceedings of International Wireless Communications and Mobile Computing Conference (IWCMC), August 2015, pp. 188-193
158. A. Khanafer, W. Saad, T. Basar, Context-aware wireless small cell networks: how to exploit user information for resource allocation, in Proceedings of IEEE International Conference on Communications (ICC), June 2015, pp. 3341-3346
159. M. Aghassi, D. Bertsimas, Robust game theory. Math. Program. 107(1), 231-273 (2006)
160. S. Hayashi, N. Yamashita, M. Fukushima, Robust Nash equilibria and second-order cone complementarity problems. J. Nonlinear Convex Anal. 6(2), 283-296 (2005)
161. R. Nishimura, S. Hayashi, M. Fukushima, Robust Nash equilibria in N-person non-cooperative games: uniqueness and reformulation. Pac. J. Optim. 5(2), 237-259 (2009)
162. A. Ben-Tal, A. Nemirovski, Selected topics in robust convex optimization. Math. Program. 112(1), 125-158 (2007)
163. A.B. Gershman, N.D. Sidiropoulos, Space-Time Processing for MIMO Communications (Wiley, New York, 2005)
164. R.H. Gohary, TJ. Willink, Robust IWFA for open-spectrum communications. IEEE Trans. Signal Process. 57(12), 4964-4970 (2009)
165. F. Facchinei, J.S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems (Springer, New York, 2003)
166. J.P. Aubin, Mathematical Methods of Game and Economic Theory (North-Holland, Amsterdam, New York, 2007)
167. T. Basar, G.J. Olsder, Dynamic Noncooperative Game Theory (Academic, New York, 1995)
168. I.V. Konnov, Stability and Perfection of Nash Equilibria, 2nd revised and enlarged edn. (Springer, Berlin, 1991)
169. I. Konnov, Equilibrium Models and Variational Inequalities (Elsevier, Amsterdam, 2007)
170. J.B. Rosen, Existence and uniqueness of equilibrium points for concave N-person games. Econometrica 33(3), 520-534 (1965)
171. D. Monderer, L. Shapley, Potential games. Games Econ. Behav. 14(1), 124-143 (1996)
172. T. Ui, A shapley value representation of potential games. Games Econ. Behav. 31(1), 121-135 (2000)
173. D. Topkis, Supermodularity and Complementarity. Frontiers of Economic Research (Princeton University Press, Princeton, 1998)
174. R.D. Yates, A framework for uplink power control in cellular radio systems. IEEE J. Sel. Areas Commun. 17(7), 1341-1347 (1995)
175. Y. Su, M. van der Schaar, Structural solutions for additively coupled sum constrained games. IEEE Trans. Commun. 60(12), 3779-3796 (2012)
176. Y. Su, M. van der Schaar, Decentralized knowledge and learning in strategic multi-user communication. (2011). [Online] Available: http://arxiv.org/abs/0804.2831
177. Y. Su, M. van der Schaar, Linearly coupled communication games. IEEE Trans. Commun. 59(9), 2543-2553 (2011)
178. S. Parsaeefard, A.R. Sharafat, M. van der Schaar, Robust additively coupled games in the presence of bounded uncertainty in communication networks. IEEE Trans. Veh. Technol. 63(3), 1436-1452 (2014)
179. F. Meshkati, A.J. Goldsmith, H.V. Poor, S.C. Schwartz, A game-theoretic approach to energy-efficient modulation in CDMA networks with delay QoS constraints. IEEE J. Sel. Areas Commun. 25(6), 1069-1078 (2007)
180. W. Yu, G. Ginis, J.M. Cioffi, Distributed multiuser power control for digital subscriber lines. IEEE J. Sel. Areas Commun. 20(5), 1105-1115 (2002)
181. G. Scutari, D.P. Palomar, S. Barbarossa, Competitive design of multiuser MIMO systems based on game theory: a unified view. IEEE J. Sel. Areas Commun. 26(7), 1089-1103 (2008)
182. G. Scutari, D.P. Palomar, S. Barbarossa, Asynchronous iterative water-filling for gaussian frequency-selective interference channels. IEEE Trans. Inf. Theory 54(7), 2868-2878 (2008)
