Fundamentals of resource allocation in wireless networks

Foundations in Signal Processing, Communications and Networking

Volumn 3, Issue , 2008, Pages 1-427

  Stańczak, Sławomir ^a   Wiczanowski, Marcin ^a   Boche, Holger ^a  

^a FRAUNHOFER HEINRICH HERTZ INSTITUTE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRICAL ENGINEERING; SIGNAL PROCESSING;

WIRELESS NETWORKS;

EID: 85101162858     PISSN: 18638538     EISSN: 18638546     Source Type: Book Series    
DOI: None     Document Type: Chapter

References (196)

1. Tang A, Wang J, Low S. Is Fair Allocation Always Inefficient? In: Proc. 23rd IEEE Conference on Computer Communications (INFOCOM), Hong Kong; 2004.
2. Bertsekas DP, Gallager RG. Data Networks. Prentice-Hall, Englewood Cliffs; 1992.
3. Polyak BT, Juditsky AB. Acceleration of Stochastic Approximation by Averaging. SIAM J Control Optim. 1992;30:838–855.
4. Seneta E. Non-Negative Matrices and Markov Chains. Springer, Berlin; 1981.
5. Horn RA, Johnson CR. Matrix Analysis. Cambridge University Press; 1985.
6. Gantmacher FR. Matritzentheorie. Springer, Berlin; 1986. (German translation of the Russian original).
7. Serre D. Matrices: Theory and Applications. Springer, Berlin; 2001.
8. Arnold L, Gundlach V, Demetrius L. Evolutionary Formalism for Products of positive Random Matrices. Ann Appl Probab. 1994;4(3):859–901.
9. Horn RA, Johnson CR. Topics in Matrix Analysis. Cambridge University Press; 1985.
10. Rudin W. Real and Complex Analysis. 3rd ed. McGraw Hill, New York; 1987.
11. Hiriart-Urruty JB, Lemarechal C. Fundamentals of Convex Analysis. Springer, Berlin; 2001.
12. Ahlswede R, Gacs P. Spreading of sets in product spaces and hypercontraction of the Markov operator. Ann Prob. 1976;4(6):925–939.
13. Cover TM, Thomas JA. Elements of Information Theory. Wiley Series in Telecommunications. John Wiley & Sons, Inc.; 1991.
14. Lesniewski A, Ruskai MB. Monotone Riemannian Metrics and Relative Entropy on Non-Commutative Probability Spaces. J Math Phys. 1999;40:5702– 5724.
15. Dembo A, Zeitouni O. Large Deviations Techniques and Applications. 2nd ed. Applications of Mathematics: Stochastic Modelling and Applied Probability. Springer, Berlin; 1998.
16. Boyd S, Vandenberghe L. Convex Optimization. Cambridge University Press; 2004.
17. van Lint JH, Wilson RM. A course in combinatorics. Cambridge University Press; 1994.
18. Cvetkovic DM, Doob M, Sachs H. Spectra of Graphs. Academic Press, New York; 1978.
19. Boche H, Wiczanowski M, Stanczak S. Unifying View on Min-Max Fairness, Max-Min Fairness, and Utility Optimization in Cellular Networks. EURASIP J Wireless Commun and Net. 2007;ID 34869.
20. Boche H, Stanczak S. On Systems of Linear Equations with Nonnegative Coefficients. Appl Alg Eng Comm Comp. 2004 March;14(6):397–414.
21. Boche H, Stanczak S. Convexity of Some Feasible QoS Regions and Asymptotic Behavior of the Minimum Total Power in CDMA Systems. IEEE Trans Commun. 2004 December;52(12):2190–2197.
22. Boche H, Stanczak S. Log-Convexity of the Minimum Total Power in CDMA Systems with Certain Quality-Of-Service Guaranteed. IEEE Trans Inform Theory. 2005 January;51(1):374–381.
23. Stanczak S, Boche H. The Infeasible SIR Region Is Not a Convex Set. IEEE Trans Commun. 2006 November;54(11):1905–1907.
24. Stanczak S, Boche H. Towards a better understanding of the QoS tradeoff in multiuser multiple antenna systems. In: Smart Antennas–State-of-the-Art. EURASIP Book Series on Signal Processing and Communications. Hindawi Publishing Corporation; 2005. p. 521–543.
