Matthew Andrews

An overview of limited feedback in wireless communication systems

It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.

Providing quality of service over a shared wireless link

We propose an efficient way to support quality of service of multiple real-time data users sharing a wireless channel. We show how scheduling algorithms exploiting asynchronous variations of channel quality can be used to maximize the channel capacity (i.e., maximize the number of users that can be supported with the desired QoS).

SCHEDULING IN A QUEUING SYSTEM WITH ASYNCHRONOUSLY VARYING SERVICE RATES

We consider the following queuing system which arises as a model of a wireless link shared by multiple users. There is a finite number N of input flows served by a server. The system operates in discrete time t = 0,1,2,…. Each input flow can be described as an irreducible countable Markov chain; waiting customers of each flow are placed in a queue. The sequence of server states m(t), t = 0,1,2,…, is a Markov chain with finite number of states M. When the server is in state m, it can serve mim customers of flow i (in one time slot).The scheduling discipline is a rule that in each time slot chooses the flow to serve based on the server state and the state of the queues. Our main result is that a simple online scheduling discipline, Modified Largest Weighted Delay First, along with its generalizations, is throughput optimal; namely, it ensures that the queues are stable as long as the vector of average arrival rates is within the system maximum stability region.

Optimal utility based multi-user throughput allocation subject to throughput constraints

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 function /spl Sigma//sub i/H/sub i/(R/sub i/) of the user throughputs R/sub i/, subject to certain lower and upper throughput bounds: R/sub i//sup min//spl les/R/sub i//spl les/R/sub i//sup max/. 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 /spl Sigma//sub i/log R/sub i/ and /spl Sigma//sub i/R/sub i/, corresponding to the common proportional fairness and throughput maximization objectives. We study the dynamics of user throughputs under GMR algorithm, and show that GMR is asymptotically optimal in the following sense. If, under an appropriate scaling, the throughput vector R(t) converges to a fixed vector R/sup +/ as time t/spl rarr//spl infin/ then R/sup +/ is an optimal solution to the optimization problem described above. We also present simulation results showing the algorithm performance.

Maximizing Capacity in Arbitrary Wireless Networks in the SINR Model: Complexity and Game Theory

In this paper we consider the problem of maximizing the number of supported connections in arbitrary wireless networks where a transmission is supported if and only if the signal-to-interference-plus-noise ratio at the receiver is greater than some threshold. The aim is to choose transmission powers for each connection so as to maximize the number of connections for which this threshold is met. We believe that analyzing this problem is important both in its own right and also because it arises as a subproblem in many other areas of wireless networking. We study both the complexity of the problem and also present some game theoretic results regarding capacity that is achieved by completely distributed algorithms. We also feel that this problem is intriguing since it involves both continuous aspects (i.e. choosing the transmission powers) as well as discrete aspects (i.e. which connections should be supported). Our results are: ldr We show that maximizing the number of supported connections is NP-hard, even when there is no background noise. This is in contrast to the problem of determining whether or not a given set of connections is feasible since that problem can be solved via linear programming. ldr We present a number of approximation algorithms for the problem. All of these approximation algorithms run in polynomial time and have an approximation ratio that is independent of the number of connections. ldr We examine a completely distributed algorithm and analyze it as a game in which a connection receives a positive payoff if it is successful and a negative payoff if it is unsuccessful while transmitting with nonzero power. We show that in this game there is not necessarily a pure Nash equilibrium but if such an equilibrium does exist the corresponding price of anarchy is independent of the number of connections. We also show that a mixed Nash equilibrium corresponds to a probabilistic transmission strategy and in this case such an equilibrium always exists and has a price of anarchy that is independent of the number of connections. This work was supported by NSF contract CCF-0728980 and was performed while the second author was visiting Bell Labs in Summer, 2008.