183. Z.-Q. Luo, J.-S. Pang, Analysis of iterative waterfilling algorithm for multiuser power control in digital subscriber lines. EURASIP J. Appl. Signal Process. 2006, 1-10 (2006)
184. J. Wang, G. Scutari, D. Palomar, Robust MIMO cognitive radio via game theory. IEEE Trans. Signal Process. 59(3), 1183-1201 (2011)
185. S. Parsaeefard, M. van der Schaar, A.R. Sharafat, Robust power control for heterogeneous users in shared unlicensed bands. IEEE Trans. Wirel. Commun. 13(6), 3167-3182 (2014)
186. J.-S. Pang, G. Scutari, D. Palomar, F. Facchinei, Design of cognitive radio systems under temperature-interference constraints: a variational inequality approach. IEEE Trans. Signal Process. 58(6), 3251-3271 (2010)
187. Z.-Q. Luo, S. Zhang, Dynamic spectrum management: complexity and duality. IEEE J. Sel. Areas Commun. 2(1), 57-73 (2008)
188. R. Cendrillon, W. Yu, M. Moonen, J. Verlinden, T. Bostoen, Optimal multiuser spectrum balancing for digital subscriber lines. IEEE Trans. Commun. 54(5), 922-933 (2006)
189. G. Scutari, S. Barbarossa, D. Ludovici, On the maximum achievable rates in wireless meshed networks: centralized versus decentralized solutions, in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP’04), vol. 4, May 2004, pp. 573-576
190. W. Yu, R. Lui, Dual methods for nonconvex spectrum optimization of multicarrier systems. IEEE Trans. Commun. 54(7), 1310-1322 (2006)
191. I. Das, J.E. Dennis, Normal-boundary intersection: a new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM J. Optim. 8(3), 631-657 (1998)
192. D. Niyato, E. Hossain, Competitive pricing in heterogeneous wireless access networks: issues and approaches. IEEE Netw. 22(6), 4-11 (2008)
193. C.U. Saraydar, N.B. Mandayam, D.J. Goodman, Efficient power control via pricing in wireless data networks. IEEE Trans. Commun. 50(2), 291-303 (2002)
194. D. Niyato, E. Hossain, Competitive pricing for spectrum sharing in cognitive radio networks: dynamic game, inefficiency of Nash equilibrium, and collusion. IEEE J. Sel. Areas Commun. 26(1), 192-202 (2008)
195. C. Saraydar, N.B. Mandayam, D. Goodman, Pricing and power control in a multicell wireless data network. IEEE J. Sel. Areas Commun. 19(10), 1883-1892 (2001)
196. J. Escudero Garzas, M. Hong, A. Garcia, A. Garcia-Armada, Interference pricing mechanism for downlink multicell coordinated beamforming. IEEE Trans. Commun. 62(6), 1871-1883 (2014)
197. D.P. Bertsekas, J. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods (Prentice Hall, Englewood, Cliffs, NJ, 1999)
198. G. Zheng, K.-K. Wong, B. Ottersten, Robust cognitive beamforming with bounded channel uncertainties. IEEE Trans. Signal Process. 57(12), 4871-4881 (2009)
199. E.A. Gharavol, Y.-C. Liang, K. Mouthaan, Robust downlink beamforming in multiuser MISO cognitive radio networks with imperfect channel-state information. IEEE Trans. Veh. Technol. 59(6), 2852-2860 (2010)
200. I. Stupia, L. Sanguinetti, G. Bacci, L. Vandendorpe, Power control in networks with heterogeneous users: a quasi-variational inequality approach. IEEE Trans. Signal Process. 63(21), 5691-5705 (2015)
201. J. Mo, J. Walrand, Fair end-to-end window-based congestion control. IEEE Trans. Netw. 8(5), 556-567 (2000)
202. Z.-Q. Luo, J.-S. Pang, Analysis of iterative waterfilling algorithm for multiuser power control in digital subscriber lines. EURASIP J. Appl. Signal Process. pp. 1-10 (2006)
203. A.M.F. Giannessi, P.M. Pardalos, Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models (Nonconvex Optimization and Its Applications) (Springer, New York, 2002)
204. M. Fukushima, G.-H. Lin, Smoothing methods for mathematical programs with equilibrium constraints, in Informatics Research for Development of Knowledge Society Infrastructure, Department of Applied Mathematics and Physics, Kyoto University, Kyoto, March 2004, pp. 206-213