25. Stanczak S, Boche H, Wiczanowski M. Towards a Better Understanding of Medium Access Control for Multiuser Beamforming Systems. In: Proc. IEEE Wireless Communications and Networking Conference (WCNC). New Orleans, LA, USA; 2005.
26. Imhof L, Mathar R. Capacity Regions and Optimal Power Allocation for CDMA Cellular Radio. IEEE Trans Inform Theory. 2005 June;51(6):2011– 2019.
27. Imhof L, Mathar R. The Geometry of the Capacity Region for CDMA Systems with General Power Constraints. IEEE Trans Wireless Commun. 2005 Sept;4(5).
28. Stanczak S, Boche H. Strict Log-Convexity of the Minimum Power Vector. In: Proc. IEEE International Symposium on Information Theory (ISIT). Seattle, WA, USA; 2006.
29. Kirkland SJ, Neumann M, Ormes N, Xu J. On the Elasticity of the Perron Root of a Nonnegative Matrix. SIAM J Matrix Anal Appl. 2002;24(2):454–464.
30. Friedland S, Karlin S. Some Inequalities for the Spectral Radius of Non-Negative Matrices and Applications. Duke Math J. 1975;42(3):459–490.
31. Kingman JFC. A Convexity Property of Positive Matrices. Quart, J Math Oxford Ser. 1961;12(2):283–284.
32. Catrein D, Imhof L, Mathar R. Power Control, Capacity, and Duality of Up-and Downlink in Cellular CDMA Systems. IEEE Trans Commun. 2004 Oct;52(10):1777–1785.
33. Cohen JE, Friedland S, Kato T, Kelly FP. Eigenvalue Inequalities for Products of Matrix Exponentials. Linear Algebra Appl. 1982;45:55–95.
34. Friedland S. Convex Spectral Functions. Linear Multilin Alg. 1981;9:293–316.
35. Cohen JE. Random Evolutions and the Spectral Radius of a Non-Negative matrix. Math Proc Cambridge Philos Soc. 1979;86:345–350.
36. Deutsch E, Neumann M. Derivatives of the Perron Root at an Essentially Nonnegative Matrix and the Group Inverse of an M-Matrix. J Math Anal Appl. 1984;I-29(102):1–29.
37. Elsner L. On Convexity Properties of the Spectral Radius of Nonnegative Matrices. Linear Algebra Appl. 1984;61:31–35.
38. Elsner L. Über Eigenwereinschliessungen mit Hilfe von Gerschgorin-Kreisen. Z Angew Math Mech. 1970;50:381–384.
39. Rudin W. Principles of Mathematical Analysis. McGraw-Hill, New York; 1976.
40. Goldsmith AJ, Wicker SB. Design Challenges for Energy-Constrained Ad-Hoc Wireless Networks. IEEE Wireless Commun Mag. 2002 August;9:8–27.
41. Kandukuri S, Boyd S. Optimal Power Control in Interference-Limited Fading Wireless Channels with Outage-Probability Specifications. IEEE Trans Wireless Commun. 2002 Jan;1(1):46–55.
42. Papandriopoulos J, Evans J, Dey S. Optimal Power Control for Rayleigh-Faded Multiuser Systems with Outage Constraints. IEEE Trans Wireless Commun. 2005 Nov;4(6):2705–2715.
43. Papandriopoulos J, Evans J, Dey S. Outage-Based Optimal Power Control for Generalized Multiuser Fading Channels. IEEE Trans Commun. 2006 April;54(4):693–703.
44. Borst SC, Whiting PA. Dynamic Channel-Sensitive Scheduling Algorithms for Wireless Data Throughput Optimization. IEEE Trans Veh Technol. 2003 May;52(3):569–586.
45. Lee JW, Mazumdar RR, Shroff NB. Oportunistic Power Scheduling for Dynamic Multi-Server Wireless Systems. IEEE Trans Wireless Commun. 2006 June;5(6):1506–1515.
46. Neely MJ. Dynamic Power Allocation and Routing for Satellite and Wireless Networks with Time Varying Channels. Massachusetts Institute of Technology, LIDS. Cambridge, MA, USA; 2003.
47. Neely MJ, Lee CP, Modiano E. Fairness and Optimal Stochastic Control for Heterogeneous Networks. In: Proc. 23rd IEEE Conference on Computer Communications (INFOCOM). Miami, FL, USA; 2005.
