Fast Algorithms and Performance Bounds for Sum Rate Maximization in Wireless Networks

In this paper, we consider a wireless network where interference is treated as noise, and we study the nonconvex problem of sum rate maximization by power control. We focus on finding approximately optimal solutions that can be efficiently computed to this NP-hard problem by studying the solutions to two related problems, the sum rate maximization using a signal-to-interference-plus-noise ratio (SINR ) approximation and the max-min weighted SINR optimization. We show that these two problems are intimately connected, can be solved efficiently by algorithms with fast convergence and minimal parameter configuration, and can yield high-quality approximately optimal solutions to sum rate maximization in the low interference regime. As an application of these results, we analyze the connection-level stability of cross-layer utility maximization in the wireless network, where users arrive and depart randomly and are subject to congestion control, and the queue service rates at all the links are determined by the sum rate maximization problem. In particular, we determine the stability region when all the links solve the max-min weighted SINR problem, using instantaneous queue sizes as weights.

[1]  Massimo Franceschetti,et al.  Closing the Gap in the Capacity of Wireless Networks Via Percolation Theory , 2007, IEEE Transactions on Information Theory.

[2]  YuWei,et al.  An introduction to convex optimization for communications and signal processing , 2006 .

[3]  R. Srikant,et al.  Maximizing Sum Rate and Minimizing MSE on Multiuser Downlink: Optimality, Fast Algorithms and Equivalence via Max-min SINR , 2011, IEEE Transactions on Signal Processing.

[4]  Steven H. Low,et al.  Optimization flow control—I: basic algorithm and convergence , 1999, TNET.

[5]  Wei Yu,et al.  An introduction to convex optimization for communications and signal processing , 2006, IEEE Journal on Selected Areas in Communications.

[6]  R. Srikant,et al.  Maximizing sum rate and minimizing MSE on multiuser downlink: Optimality, fast algorithms and equivalence via max-min SIR , 2009, ISIT.

[7]  E. Seneta.  Non-negative Matrices and Markov Chains , 2008 .

[8]  Chee Wei Tan,et al.  Fast Algorithms and Performance Bounds for Sum Rate Maximization in Wireless Networks , 2009, INFOCOM 2009.

[9]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[10]  Amir K. Khandani,et al.  Characterization of SINR Region for Interfering Links With Constrained Power , 2010, IEEE Transactions on Information Theory.

[11]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[12]  S. Friedland,et al.  Maximizing Sum Rates in Gaussian Interference-limited Channels ⁄ , 2008, 0806.2860.

[13]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[14]  David Gesbert,et al.  Adaptation, Coordination, and Distributed Resource Allocation in Interference-Limited Wireless Networks , 2007, Proceedings of the IEEE.

[15]  Jens Zander,et al.  Distributed cochannel interference control in cellular radio systems , 1992 .

[16]  Eytan Modiano,et al.  Distributed Cross-Layer Algorithms for the Optimal Control of Multihop Wireless Networks , 2010, IEEE/ACM Transactions on Networking.

[17]  Paul Van Dooren,et al.  An affine eigenvalue problem on the nonnegative orthant , 2005 .

[18]  Mung Chiang,et al.  Power Control in Wireless Cellular Networks , 2008, Found. Trends Netw..

[19]  Weidong Yang,et al.  Optimal downlink power assignment for smart antenna systems , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[20]  Xiaojun Lin,et al.  The impact of imperfect scheduling on cross-Layer congestion control in wireless networks , 2006, IEEE/ACM Transactions on Networking.

[21]  S. Karlin,et al.  Some inequalities for the spectral radius of non-negative matrices and applications , 1975 .

[22]  Lijun Qian,et al.  Uplink Scheduling in CDMA Packet-Data Systems , 2006, Wirel. Networks.

[23]  Shmuel Friedland,et al.  Spectrum Management in Multiuser Cognitive Wireless Networks: Optimality and Algorithm , 2011, IEEE Journal on Selected Areas in Communications.

[24]  Daniel Pérez Palomar,et al.  Power Control By Geometric Programming , 2007, IEEE Transactions on Wireless Communications.

[25]  Gerard J. Foschini,et al.  A simple distributed autonomous power control algorithm and its convergence , 1993 .

[26]  Ioannis Ch. Paschalidis,et al.  Asymptotically Optimal Transmission Policies for Large-Scale Low-Power Wireless Sensor Networks , 2007, IEEE/ACM Transactions on Networking.

[27]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[28]  ChiangMung,et al.  Power Control in Wireless Cellular Networks , 2008 .

[29]  R. Srikant,et al.  Joint congestion control, routing, and MAC for stability and fairness in wireless networks , 2006, IEEE Journal on Selected Areas in Communications.

[30]  R. Srikant,et al.  A tutorial on cross-layer optimization in wireless networks , 2006, IEEE Journal on Selected Areas in Communications.

[31]  John N. Tsitsiklis,et al.  Hardness of Low Delay Network Scheduling , 2011, IEEE Transactions on Information Theory.

[32]  Mung Chiang,et al.  Balancing transport and physical Layers in wireless multihop networks: jointly optimal congestion control and power control , 2005, IEEE Journal on Selected Areas in Communications.

[33]  R. Srikant,et al.  On the Connection-Level Stability of Congestion-Controlled Communication Networks , 2008, IEEE Transactions on Information Theory.

[34]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[35]  Slawomir Stanczak,et al.  Distributed Utility-Based Power Control: Objectives and Algorithms , 2007, IEEE Transactions on Signal Processing.

[36]  M. Ebrahimi,et al.  Power Allocation and Asymptotic Achievable Sum-Rates in Single-Hop Wireless Networks , 2006, 2006 40th Annual Conference on Information Sciences and Systems.

[37]  Zhi-Quan Luo,et al.  Dynamic Spectrum Management: Complexity and Duality , 2008, IEEE Journal of Selected Topics in Signal Processing.

[38]  U. Krause.  Concave Perron–Frobenius Theory and applications , 2001 .

[39]  Mung Chiang,et al.  Nonconvex power control in multiuser communication systems , 2008 .

[40]  Aydin Sezgin,et al.  Rate Region Frontiers for n-user Interference Channel with Interference as Noise , 2010, ArXiv.

[41]  Roy D. Yates,et al.  A Framework for Uplink Power Control in Cellular Radio Systems , 1995, IEEE J. Sel. Areas Commun..