205. C.A. Floudas, P.M. Pardalos (eds.), Encyclopedia of Optimization (Kluwer Academic, Dordrecht, 2001)
206. Y. Su, M. van der Schaar, A new perspective on multi-user power control games in interference channels. IEEE Trans. Wirel. Commun. 8(6), 2910-2919 (2009)
207. L. Lai, H. El Gamal, The water-filling game in fading multiple-access channels. IEEE Trans. Inf. Theory 54(5), 2110-2122 (2008)
208. S. Guruacharya, D. Niyato, D. I. Kim, E. Hossain, Hierarchical competition for downlink power allocation in OFDMA femtocell networks. IEEE Trans. Wirel. Commun. 12(4), 1543-1553 (2013)
209. B. Fu, Z. Wei, X. Yan, K. Zhang, Z. Feng, Q. Zhang, A game-theoretic approach for bandwidth allocation and pricing in heterogeneous wireless networks, in Proceedings of IEEE Wireless Communications and Networking Conference (WCNC 2015), March 2015, pp. 1684-1689
210. S. Hamouda, M. Zitoun, S. Tabbane, A new spectrum sharing trade in heterogeneous networks, in Proceedings of IEEE 78th Vehicular Technology Conference (VTC Fall 2013), September 2013, pp. 1-5
211. V. Di Valerio, V. Cardellini, F. Lo Presti, Optimal pricing and service provisioning strategies in cloud systems: a Stackelberg game approach, in Proceedings of IEEE 6th International Conference on Cloud Computing (CLOUD 2013), June 2013, pp. 115-122
212. L. Rose, E. Belmega, W. Saad, M. Debbah, Pricing in heterogeneous wireless networks: hierarchical games and dynamics. IEEE Trans. Wirel. Commun. 13(9), 4985-5001 (2014)
213. Y. Xu, S. Mao, Stackelberg game for cognitive radio networks with MIMO and distributed interference alignment. IEEE Trans. Veh. Technol. 63(2), 879-892 (2014)
214. M. Ahmed, M. Peng, I. Ahmad, Y. Li, M. Abana, Stackelberg game based optimized power allocation scheme for two-tier femtocell network, in Proceedings ofInternational Conference on Wireless Communications Signal Processing (WCSP 2013), October 2013, pp. 1-6
215. J. Zhang, Z. Zhao, W. Li, Z. Liu, L. Xin, Joint pricing and power control for OFDMA femtocell networks using Stackelberg game, in Proceedings of 15th International Symposium on Wireless Personal Multimedia Communications (WPMC 2012), September 2012, pp. 619-622
216. L. Duan, J. Huang, B. Shou, Investment and pricing with spectrum uncertainty: a cognitive operator’s perspective. IEEE Trans. Mobile Comput. 10(11), 1590-1604 (2011)
217. L. Yang, H. Kim, J. Zhang, M. Chiang, C.W. Tan, Pricing-based decentralized spectrum access control in cognitive radio networks. IEEE/ACM Trans. Netw. 21(2), 522-535 (2013)
218. M. Haddad, S.-E. Elayoubi, E. Altman, Z. Altman, A hybrid approach for radio resource management in heterogeneous cognitive networks. IEEE J. Sel. Areas Commun. 29(4), 831-842 (2011)
219. Y. Wu, T. Zhang, D.H.K. Tsang, Joint pricing and power allocation for dynamic spectrum access networks with Stackelberg game model. IEEE Trans. Wirel. Commun. 10(1), 12-19 (2011)
220. Y. Li, X. Wang, M. Guizani, Resource pricing with primary service guarantees in cognitive radio networks: a Stackelberg game approach, in Proceedings of 28th IEEE Conference on Global Telecommunications (GLOBCOM 2009), pp. 1563-1567
221. X. Kang, R. Zhang, M. Motani, Price-based resource allocation for spectrum-sharing femtocell networks: a Stackelberg game approach. IEEE J. Sel. Areas Commun. 30(3), 538-549 (2012)
222. E. Altman, T. Boulogne, R.E. Azouzi, T. Jiménez, L. Wynter, A survey on networking games in telecommunications. Comput. Oper. Res. 33, 286-311 (2006)