48. Stolyar AL. Maximizing Queueing Network Utility Subject to Stability. Queueing Systems. 2005 Aug;50(4):401–457.
49. Aein JM. Power Balancing in Systems Employing Frequency Reuse. COMSAT Tech Rev. 1973;3(2):277–300.
50. Meyerhoff HJ. Method for computing the optimum Power Balance in Multibeam Satellites. COMSAT Tech Rev. 1974;4(1):139–146.
51. Alavi H, Nettleton RW. Downstream Power Control for a Spread Spectrum Cellular Mobile Radio System. In: Proc. IEEE Global Communications Conference (GLOBECOM); 1982. p. 84–88.
52. Zander J. Distributed Cochannel Interference Control in Cellular Radio Systems. IEEE Trans Veh Technol. 1992 August;41:305–311.
53. Zander J. Performance of Optimum Transmitter Power Control in Cellular Radio Systems. IEEE Trans Veh Technol. 1992 February;41(1):57–62.
54. Foschini GJ, Miljanic Z. A Simple Distributed Autonomous Power Control Algorithm and its Convergence. IEEE Trans Veh Technol. 1993 Nov;42(4):641– 646.
55. Yates RD. A Framework for Uplink Power Control in Cellular Radio Systems. IEEE J Select Areas Commun. 1995 September;13(7):1341–1347.
56. Yates RD, Huang CY. Integrated Power Control and Base Station Assignment. IEEE Trans Veh Technol. 1995 August;44(3):638–644.
57. Gerlach D, Paulraj A. Base Station Transmitting Antenna Arrays for Multipath Environments. Signal Processing (Elsevier Science). 1996;54:59–73.
58. He B, Wang MZ, Li EC. A new distributed power balancing algorithm for CDMA cellular systems. In: Proc. IEEE International Symposium on Circuits and Systems (ISCAS). vol. 3; 1997. p. 1768–1771.
59. Bambos N. Toward Power-Sensitive Network Architectures in Wireless Communications: Concepts, Issues, and Design Aspects. IEEE Personal Commun Mag. 1998 June;5:50–59.
60. Montalbano G, Ghauri I, Slock DTM. Spatio-Temporal Array Processing for CDMA/SDMA Downlink Transmission. In: Proc. Asilomar Conf. on Signals, Systems and Computers, Monterey,CA,USA; 1998. p. 1337–1341.
61. Hongyu W, Aiging H, Rong H, Weikang G. Balanced distributed power control. In: IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC). vol. 2; 2000. p. 1415–1419.
62. Wu Q. Optimum Transmitter Power Control in Cellular Systems with Heterogeneous SIR Thresholds. IEEE Trans Veh Technol. 2000 July;49(4):1424–1429.
63. Bambos N, Chen SC, Pottie GJ. Channel Access Algorithms with Active Link Protection for Wireless Communication Networks with Power Control. IEEE/ACM Trans Networking. 2000 October;8(5):583–597.
64. Zander J, Kim SL. Radio Resource Management for Wireless Networks. Artech House, Boston, London; 2001.
65. ElBatt T, Ephremides A. Joint Scheduling and Power Control for Wireless Ad Hoc Networks. IEEE Trans Wireless Commun. 2004 January;3(1):74–85.
66. Feiten A, Mathar R. Optimal Power Control for Multiuser CDMA Channels. In: Proc. 2005 IEEE International Symposium on Information Theory (ISIT). Adelaide, Australia; 2005.
67. Cruz RL, Santhanam AV. Optimal Routing, Link Scheduling and Power Control in Multi-hop Wireless Networks. In: Proc. 22nd IEEE Conference on Computer Communications (INFOCOM), San Francisco, CA, USA; 2003.
68. Hanly SV. An algorithm for combined cell-site selection and power control to maximize cellular spread spectrum capacity. IEEE Journal on Selected Areas in Communications. 1995;13(7):1332–1340.
69. Kelly FP, Maulloo AK, Tan DKH. Rate Control for Communication Networks: Shadow Prices, Proportional Fairness and Stability. J Oper Res Soc. 1998 March;49(3):237–252.
70. Mo J, Walrand J. Fair End-to-End Window-Based Congestion Control. IEEE/ACM Trans on Networking. 2000 October;8(5):556–567.
71. Goodman D, Mandayam N. Power Control for Wireless Data. IEEE Personal Commun Mag. 2000 April;7:48–54.
72. Saraydar CU, Mandayam NB, Goodman DJ. Pricing and Power Control in a Multicell Wireless Data Network. IEEE J Select Areas Commun. 2001;19(10):1883–1892.