Universal-stability results and performance bounds for greedy contention-resolution protocols

In this paper, we analyze the behavior of packet-switched communication networks in which packets arrive dynamically at the nodes and are routed in discrete time steps across the edges. We focus on a basic adversarial model of packet arrival and path determination for which the time-averaged arrival rate of packets requiring the use of any edge is limited to be less than 1. This model can reflect the behavior of connection-oriented networks with transient connections (such as ATM networks) as well as connectionless networks (such as the Internet). We concentrate on greedy (also known as work-conserving) contention-resolution protocols. A crucial issue that arises in such a setting is that of stability—will the number of packets in the system remain bounded, as the system runs for an arbitrarily long period of time? We study the universal stability of network (i.e., stability under all greedy protocols) and universal stability of protocols (i.e., stability in all networks). Once the stability of a system is granted, we focus on the two main parameters that characterize its performance: maximum queue size required and maximum end-to-end delay experienced by any packet. Among other things, we show: (i) There exist simple greedy protocols that are stable for all networks.(ii) There exist other commonly used protocols (such as FIFO) and networks (such as arrays and hypercubes) that are not stable.(iii) The n-node ring is stable for all greedy routing protocols (with maximum queue-size and packet delay that is linear in n).(iv) There exists a simple distributed randomized greedy protocol that is stable for all networks and requires only polynomial queue size and polynomial delay.Our results resolve several questions posed by Borodin et al., and provide the first examples of (i) a protocol that is stable for all networks, and (ii) a protocol that is not stable for all networks.

Joint Scheduling and Congestion Control in Mobile Ad-Hoc Networks

In this paper we study the problem of jointly performing scheduling and congestion control in mobile ad-hoc networks so that network queues remain bounded and the resulting flow rates satisfy an associated network utility maximization problem. In recent years a number of papers have presented theoretical solutions to this problem that are based on combining differential-backlog scheduling algorithms with utility-based congestion control. However, this work typically does not address a number of issues such as how signaling should be performed and how the new algorithms interact with other wireless protocols. In this paper we address such issues. In particular: ldr We define a specific network utility maximization problem that we believe is appropriate for mobile adhoc networks. ldr We describe a wireless greedy primal dual (wGPD) algorithm for combined congestion control and scheduling that aims to solve this problem. ldr We show how the wGPD algorithm and its associated signaling can be implemented in practice with minimal disruption to existing wireless protocols. ldr We show via OPNET simulation that wGPD significantly outperforms standard protocols such as 802.11 operating in conjunction with TCP. This work was supported by the DARPA CBMANET program.

Instability of the proportional fair scheduling algorithm for HDR

In this letter, we study the Proportional Fair scheduler that has been proposed for scheduling in the high data rate (HDR) wireless data system. We consider a single basestation transmitting to a set of mobile users. In each time slot, the scheduler has to decide on a mobile to which it will transmit data. The decision is based on information that the basestation receives about the time-varying channels between itself and the mobiles. We focus on deciding whether or not Proportional Fair is stable in a situation with finite queues and a data arrival process. That is, we wish to decide if Proportional Fair keeps all queues bounded whenever this is feasible. There are, in fact, multiple versions of Proportional Fair, depending on how it treats small queues. In this letter, we consider six different versions and show that all are unstable for one simple example.

Scheduling algorithms for multi-carrier wireless data systems

We consider the problem of scheduling multicarrier wireless data in systems such as IEEE 802.16 (WiMAX). Each scheduling decision involves assigning carriers to users for each time slot, subject to the constraint that each carrier is assigned to at most one user, but multiple carriers can potentially be assigned to the same user. One important aspect of our problem is that a scheduler knows the channel rates across all users and all carriers whenever a scheduling decision is made. This “global” information may give a potential for enhancing performance via an optimized allocation of carriers to users. We analyze this problem in a situation where finite queues are fed by a data arrival process. The well-known MaxWeight algorithm for the single-carrier setting maximizes the product of queue size and service rate. We focus on how to adapt MaxWeight to the multicarrier setting. If the same objective is pursued, more service than needed may be assigned to drain a queue, thereby creating wastage. While a simple variant in the objective forbids this wastage, it turns an easy-to-compute old objective into an intractable new objective. We state the hardness of the new optimization problems and propose several extremely simple algorithms with provable performance bounds. We conclude with supporting simulation examples.

Probabilistic end-to-end delay bounds for earliest deadline first scheduling

We analyze the earliest-deadline-first (EDF) scheduling discipline within the framework of statistical multiplexing. We derive techniques for bounding the probability of delay violations when the session injections are independent. This enables us to determine whether a given set of sessions can all meet their delay bounds with the required violation probability. These techniques can be used by a connection admission control (CAC) scheme to decide whether to admit a new session. Our analysis applies to both the single node problem and the network problem in which the sessions have multiple hops. We also give extensive numerical results to illustrate how our bounds may be calculated and to compare the results with estimates that have been derived for generalized processor sharing (GPS). In addition we show that by altering the deadlines for EDF we can match the desired violation probabilities more closely.