223. B. Colson, P. Marcotte, G. Savard, Bilevel programming: a survey. Quart. J. Oper. Res. 3(2), 87-107 (2005)
224. J. Wang, D.P. Palomar, Worst-case robust MIMO transmission with imperfect channel knowledge. IEEE Trans. Signal Process. 57(8) (2009)
225. A. Pascual-Iserte, D. Palomar, A. Perez-Neira, M. Lagunas, A robust maximin approach for MIMO communications with imperfect channel state information based on convex optimization. IEEE Trans. Signal Process. 54(1), 346-360 (2006)
226. Z.-Q. Luo, S. Zhang, Dynamic spectrum management: complexity and duality. IEEE J. Sel. Top. Signal Process. 2(1), 57-72 (2008)
227. C.W. Tan, S. Friedland, S. Low, Spectrum management in multiuser cognitive wireless networks: optimality and algorithm. IEEE J. Sel. Areas Commun. 29(2), 421-430 (2011)
228. C.W. Tan, M. Chiang, R. Srikant, Maximizing sum rate and minimizing MSE on multiuser downlink: optimality, fast algorithms and equivalence via max-min SINR. IEEE Trans. Signal Process. 59(12), 6127-6143 (2011)
229. C.W. Tan, S. Friedland, S.H. Low, Nonnegative matrix inequalities and their application to nonconvex power control optimization. SIAM J. Matrix Anal. Appl. 32(3), 1030-1055 (2011)
230. K. Zhu, E. Hossain, A. Anpalagan, Downlink power control in two-tier cellular OFDMA networks under uncertainties: a robust Stackelberg game. IEEE Trans. Commun. 63(2), 520-535 (2015)
231. D.H. Cansever, T. Basar, A minimum sensitivity approach to incentive design problems. Large Scale Syst. 5, 233-244 (1983)
232. J. Pita, M. Jain, M. Tambe, F. Ordóñez, S. Kraus, Robust solutions to Stackelberg games: addressing bounded rationality and limited observations in human cognition. Artif. Intell. 174(15), 1142-1171 (2010)
233. K. Arrow, G. Debreu, Existence of an equilibrium for a competitive economy. Econometrica 22(3), 265-290 (1954)
234. F. Facchinei, C. Kanzow, Generalized Nash equilibrium problems. Quart. J. Oper. Res. (40R) 5(3), 173-210 (2007)
235. S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, 2004)
236. W.A. Brock, S.N. Durlauf, Local robustness analysis: theory and application. Elsevier J. Econ. Dyn. Control 29(11), 2067-2092 (2005)
237. P.D. Miller, Applied Asymptotic Analysis. Graduate Studies in Mathematics, vol. 75 (The American Mathematical Society, Providence, RI, 2006)
238. S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, 2004)
239. A. Charnes, W.W. Cooper, Programming with linear fractional functionals. Nav. Res. Logist. Q. 9, 181-186 (1962)
240. J. Gallier, The Schur complement and symmetric positive semidefinite (and definite) matrices. Penn Engineering (2010). Unpublished note, available online: http://www.cis.upenn.edu/~jean/schur-comp.pdf
241. F. Zhang, The Schur Complement and Its Applications, vol. 4 (Springer, New York, 2005)
242. Q. Li, W.K. Ma, Optimal and robust transmit designs for MISO channel secrecy by semidefinite programming. IEEE Trans. Signal Process. 59(8), 3799-3812 (2011)
243. J. Huang, A.L. Swindlehurst, Robust secure transmission in MISO channels based on worst-case optimization. IEEE Trans. Signal Process. 60(4), 1696-1707 (2012)
244. G. Zheng, K.-K. Wong, B. Ottersten, Robust cognitive beamforming with bounded channel uncertainties. IEEE Trans. Signal Process. 57(12), 4871-4881 (2009)
245. G. Zheng, K.-K. Wong, N. D. Sidiropoulos, A. Paulraj, B. Ottersten, Robust collaborative-relay beamforming. IEEE Trans. Signal Process. 57(8), 3130-3143 (2009)
246. K. Derinkuyu, M.C. Pinar, On the S-procedure and some variants. Math. Methods Oper. Res. 64(1), 55-77 (2006)
247. V. Jeyakumar, N.Q. Huy, G. Li, Necessary and sufficient conditions for S-lemma and nonconvex quadratic optimization. Optim. Eng. 10(4), 491-503 (2009)