73. Xiao M, Schroff NB, Chong EKP. A Utility-Based Power Control Scheme in Wireless Cellular Systems. IEEE/ACM Trans Networking. 2003 April;11(2):210–221.
74. Johansson M, Xiao L, Boyd S. Simultaneous routing and resource allocation in CDMA wireless data networks. In: Proc. IEEE International Conference on Communications, Anchorage, Alaska; 2003.
75. O’Neill D, Julian D, Boyd S. Seeking Foschini’s Genie: Optimal Rates and Powers in Wireless Networks. IEEE Trans Veh Technol. 2003 (accepted);Available from http://www.stanford.edu/boyd/.
76. Chiang M. To Layer or Not To Layer: Balancing Transport and Physical Layers in Wireless Multihop Networks. In: Proc. 23rd IEEE Conference on Computer Communications (INFOCOM), Hong Kong; 2004.
77. Feng N, Mau SC, Mandayam NB. Pricing and Power Control for Joint Network-Centric and User-Centric Radio Resource Management. IEEE Trans Commun. 2004;52(9):1547–1557.
78. Chiang M. Balancing Transport and Physical Layers in Wireless Multihop Networks: Jointly Optimal Congestion Control and Power Control. IEEE J Select Areas Commun. 2005 Jan;23(1):104–116.
79. Price J, Javidi T. Decentralized Rate Assignments in a Multi-Sector CDMA Network. IEEE Trans Wireless Commun. 2006 Dec;5(12):3537–3547.
80. Subramanian A, Sayed AH. Joint Rate and Power Control Algorithms for Wireless Networks. IEEE Trans Signal Processing. 2005 Nov;53(11):4204–4214.
81. Palomar DP, Chiang M. A Tutorial on Decomposition Methods for Network Utility Maximization. IEEE J Select Areas Commun. 2006 Aug;24(8):1439– 1451.
82. Stanczak S, Wiczanowski M, Boche H. Distributed Utility-Based Power Control: Objectives and Algorithms. IEEE Trans Signal Processing. 2007 Oct;55(10):5058–5068.
83. Hande P, Rangan S, Chiang M, Wu X. Distributed Uplink Power Control for Optimal SIR Assignment in Cellular Data Networks. IEEE/ACM Trans Networking. 2008 Dec;16(6):1420–1433.
84. Wiczanowski M, Stanczak S, Boche H. Providing quadratic convergence of decentralized power control in wireless networks – The method of min-max functions. IEEE Trans Signal Processing. 2008 Aug;56(8):4053–4068.
85. Huang J, Subramanian VG, Agrawal R, Berry R. Joint Scheduling and Resource Allocation in Uplink OFDM Systems for Broadband Wireless Access Networks. IEEE J Select Areas Commun. 2009 Feb;27(2):288–296.
86. Berry R, Liu P, Honig M. Design and Analysis of Downlink Utility-Based Schedulers. In: Proc. 43nd Annual Allerton Conference on Communication, Control and Computing; 2002.
87. Chen L, Low S, Chiang M, Doyle J. Optimal Cross-Layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks. In: Proc. 25th IEEE Conference on Computer Communications (INFOCOM), Barcelona; 2006.
88. Georgiadis L, Neely MJ, Tassiulas L. Resource Allocation and Cross-Layer Control in Wireless Networks. Now Publishers Inc.; 2006.
89. Huang J, Berry R, Honig ML. A Game Theoretic Analysis of Distributed Power Control for Spread Spectrum Ad Hoc Networks. In: Proc. IEEE International Symposium on Information Theory (ISIT). Adelaide, Australia; 2005.
90. Huang J, Berry R, Honig ML. Distributed Interference Compensation for Wireless Networks. IEEE J Select Areas Commun. 2006 May;24(5):1074–1084.
91. Huang J, Berry R, Honig ML. Distributed Interference Compensation for Multi-Channel Wireless Networks. In: Proc. 43nd Annual Allerton Conference on Communication, Control and Computing. Monticello, IL, USA; 2005.
92. Alpcan T, Basar T, Srikant R, Altman E. CDMA uplink power control as a noncooperative game. Wireless Networks. 2002 Nov;8(6):659–670.
93. Saraydar CU, Mandayam NB, Goodman DJ. Efficient Power Control via Pricing in Wireless Data Networks. IEEE Trans Commun. 2002;50(2):291–303.
