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 multi-hop wireless networks. Towards this end, we show that a clean-slate optimization based approach to the multi-hop resource allocation problem naturally results in a “loosely coupled” crosslayer solution. That is, the algorithms obtained map to different layers (transport, network, and MAC/PHY) of the protocol stack are coupled through a limited amount of information 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 crosslayer framework and describe recently developed distributed algorithms along these lines. We conclude by describing a set of open research problems.

We consider the problem of allocating resources (time slots, frequency, power, etc.) at a base station to many competing flows, where each flow is intended for a different receiver. The channel conditions may be time-varying and different for different receivers. It is well-known that appropri-ately chosen queue-length based policies are throughput-optimal while other policies based on the estimation of channel statistics can be used to allocate resources fairly (such as proportional fairness) among competing users. In this paper, we show that a combination of queue-length-based scheduling at the base station and congestion control implemented either at the base station or at the end users can lead to fair resource allocation and queue-length stability.

This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with timevarying channels and adaptive multi-rate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with time-varying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dual-based algorithm remains stable and optimal when the constraint set is modulated by an irreducible finite-state Markov chain. This paper thus presents a step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition” for time-varying channel models.

In this work, we describe and analyze a joint scheduling, routing and congestion control mecha-nism for wireless networks, that asymptotically guarantees stability of the buffers and fair allocation of the network resources. The queue lengths serve as common information to different layers of the network protocol stack. Our main contribution is to prove the asymptotic optimality of a primal-dual congestion controller, which is known to model different versions of TCP well.

Abstract — We consider a multi-hop wireless network shared by many users. For an interference model that only constrains a node to either transmit or receive at a time, but not both, we propose an architecture for fair resource allocation that consists of a distributed scheduling algorithm operating in conjunction with an asynchronous congestion control algorithm. We show that the proposed joint congestion control and scheduling algorithm supports at least one-third of the throughput supportable by any other algorithm, including centralized algorithms. I.

Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent cross-layer designs are conducted through piecemeal approaches. They may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of “layering ” as “optimization decomposition”, where the overall communication network is modeled by a generalized Network Utility Maximization (NUM) problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, each leading to a different layering architecture. This paper summarizes the current status of horizontal decomposition into distributed computation and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent work are listed, and open issues discussed. Through case studies, it is illustrated how “Layering as Optimization Decomposition” provides a common language to think

In this paper, we propose and study a general framework that allows the development of distributed mechanisms to achieve full utilization of multi-hop wireless networks. In particular, we develop a generic randomized routing, scheduling and flow control scheme that is applicable to a large class of interference models. We prove that any algorithm which satisfies the conditions of our generic scheme maximizes network throughput and utilization. Then, we focus on a specific interference model, namely the two-hop interference model, and develop distributed algorithms with polynomial communication and computation complexity. This is an important result given that earlier throughput-optimal algorithms developed for such a model relies on the solution to an NP-hard problem. To the best of our knowledge, this is the first polynomial complexity algorithm that guarantees full utilization in multi-hop wireless networks. We further show that our algorithmic approach enables us to efficiently approximate the capacity region of a multi-hop wireless network.

We consider the problem of scheduling multiple users sharing a time-varying wireless channel. (As an example, this is a model of scheduling in 3G wireless technologies, such as CDMA2000 3G1xEV-DO downlink scheduling.) We introduce an algorithm which seeks to optimize a concave utility H i (R i ) of the user throughputs R i , subject to certain lower and upper throughput bounds: R i R i i . The algorithm, which we call the Gradient algorithm with Minimum/Maximum Rate constraints (GMR) uses a token counter mechanism, which modifies an algorithm solving the corresponding unconstrained problem, to produce the algorithm solving the problem with throughput constraints. Two important special cases of the utility functions are log R i and R i , corresponding to the common Proportional Fairness and Throughput Maximization objectives.

Abstract—We consider scheduling and resource allocation for the downlink of a cellular OFDM system, with various practical considerations including integer carrier allocations, different subchannelization schemes, a maximum SNR constraint per tone, and “self-noise ” due to channel estimation errors and phase noise. During each time-slot a subset of users must be scheduled for transmission, and the available tones and transmission power must be allocated among the selected users. Employing a gradient-based scheduling scheme presented in earlier papers reduces this to an optimization problem to be solved in each time-slot. Using dual decomposition techniques, we give an optimal algorithm for this problem when multiple users can time-share each carrier. We then give several low complexity heuristics that enforce an integer constraint on the carrier allocation. Simulations show that the algorithms presented all achieve similar performance under a wide range of scenarios, and that the performance gap between the optimal and suboptimal algorithms widens when per user SNR constraints or channel estimation errors are considered. I.

Recently, network coding emerged as a promising technology that can provide significant improvements in throughput and energy efficiency of wireless networks, even for unicast communication. Often, network coding schemes are designed as an autonomous layer, independent of the underlying Phy and MAC capabilities and algorithms. Consequently, these schemes are greedy, in the sense that all opportunities of broadcasting combinations of packets are exploited. We demonstrate that this greedy design principle may in fact reduce the network throughput. This begets the need for adaptive network coding schemes. We further show that designing appropriate MAC scheduling algorithms is critical for achieving the throughput gains expected from network coding. In this paper, we propose a general framework to develop optimal and adaptive joint network coding and scheduling schemes. Optimality is shown for various Phy and MAC constraints. We apply this framework to two different network coding architectures: COPE, a scheme recently proposed in [7], and XOR-Sym, a new scheme we present here. XOR-Sym is designed to achieve a lower implementation complexity than that of COPE, and yet to provide similar throughput gains.