248. D. Palomar, Y. Eldar, Convex Optimization in Signal Processing and Communications (Cambridge University Press, Cambridge, 2010)
249. Z.Q. Luo, W.K. Ma, A.M.C. So, Y. Ye, S. Zhang, Semidefinite relaxation of quadratic optimization problems. IEEE Signal Process. Mag. 27(3), 20-34 (2010)
250. H. Wolkowicz, R. Saigal, L. Vandenberghe, Handbook of Semidefinite Programming Theory, Algorithms, and Applications. Springer International Series in Operations Research and Management Science, vol. 27 (Kluwer Academic Publishers, Boston, 2000)
251. L. Vandenberghe, S. Boyd, Semidefinite programming. SIAM Rev. 38(1), 49-95 (1996)
252. M. Grant, S. Boyd, CVX: Matlab software for disciplined convex programming (web page and software) (2009), available: http://stanford.edu/~boyd/cvx
253. J. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11, 625-653 (1999). Available: http://sedumi.ie.lehigh.edu/ [Online]
254. A. Shapiro, Rank-reducibility of a symmetric matrix and sampling theory of minimum trace factor analysis. Psychometrika 47(2), 187-199 (1982)
255. A.I. Barvinok, Problems of distance geometry and convex properties of quadratic maps. Discrete Comput. Geom. 13(1), 189-202 (1995)
256. G. Pataki, On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues. Math. Oper. Res. 23(2), 339-358 (1998)
257. W. Ai, S. Zhang, Strong duality for the CDT subproblem: a necessary and sufficient condition. SIAM J. Optim. 19(4), 1735-1756 (2009)
258. W. Ai, Y.W. Huang, S. Zhang, New results on Hermitian matrix rank-one decomposition. Math. Program. 128(1-2), 253-283 (2011)
259. K.T. Phan, S.A. Vorobyov, N.D. Sidiropoulos, C. Tellambura, Spectrum sharing in wireless networks via QoS aware secondary multicast beamforming. IEEE Trans. Signal Process. 57(6), 2323-2335 (2009)
260. K. Hamdi, M.O. Hasna, A. Ghrayeb, K.B. Letaief, Opportunistic spectrum sharing in relay-assisted cognitive systems with imperfect CSI. IEEE Trans. Veh. Technol. 63(5), 2224-2235 (2014)
261. E.A. Gharavol, Y.C. Liang, K. Mouthaan, Robust downlink beamforming in multiuser MISO cognitive radio networks with imperfect channel-state information. IEEE Trans. Veh. Technol. 59(6), 2852-2860 (2010)
262. J. Peypouquet, Convex Optimization in Normed Spaces: Theory, Methods and Examples (Springer, Cham, 2015)
263. D. Golovin, A. Gupta, A. Kumar, K. Tangwongsan, All-norms and all-lp-norms approximation algorithms, in Foundations of Software Technology and Theoretical Computer Science (Springer, Berlin, 2008)
264. K.-Y. Wang, N. Jacklin, Z. Ding, C.Y. Chi, Robust MISO transmit optimization under outage-based QoS constraints in two-tier heterogeneous networks. IEEE Trans. Wireless Commun. 12(4), 1883-1897 (2013)
265. Y. Shi, J. Zhang, K.B. Letaief, Optimal stochastic coordinated beamforming for wireless cooperative networks with CSI uncertainty. IEEE Trans. Signal Process. 63(4), 960-973 (2015)
266. D. Ponukumati, F. Gao, C. Xing, Robust peer-to-peer relay beamforming: a probabilistic approach. IEEE Commun. Lett. 17(2), 1883-1897 (2013)
267. H. Stark, J.W. Woods, Probability and Random Processes with Applications to Signal Processing, 3rd edn. (Prentice Hall, Upper Saddle River, 2001)
268. X. He, Y.C. Wu, Probabilistic QoS constrained robust downlink multiuser MIMO transceiver design with arbitrarily distributed channel uncertainty. IEEE Trans. Wireless Commun. 12(12), 6292-9302 (2013)
269. A. Ben-Tal, A. Nemirovski, Selected topics in robust convex optimization. Math. Program. 1(1), 125-158 (2007)
270. A. Nemirovski, A. Shapiro, Convex approximations of chance constrained programs. SIAM J. Optim. 17(4), 969-996 (2006)