94. Helleseth T, Kumar PV. Sequences with Low Correlation. In: Handbook of Coding Theory. vol. 2. Elsevier Science, Amsterdam; 1998. p. 1765–1853.
95. M K Simon MSA. Digital Communication over Fading Channels: A Unified Approach to Performance Analysis. John Wiley & Sons, Inc.; 2000.
96. Proakis JG. Digital Communications. 3rd ed. McGraw Hill, New York; 1995.
97. Verdu S. Multiuser Detection. Cambridge University Press; 1998.
98. Tse D, Viswanath P. Fundamentals of Wireless Communication. 1st ed. Cambridge University Press; 2005.
99. IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed Broadband Wireless Access Systems. IEEE Std 80216-2004 (Revision of IEEE Std 80216-2001). 2004;p. 1–857.
100. Franks LE. Signal Theory. Prentice-Hall, Englewood Cliffs; 1969.
101. Tse D, Hanly S. Linear Multiuser Receivers: Effective Interference, Effective Bandwidth and User Capacity. IEEE Trans Inform Theory. 1999 March;45(2):641–657.
102. Viswanath P, Anantharam V, Tse DNC. Optimal Sequences, Power Control, and User Capacity of Synchronous CDMA Systems with Linear MMSE Multiuser Receivers. IEEE Trans Inform Theory. 1999 September;45(6):1968–1983.
103. Viswanath P, Anantharam V. Optimal Sequences and Sum Capacity of Synchronous CDMA Systems. IEEE Trans Inform Theory. 1999 September;45(6):1984–1991.
104. Verdu S. Spectral Efficiency of CDMA with Random Spreading. IEEE Trans Inform Theory. 1999 March;45(2):622–640.
105. Rasmussen LK, Lim TJ, Johansson AL. A Matrix Algebraic Approach to Successive Interference Cancellation in CDMA. IEEE Trans Commun. 2000 Jan;48(1):145–151.
106. Poor HV, Verdu S. Probability of Error in MMSE Multiuser Detection. IEEE Trans Inform Theory. 1997 May;43:858–871.
107. Lancaster P. Theory of Matrices. Academic Press, Inc.; 1969.
108. Han SH, Lee JH. An overview of peak-to-average power ratio reduction techniques for multicarrier transmission. IEEE Trans Wireless Commun. 2005 April;12(2):56–65.
109. Koskie A, Gajic Z. A Nash Game Algorithm for SIR-Based Power Control for 3G Wireless CDMA Networks. IEEE/ACM Trans Networking. 2005 Oct;13(5).
110. Schubert M, Boche H. Iterative Multiuser Uplink and Downlink Beamforming under SINR Constraints. IEEE Trans Signal Processing. 2005 July;53(7):2324– 2334.
111. Boche H, Schubert M. Duality Theory for Uplink and Downlink Multiuser Beamforming. In: Smart Antennas–State-of-the-Art. EURASIP Book Series on Signal Processing and Communications. Hindawi Publishing Corporation; 2005. p. 545–575.
112. Alamouti SM. A Simple Transmitter Diversity Scheme for Wireless Communications. IEEE Journal on Selected Areas in Communications. 1998 October;SAC-16:1451–1458.
113. Schnurr C, Stanczak S, Sezgin A. The Impact of Different MIMO Strategies on the Network-Outage Performance. In: Proc. ITG/IEEE International Workshop on Smart Antennas (WSA), 2007. Wien, Austria; 2007.
114. Massoulie L, Roberts J. Bandwidth Sharing: Objectives and Algorithms. IEEE/ACM Trans on Networking. 2002 June;10(3):320–328.
115. Hahne E. Round-Robin Scheduling for Fair Flow Control in Data Communication Networks. MIT, Deptartment of Electrical Engineering and Computer Science. Cambridge, MA, USA; 1986.
116. Hahne E. Round-robin Scheduling for Max-Min Fairness in Data Networks. IEEE J Select Areas Commun. 1991 Sep;9(7):1024–1039.
117. Charny A, Clark D, Jain R. Congestion Control with Explicit Rate Indication. In: Proc. IEEE International Conference on Communications (ICC); 1995.
118. Ji H, Huang CY. Non-Cooperative Uplink Power Control in Cellular Radio Systems. Wireless Networks. 1998 April;4:233–240.
