1452 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 8, AUGUST 2006 A Tutorial on Cross-Layer Optimization in Wireless Networks Xiaojun Lin, Member, IEEE, Ness B. Shroff, Senior Member, IEEE, and R. Srikant, Fellow, IEEE Tutorial Paper Abstract—This tutorial paper overviews recent developments in optimization-based approaches for resource allocation problems in wireless systems. We begin by overviewing important results in the area of opportunistic (channel-aware) scheduling for cellular (single-hop) networks, where easily implementable myopic policies are shown to optimize system performance. We then describe key lessons learned and the main obstacles in extending the work to general resource allocation problems for multihop wireless networks. Towards this end, we show that a clean-slate optimiza- tion-based approach to the multihop resource allocation problem naturally results in a “loosely coupled” cross-layer solution. That is, the algorithms obtained map to different layers [transport, network, and medium access control/physical (MAC/PHY)] of the protocol stack, and are coupled through a limited amount of infor- mation being passed back and forth. It turns out that the optimal scheduling component at the MAC layer is very complex, and thus needs simpler (potentially imperfect) distributed solutions. We demonstrate how to use imperfect scheduling in the cross-layer framework and describe recently developed distributed algo- rithms along these lines. We conclude by describing a set of open research problems. Index Terms—Cellular networks, congestion control, cross-layer optimization, imperfect schedule, multihop wireless networks, op- portunistic scheduling. I. INTRODUCTION O PTIMIZATION-based approaches have been extensively used over the past several years to study resource allo- cation problems in communication networks. For example, Internet congestion control can be viewed as distributed primal or dual solutions to a convex optimization problem that max- imizes the aggregate system performance (or utility). Such approaches have resulted in a deep understanding of the ubiq- uitous transmission control protocol (TCP) and resulted in improved solutions for congestion control [1]–[6]. The key question is whether such approaches can be applied to emerging multihop wireless networks to enable a clean-slate Manuscript received April 30, 2006; revised May 8, 2006. X. Lin and N. B. Shroff are with the Center for Wireless Systems and Appli- cations and the School of Electrical and Computer Engineering, Purdue Univer- sity, West Lafayette, IN 47907 USA (e-mail: linx@ecn.purdue.edu; shroff@ecn. purdue.edu). R. Srikant is with the Department of Electrical and Computer Engineering and Coordinated Science Laboratory, University of Illinois at Urbana–Champaign, Urbana, IL 61801-2307 USA (e-mail: rsrikant@uiuc.edu). Digital Object Identifier 10.1109/JSAC.2006.879351 design of the protocol stack. 1 Indeed there are unique challenges in the wireless context that do not allow a direct application of such techniques from the Internet setting. In particular, the wireless medium is an inherently multiaccess medium where the transmissions of users interfere with each other and where the channel capacity is time-varying (due to user mobility, multipath, and shadowing). This causes interdependencies across users and network layers that are simply not present in their wireline counterparts. In spite of these difficulties, there have been significant recent advances that demonstrate that wireless resources across multiple layers (such as time, frequency, power, link data rates, and end-user data rates), can be incorporated into a unified optimization framework. Interestingly, as will be described in detail in Section III, the solution of such an optimization framework will itself exhibit a layered structure with only a limited degree of cross-layer coupling. We will illustrate the use of such an optimization approach for two classes of cross-layer problems, namely, the oppor- tunistic scheduling problem in cellular (or access-point-based single-hop networks), and the joint congestion-control and scheduling problem in multihop wireless networks. We will see that convex programming is an important tool for this optimization approach; in particular, Lagrange duality is a key tool in decomposing the otherwise complex optimization problem into easily solvable components. However, we will also see that convex programming is often not enough. In fact, unlike their wireline counterparts, the essential features of many wireless cross-layer control problems are not convex. For example, due to interference, wireless networks typically require sophisticated “scheduling” mechanisms to carefully select only a subset of links to be activated at each time. In wireless networks, the capacity of each link depends on the signal and interference levels, and thus depends on the power and transmission schedule at other links. This relationship between the link capacity, power assignment, and the transmis- sion schedule is typically nonconvex. Therefore, the scheduling component needs to solve a difficult nonconvex problem, and usually becomes the bottleneck of the entire solution. These inherent nonconvex features require that advanced techniques in addition to convex programming be used to 1 The notion of a clean-slate design becomes especially attractive for multihop wireless networks, where the burdens of legacy systems are far less than for the Internet. 0733-8716/$20.00 © 2006 IEEE