271. N.Y. Soltani, S.J. Kim, G.B. Giannakis, Chance-constrained optimization of OFDMA cognitive radio uplinks. IEEE Trans. Wireless Commun. 12(3), 1098-1107 (2013)
272. L.J. Hong, Y. Yang, L. Zhang, Sequential convex approximations to joint chance constrained programs: a Monte Carlo approach. Oper. Res. 59(3), 617-630 (2011)
273. A. Ben-Tal, L.E. Ghaoui, A. Nemirovski, Robust Optimization. Princeton Series in Applied Mathematics (Princeton University Press, Princeton, NJ, 2009)
274. K.-Y. Wang, A.M.C. So, T.H. Chang, W.K. Ma, C.Y Chi, Outage constrained robust transmit optimization for multiuser MISO downlinks: tractable approximations by conic optimization. IEEE Trans. Signal Process. 62(21), 5690-5705 (2014)
275. S.S. Cheung, A.M.-C. So, K. Wang, Linear matrix inequalities with stochastically dependent perturbations and applications to chance constrained semidefinite optimization. SIAM J. Optim. 22(4), 1394-1430 (2012)
276. S. Janson, Large deviations for sums of partly dependent random variables. Random Struct. Algorithm. 24(3), 234-248 (2004)
277. I. Bechar, A Bernstein-type inequality for stochastic processes of quadratic forms of Gaussian variables (2009). Available: http://arxiv.org/abs/0909.3595s [Online]
278. K.Y. Wang, N. Jacklin, Z. Ding, C.-Y. Chi, Robust MISO transmit optimization under outage-based QoS constraints in two-tier heterogeneous networks. IEEE Trans. Wireless Commun. 12(4), 1883-1897 (2013)
279. N. Vucic, H. Boche, A tractable method for chance-constrained power control in downlink multiuser MISO systems with channel uncertainty. IEEE Signal Process. Lett. 16(5), 346-349 (2009)
280. S. Dharmadhikari, K. Joag-dev, Unimodality, Convexity, and Applications (Academic Press, Boston, 1988)
281. S. Dharmadhikari, K. Joag-dev, The Gauss-Tchebyshev inequality for unimodal distributions. Theory Probab. Appl. 30(2), 867-871 (1985)
282. A.W. Marshall, I. Olkin, Inequalities: Theory of Majorization and Its Applications (Academic Press, New York, 1979)
283. D. Zheng, J. Liu, K.K. Wong, H. Chen, L. Chen, Robust peer-to-peer collaborative-relay beamforming with ellipsoidal CSI uncertainties. IEEE Commun. Lett. 16(4), 442-445 (2012)
284. L. Mirsky, A trace inequality of John von Neumann. Monatsh. Math. 79(4), 303-306 (1975)
285. Z. Chu, K. Cumanan, Z. Ding, M. Johnston, S.L. Goff, Secrecy rate optimizations for a MIMO secrecy channel with a cooperative jammer. IEEE Trans. Veh. Technol. 64(5), 1833-1847 (2015)
286. W. Dinkelbach, On nonlinear fractional programming. Manag. Sci. 13(7), 492-498 (1967)
287. S. Schaible, Fractional programming. II, on Dinkelbach’s algorithm. Manag. Sci. 22(8), 868-873 (1976)
288. A. Beck, A. Ben-Tal, L. Tetruashvili, A sequential parametric convex approximation method with applications to nonconvex truss topology design problems. J. Glob. Optim. 47(1), 29-51 (2010)
289. W. Yu, R. Lui, Dual methods for nonconvex spectrum optimization of multicarrier systems. IEEE Trans. Commun. 54(7), 1310-1322 (2006)
290. A. Ben-Tal, A. Nemirovski, Robust solutions of linear programming problems contaminated with uncertain data. Math. Program. 88(3), 411-424 (2000)
291. R.J. Stern, H. Wolkowicz, Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations. SIAM J. Optim. 5(2), 286-313 (1995)
292. R. Feng, Q. Li, Q. Zhang, J. Qin, Robust secure beamforming in MISO full-duplex two-way secure communications. IEEE Trans. Veh. Technol. 65(1), 408-414 (2016)
293. M. Tian, X. Huang, Q. Zhang, J. Qin, Robust AN-aided secure transmission scheme in MISO channels with simultaneous wireless information and power transfer. IEEE Signal Process. Lett. 22(6), 723-727 (2015)