119. Kozat UC, Koutsopoulos I, Tassiulas L. A Framework for Cross-layer Design of Energy-efficient Communication with QoS Provisioning in Multi-hop Wireless Networks. In: Proc. 23rd IEEE Conference on Computer Communications (INFOCOM), Hong Kong; 2004.
120. Neely MJ, Modiano E, Rohrs CE. Dynamic Power Allocation and Routing for Time Varying Wireless Networks. In: Proc. 22nd IEEE Conference on Computer Communications (INFOCOM), San Francisco, CA, USA; 2003.
121. Low S, Peterson L, Wang L. Understanding TCP Vegas: A Duality Model. Journal of the ACM (JACM). 2002 March;49(2):207–235.
122. Yi Y, Shakkottai S. Hop-by-hop Congestion Control over a Wireless Multihop Network. In: Proc. 23rd IEEE Conference on Computer Communications (INFOCOM), Hong Kong; 2004.
123. Sarkar S, Tassiulas L. End-to-End Bandwidth Guarantees Through Fair Local Spectrum Share in Wireless Ad Hoc Networks. IEEE Trans Automat Contr. 2005 Sept;50(9):1246–1259.
124. Nandagopal T, Kim T, Gao X, Bharghavan V. Achieving MAC Layer Fairness in Wireless Packet Networks. In: Proc. ACM Mobicom, Boston, MA, USA; 2000. p. 87–98.
125. Tassiulas L, Ephremides A. Stability Properties of Constrained Queueing Systems and Scheduling Policies for Maximum Throughput in Multihop Radio Networks. IEEE Trans Automat Contr. 1992 December;37(12):1936–1948.
126. Tassiulas L, Ephremides A. Jointly optimal routing and scheduling in packet radio networks. IEEE Trans Inform Theory. 1992 January;38(1):165–168.
127. Boche H, Wiczanowski M, Stanczak S. Characterization of Optimal Resource Allocation in Cellular Networks. In: Proc. 5th IEEE Workshop on Signal Processing Advances in Wireless Communications. Lisboa, Portugal; 2004.
128. Stanczak S, Wiczanowski M. Distributed Fair Power Control for Wireless Networks: Objectives and Algorithms. In: Proc. the 43rd Annual Allerton Conference on Communications, Control, and Computing; 2005. invited paper.
129. Mas-Colell A, Whinston MD, Green JR. Microeconomic Theory. Oxford University Press; 1995.
130. Pratt JW. Risk Aversion in the Small and in the Large. Econometrica. 1964;32:300–307.
131. Dianati MD, Shen XS, Naik S. A New Fairness Index for Radio Resource Allocation in Wireless Networks. In: Proc. IEEE Wireless Communications and Networking Conference (WCNC). New Orleans, LA, USA; 2005.
132. Marshall AW, Olkin I. Inequalities: Theory of Majorization and its Applications. New York: Academic; 1979.
133. Mitrinovic DS. Analytic Inequalities. Springer, Berlin; 1970.
134. Verdu S. On Channel Capacity per Unit Cost. IEEE Trans Inform Theory. 1990 Sept;36(5):1019–1030.
135. Verdu S. Recent Results on the Capacity of Wideband Channels in the Low-Power Regime. IEEE Wireless Commun Mag. 2002 August;9:40–45.
136. Schubert M, Boche H. QoS-Based Resource Allocation and Transceiver Optimization. Foundation and Trends in Communications and Information Theory. 2006;2(6).
137. Jorswieck EA, Boche H. Performance Analysis of Capacity of MIMO Systems under Multiuser Interference based on Worst Case Noise Behavior. EURASIP Journal on Wireless Communications and Networking. 2004;2:273–285.
138. Schubert M, Boche H. Advanced Network Calculus–A General Framework for Interference Management and Network Utility Optimization. Lecture Notes in Computer Science. Springer, Berlin; 2009. To appear.
139. Debreu G. Theory of Value. Yale University Press; 1959.
140. Ulukus S, Yates R. Stochastic Power Control for Cellular Radio Systems. IEEE Trans Commun. 1998;46(6):784–798.
141. Luo J, Ulukus S, Ephremides A. Standard and Quasi-Standard Stochastic Power Control Algorithms. IEEE Trans Inform Theory. 2005 July;51(7):2612– 2624.
142. Grandhi SA, Zander J, Yates R. Constrained Power Control. Wireless Personal Communications, Kluwer. 1995;2(3):257–270.