294. C. Wang, H.M. Wang, Robust joint beamforming and jamming for secure AF networks: low complexity design. IEEE Trans. Veh. Technol. 64(5), 2192-2198 (2015)
295. N. Mokari, S. Parsaeefard, H. Saeedi, P. Azmi, E. Hossain, Secure robust ergodic uplink resource allocation in relay-assisted cognitive radio networks. IEEE Trans. Signal Process. 63(2), 291-1756 (2015)
296. B.K. Chalise, L. Vandendorpe, Optimization of MIMO relays for multipoint-to-multipoint communications: Nonrobust and robust designs. IEEE Trans. Signal Process. 58(12), 6355-6368 (2010)
297. M. Tao, R. Wang, Robust relay beamforming for two-way relay networks. IEEE Commun. Lett. 16(7), 1052-1055 (2012)
298. M. Hasan, E. Hossain, D.I. Kim, Resource allocation under channel uncertainties for relay-aided device-to-device communication underlaying LTE-A cellular networks. IEEE Trans. Wireless Commun. 3(4), 2322-2338 (2014)
299. L. Wang, M. Sheng, Y. Zhang, X. Wang, C. Xu, Robust energy efficiency maximization in cognitive radio networks: the worst-case optimization approach. IEEE Trans. Commun. 63(1), 51-64 (2015)
300. N. Mokari, S. Parsaeefard, P. Azmi, H. Saeedi, E. Hossian, Robust ergodic uplink resource allocation in underlay OFDMA cognitive radio networks. IEEE Trans. Mobile Comput. 15(2), 419-431 (2016)
301. S. Umarov, C. Tsallis, S. Steinberg, On a q-central limit theorem consistent with nonextensive statistical mechanics. Milan J. Math. 48(1), 307-328 (2008)
302. R.D. Yates, A framework for uplink power control in cellular radio systems. IEEE J. Sel. Areas Commun. 13(7), 346-349 (1995)
303. M.K. Simon, M.S. Alouini, Some new results for integrals involving the generalized Marcum Q- function and their application to performance evaluation over fading channels. IEEE Trans. Wireless Commun. 2(4), 611-615 (2003)
304. D. Berstimas, O. Nohadani, K.M. Teo, Robust optimization for unconstrained simulation-based problems. Oper. Res. 58(1), 161-178 (2010)
305. D. Bertsimas, V. Goyal, On the approximability of adjustable robust convex optimization under uncertainty. Math. Methods Oper. Res. 77(3), 323-343 (2013)
306. V. Gabrel, C. Murat, A. Thiel, Recent advances in robust optimization: an overview. Eur J. Oper. Res. 235(3), 471-483 (2014)
307. C. Bandi, D. Bertsimas, Optimal design for multi-item auctions: a robust optimization approach. Math. Oper. Res. 39(4), 1012-1038 (2014)
308. I. Yanikoglu, Robust optimization methods for chance constrained, simulation-based, and bilevel problems. Tilburg University, School of Economics and Management, Other Publications TiSEM (2014)
309. B.L. Gorissen, I. Yanikoglu, D. den Hertog, A practical guide to robust optimization. arXiv:1501.02634v1 [math.OC] 12 Jan 2015
310. R. Duzgun, A. Thiele, Evaluating two-range robust optimization for project selection, in Proceedings of 2015 Winter Simulation Conference, pp. 2740-2751 (2015)
311. D. Bertsimas, A. Takeda, Optimizing over coherent risk measures and non-convexities: a robust mixed integer optimization approach. Comput. Optim. Appl. 62(3), 613-639 (2015)
312. S. Siddiqui, S. Gabriel, S. Azarm, Solving mixed-integer robust optimization problems with interval uncertainty using benders decomposition. J. Oper. Res. Soc. 66(4), 664-673 (2015)
313. J. Andrews, S. Buzzi, W. Choi, S. Hanly, A. Lozano, A. Soong, J. Zhang, What will 5G be? IEEE J. Sel. Areas Commun. 32(6), 1065-1082 (2014)
314. P. Agyapong, M. Iwamura, D. Staehle, W. Kiess, A. Benjebbour, Design considerations for a 5G network architecture. IEEE Commun. Mag. 52(11), 65-75 (2014)
315. A. Gupta, R. Jha, A survey of 5G network: architecture and emerging technologies. IEEE Access 3, 1206-1232 (2015)
316. E. Hossain, M. Hasan, 5G cellular: key enabling technologies and research challenges. IEEE Instrum. Meas. Mag. 18(3), 11-21 (2015)
317. M. Palattella, M. Dohler, A. Grieco, G. Rizzo, J. Torsner, T. Engel, L. Ladid, Internet of things in the 5G era: enablers, architecture and business models. IEEE J. Sel. Areas Commun. 34(3), 510-527 (2016)
318. M. Agiwal, A. Roy, N. Saxena, Next generation 5G wireless networks: a comprehensive survey. IEEE Commun. Surv. Tutor. 18(13), 1617-11655 (2016)
319. Q. Zhang, Q. Li, J. Qin, Robust beamforming for non-orthogonal multiple access systems in MISO channels. IEEE Trans. Veh. Technol. PP(99), 1-1 (2016)
320. X. Sun, K. Xu, W. Ma, Y. Xu, X. Xia, D. Zhang, Multi-pair two-way massive MIMO AF full-duplex relaying with imperfect CSI over Ricean fading channels. IEEE Access 4, 4933-4945 (2016)
321. M. Chiang, P. Hande, T. Lan, C.W. Tan, Power control in wireless cellular networks. Found. Trends Netw. 2(4), 381-533 (2008)
322. T.S. Rappaport, R.W. Heath Jr, R.C. Daniels, J.N. Murdock, Millimeter Wave Wireless Communications (Prentice Hall, Upper Saddle River, 2015)
323. T.S. Rappaport, G.R. MacCartney, M.K. Samimi, S. Sun, Wideband millimeter-wave propagation measurements and channel models for future wireless communication system design. IEEE Trans. Commun. 63(9), 3029-3056 (2015)
324. M.K. Samimi, T.S. Rappaport, G.R. MacCartney, Probabilistic omnidirectional path loss models for millimeter-wave outdoor communications. IEEE Wireless Commun. Lett. 4(4), 357-360 (2015)
325. D.F. Macedo, D. Guedes, L.F.M. Vieira, M.A.M. Vieira, M. Nogueira, Programmable networks- from software-defined radio to software-defined networking. IEEE Commun. Surv. Tutorials 17(2), 1102-1125 (2015)
326. H.-H. Cho, C.-F. Lai, T. Shih, H.-C. Chao, Integration of SDR and SDN for 5G. IEEE Access 2, 1196-1204 (2014)
327. B. Nunes, M. Mendonca, X.-N. Nguyen, K. Obraczka, T. Turletti, A survey of software-defined networking: past, present, and future of programmable networks. IEEE Commun. Surv. Tutorials 16(3), 1617-1634 (2014)
328. D. Kreutz, F. Ramos, P.E. Verissimo, C.E. Rothenberg, S. Azodolmolky, S. Uhlig, Software-defined networking: a comprehensive survey. Proc. IEEE 103(1), 14-76 (2015)
329. J. Wickboldt, W. De Jesus, P. Isolani, C. Both, J. Rochol, L. Granville, Software-defined networking: management requirements and challenges. IEEE Commun. Mag. 53(1), 278-285 (2015)
330. W. Xia, Y. Wen, C.H. Foh, D. Niyato, H. Xie, A survey on software-defined networking. IEEE Commun. Surv. Tutorials 17(1), 27-51 (2015)
331. C. Niephaus, G. Ghinea, O. Aliu, S. Hadzic, M. Kretschmer, SDN in the wireless context- towards full programmability of wireless network elements, in Proceedings of 1st IEEE Conference on Network Softwarization (NetSoft), April 2015, pp. 1-6
332. T. Chen, M. Matinmikko, X. Chen, X. Zhou, P. Ahokangas, Software defined mobile networks: concept, survey, and research directions. IEEE Commun. Mag. 53(11), 126-133 (2015)
333. S. Sun, M. Kadoch, L. Gong, B. Rong, Integrating network function virtualization with SDR and SDN for 4G/5G networks. IEEE Netw. 29(3), 54-59 (2015)
334. C. Liang, F. Yu, X. Zhang, Information-centric network function virtualization over 5G mobile wireless networks. IEEE Netw. 29(3), 68-74 (2015)
335. Y. Li, M. Chen, Software-defined network function virtualization: a survey. IEEE Access 3, 2542-2553 (2015)
336. T.S. Rappaport, S. Sun, R. Mayzus, H. Zhao, Y. Azar, K. Wang, G.N. Wong, J.K. Schulz, M.K. Samimi, F. Gutierrez, Millimeter wave mobile communications for 5G cellular: it will work! IEEE Access 1(9), 335-349 (2013)