143. Kushner HJ, Yin GG. Stochastic Approximation and Recursive Algorithms and Applications. Springer, Berlin; 2003.
144. Robinson H, Monro S. A Stochastic Approximation Method. Ann Math Statist. 1951;22:400–407.
145. Qi L. Convergence Analysis of Some Algorithms for Solving Non-Smooth Equations. Math Oper Res. 1993 Feb;18(1):227–244.
146. Bertsekas DP. Nonlinear Programming. Athena Scientific, Belmont, Massachusetts; 2003.
147. Wunder G, Michel T. On optimization of multiuser systems using interference calculus. In: Proc. 41st Asilomar Conference on Signals, Systems, and Computers. Pacific Grove, CA, USA; 2007. Invited.
148. Ortega JM, Rheinboldt WC. Iterative Solution of Nonlinear Equations in Several Variables. Classics in Applied Mathematics 30, SIAM, Philadelphia; 2000.
149. Boche H, Stanczak S. Iterative algorithm for finding resource allocation in symbol-asynchronous CDMA channels with different SIR requirements. In: Proc. 36th Asilomar Conference on Signals, Systems, and Computers. Monterey, CA, USA; 2002.
150. Mahdavi-Doost H, Ebrahimi M, Khandani AK. Characterization of Rate Region in Interference Channels with Constrained Power. In: Proc. IEEE International Symposium on Information Theory (ISIT). Nice, France; 2007.
151. Stanczak S, Kaliszan M, Bambos N, Wiczanowski M. A Characterization of Max-Min SIR-Balanced Power Allocation with Applications. In: Proc. IEEE International Symposium on Information Theory (ISIT). Seoul, Korea; 2009.
152. Tan CW, Chiang M, Srikant R. Fast Algorithms and Performance Bounds for Sum Rate Maximization in Wireless Networks. In: Proc. 28th IEEE Conference on Computer Communications (INFOCOM). Rio de Janeiro, Brazil; 2009.
153. Rockafellar RT. Saddle Points and Convex Analysis. In: Kuhn HW, Szego GP, editors. Differential Games and Related Topics. Amsterdam, The Netherlands: North-Holland; 1971. p. 109–127.
154. Neely MJ, Modiano E, Rohrs CE. Power Allocation and Routing in Multibeam Satellites with Time-Varying Channels. IEEE/ACM Trans Networking. 2003 February;11(1):138–152.
155. Stanczak S, Feistel A, Tomecki D. On Utility-Based Power Control and Receive Beamforming. In: Proc. 41st Annual Conference on Information Sciences and Systems (CISS). Baltimore, MD, USA; 2007.
156. Giannakis GB, Hua Y, Stoica P, Tong L, editors. Signal Processing Advances in Wireless and Mobile Communications. Prentice-Hall, Englewood Cliffs; 2000.
157. Fan P, Darnell M. Sequence Design For Communications Applications. Research Studies Pr; 1996.
158. Stanczak S, Wunder G, Boche H. On Pilot-based Multipath Channel Estimation for Uplink CDMA Systems: An Overloaded Case. IEEE Trans Signal Processing. 2006 February;54(2):512–519.
159. Boche H, Schubert M. Resource Allocation in Multiantenna Systems-Achieving max-min fairness by optimizing a sum of inverse SIRs. IEEE Trans Signal Processing. 2006 June;54(6).
160. Bertsekas DP, Tsitsiklis JN. Parallel and Distributed Computation. Prentice-Hall, Englewood Cliffs; 1989.
161. Boche H, Stanczak S. Log-Concavity of SIR and Characterization of the Feasible SIR Region for CDMA Channels. In: Proc. 37th Asilomar Conference on Signals, Systems, and Computers. Monterey, CA, USA; 2003.
162. Bertsekas DP. Nonlinear Programming. Athena Scientific, Belmont, Massachusetts; 1995.
163. Wiczanowski M, Stanczak S, Boche H. Distributed Optimization and Duality in QoS Control for Wireless Best-Effort Traffic. In: Proc. 39th Asilomar Conference on Signals, Systems and Computers. Monterey, CA, USA; 2005.
164. Stanczak S, Wiczanowski M, Boche H. Distributed Power Control for Optimizing a Weighted Sum of QoS Parameter Values. In: Proc. IEEE Global Telecommunications Conference (GLOBECOM). St. Louis, MO, USA; 2005.
165. Stanczak S, Wiczanowski M, Boche H. Theory and Algorithms for Resource Allocation in Wireless Networks. Lecture Notes in Computer Science (LNCS 4000). Springer, Berlin; 2006.
166. Poor HV. An Introduction to Signal Detection and Estimation. Springer, Berlin; 1998.
167. Ljung L. Analysis of Recursive Stochastic Algorithms. IEEE Trans Automat Contr. 1977 August;AC-22(4):551–575.
168. Williams D. Probability with Martingales. Cambridge University Press; 1991.
169. Bertsekas DP. Convex Analysis and Optimization. Athena Scientific; 2003.
170. Stanczak S, Feistel A, Boche H, Wiczanowski M. Towards Efficient and Fair Resource Allocation in Wireless Networks. In: Proc. 6th Intl. Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt). Berlin, Germany; 2008. Keynote speech.
171. Stanczak S, Feistel A, Boche H. QoS Support with Utility-Based Power Control. In: Proc. 2008 IEEE International Symposium on Information Theory (ISIT). Toronto, Canada; 2008.
172. Bazaraa MS, Sherali HD, Shetty CM. Nonlinear programming. John Wiley & Sons, Inc.; 1993.
173. Wright SJ. Primal dual interior point methods. Philadelphia: Soc. for Industrial and Applied Math. (SIAM); 1997.
174. Hestenes MR. Multiplier and Gradient Methods. Journal of Optimization Theory and Applications. 1969;4:303–320.
175. Bertsekas DP. Combined Primal-Dual and Penalty Methods for Constrained Minimization. SIAM Journal on Control and Optimization. 1975 May;13(3):521–544.
176. Mangasarian OL. Unconstrained Lagrangians in Nonlinear Programming. SIAM Journal on Control and Optimization. 1975 May;13(4):772–791.
177. Rockafellar RT. Augmented Lagrange multiplier functions and duality in nonconvex programming. SIAM Journal on Control and Optimization. 1974;12:268–285.
178. Karmarkar N. A New Polynomial-Time Algorithm for Linear Programming. Combinatorica. 1984;4:373–395.
179. Wiczanowski M, Stanczak S, Boche H. Performance and interference control in wireless ad-hoc and mesh networks – The generalized Lagrangian approach. IEEE Trans Signal Processing. 2008 Aug;56(8):4039–4052.
180. Akyildiz IF, Wang X, Wang W. Wireless mesh networks: a survey. Computer Networks and ISDN Systems. 2005 Mar;47(4):445–487.
181. Fiacco AV, McCormick GP. Nonlinear Programming: Sequential Unconstrained Minimization Techniques. John Wiley & Sons, Inc.; 1968.
182. Li D. Zero Duality Gap for a Class of Nonconvex Optimization Problems. Journal of Optimization Theory and Applications. 1995;85:309–324.
183. Mangasarian OL. Nonlinear Programming. McGraw Hill, New York; 1969.
184. Evtushenko Y. Generalized Lagrange multiplier technique for nonlinear programming. Journal of Optimization Theory and Application. 1977;21(2):121– 135.
185. Debreu G. Definite and semidefinite quadratic forms. Econometrica. 1952;20:295–300.
186. Rockafellar RT. Convex Analysis. New Jersey: Princeton University Press; 1972.
187. Horn RA. Elements of Matrix Analysis. New York: Prenctice Hall; 1994.
188. Evtushenko Y. Iterative Methods for Solving Minimax Problems. USSR Computational Mathematics and Physics. 1974;14(5):1138–1149.
189. Meyer CD. Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia; 2000.
190. Rudin W. Functional Analysis. 2nd ed. McGraw Hill, New York; 1991.
191. Bartle RG, Sherbert DR. Introduction to Real Analysis. John Wiley & Sons, Inc.; 1982.
192. Golub GH, Loan CFV. Matrix Computations. New York: John Hopkins University Press; 1996.
193. Hardy G, Littlewood JE, Polya G. Inequalities. 2nd ed. Cambridge University Press; 1952.
194. Luenberger DG. Optimization by vector space methods. John Wiley & Sons, Inc.; 1969.
195. Evtushenko Y. Some local properties of minimax problem. USSR Computational Mathematics and Physics. 1974;14(3):129–138.
196. Ricceri B. Minimax Theory and Applications. Dordrecht: Kluwer Academic Publishers; 1998.