Gyouhwan Kim

A scheduling framework for UWB & cellular networks

The max-min fair scheduling problem in wireless ad-hoc networks is a non-convex optimization problem. A general framework is presented for this optimization problem and analyzed to obtain a dual problem, which involves solving a series of optimization sub-problems. In the limit of infinite bandwidth (W /spl rarr/ /spl infin/), the scheduling solution reduces to simultaneous transmission (spread spectrum) on all links (R. Negi and A. Rajeswaran, March 2004). This motivates the analysis of the scheduling problem in the ultra wide band (UWB) regime (W /spl Gt/ 1, but finite), a model for certain practical radios. A quadratic (in 1/W) lower bound to the single link capacity function is developed, which simplifies the dual sub-problem to a quadratic optimization (R. Negi and A. Rajeswaran, December 2004). The solution to this sub-problem is then obtained under both total power and power spectral density constraints. This solution is utilized to iteratively construct the schedule (subband sizes) and power allocation, thus optimally solving the UWB max-min fair scheduling problem, to within any desired precision. Simulations on medium sized networks demonstrate the excellent performance of this scheme. A cellular architecture (not necessarily UWB) may also be considered in this framework. It is proved that frequency division multiple access is the optimal scheduling for a multi-band cellular architecture.

Maximal Scheduling in a Hypergraph Model for Wireless Networks

We introduce a hypergraph based interference model for scheduling in wireless networks. As a generalization of the graph model, hypergraph considers the conflicts caused by sum interference. We show in an arbitrary network, the successful transmissions under any graph model can be improved by a hypergraph. In some networks, a hypergraph can double the uniform throughput compared to the disk graph. We then analyze the capacity region of maximal scheduling in the hypergraph, where a linear programming (LP) based lower bound is formulated and proven to be tight. We also show that the maximal scheduling in hypergraph can guarantee a certain fraction of the capacity region. Simulation results show that maximal scheduling in hypergraph can achieve about 40% more uniform throughput than in graph for random networks.

Joint Power Adaptation, Scheduling, and Routing for Ultra Wide Band Networks

A general cross-layer optimization problem, to maximize network efficiency (min-max power) of ad-hoc networks, is formulated including power adaptation, scheduling and routing functionalities. The non-convexity of the link capacity, high dimensionality of multi-hop routing and inter-layer interactions among the protocol layers, renders the problem hard. Conversion to an equivalent form, results in two clearly separable sub-problems, demonstrating the functionalities of the protocol layers. This decomposition allows the application of a simple shortest path based algorithm to the high-dimensional routing sub-problem. Further, in the case of UWB networks, the non-convex scheduling & power adaptation sub-problem can be effectively approximated and solved by applying a novel quadratic lower bound to the link capacity function. Using these algorithmic solutions to these sub-problems, an interior point solver generating solutions to the joint UWB network problem is developed. The various simulation results demonstrate interesting characteristics of the optimal routing and scheduling solutions, and provide benchmarks for UWB network design. Comparison with prior information theoretic capacity results, validates the importance of this cross-layer optimization framework

Joint power adaptation, scheduling and routing framework for wireless ad-hoc networks

In wireless ad-hoc networks, there exists strong interdependency between protocol layers, due to the shared wireless medium. Hence we cast the power adaptation (physical layer), scheduling (link layer) and routing (network layer) problems into a joint optimization framework. We analyze this hard non-convex optimization problem, and obtain a dual form consisting of a series of sub-problems. The sub-problem demonstrates the functionalities of the protocol layers and their interaction. We show that the routing problem may be solved by a shortest path algorithm. In the case of ultra wide band (UWB) networks, the power adaptation & scheduling problem is simplified and may be solved. Thus, an algorithmic solution to the joint problem, in the UWB case, is developed. Comparison of results with the previous information theoretic capacity results on UWB networks, demonstrates the importance of this cross-layer optimization framework.

A Graph-Based Algorithm for Scheduling with Sum-Interference in Wireless Networks

For decades, a disk-graph model has been used to design scheduling (coloring) in wireless networks, influencing many practical medium access control schemes. The pairwise - interference model used by a disk graph, however, has a fundamental limitation because it does not account for the sum- interference. Thus, a coloring algorithm that uses such a model cannot guarantee the originally intended rate on all links. In this paper, we specify a mapping to a flow-contention graph, which fully considers the aggregated effect of all interferers (sum- interference), and thus, guarantees the originally intended rate on all links. A coloring algorithm, specific to the generated graph, is presented along with a bound on the required number of colors (channels). Further, a mathematical analysis of the scheduling is presented along with simulation results, to show that the minimum number of channels required in a random network is Theta(logn/log log n), where n is the number of links, even after accounting for the sum-interference. This allows us to investigate the effect of the underlying physical layer, thus demonstrating the utility of the presented algorithm and analysis results.

UWB versus 802.11 - a Network Perspective

Debate has been raging on the relative merits of Ultra Wide Band (UWB) and 802.11 as the technology of choice to achieve high speed wireless networking. The comparisons have focused on the single-link rate versus range issues. However, in real world applications, these radios will operate in a networking environment with significant interference effects. The interference handling capabilities of these two radios are drastically different due to their dramatically opposite power-bandwidth trade-offs. In this paper, a networking comparison, of UWB and 802.11, is performed through the application of a formal optimization theoretic framework. Simulations are conducted for network topologies typical of WPAN and WLAN scenarios. It is demonstrated that the link range over which UWB outperforms 802.11 is larger than is to be expected from a single-link comparison. Thus, a network-level comparison of different physical layers is shown to be essential in choosing the appropriate wireless technologies. A few possible future variations of 802.11 and UWB are also investigated in this flexible framework.

Dynamic Programming for Scheduling a Single Route in Wireless Networks

Multi-slot resource scheduling in a general two dimensional wireless ad hoc network, is a hard problem with no known polynomial-time solution. Recent optimization theoretic analysis, structures this multi-slot scheduling problem into a polynomial number of particular single-slot sub-problems, thus isolating the hardness. We consider this hard sub-problem, under the useful topology restriction of a single route of many links. We introduced a novel interference model that allows for a dynamic programming (DP) algorithm to solve this sub-problem. The developed DP algorithm provides a solution with a provable accuracy in polynomial time. Incorporating this novel solution in a general resource scheduling framework, a multi-slot scheduling algorithm for single route networks is developed. The excellent accuracy of the algorithms is demonstrated through extensive simulations in various scenarios.

Interference Handling in UWB Versus 802.11n Networks

UWB and 802.11n have both been touted as technologies for next generation wireless networks. UWB exploiting a large bandwidth, and 802.11n utilizing MIMO, demonstrate high data rates in single links. However, in real world applications these two technologies will not operate as isolated single links, but in a network environment characterized by interference. Through the application of a formal optimization theoretic framework, we demonstrate that their relative network performance is very different from a physical layer comparison. The interference handling capabilities of UWB and 802.11n cause this significant network performance result. We explore practical effects that alter the perceived interference and so, relative network performance. Further, recommendations for the use of multiple antennas in 802.11n radios are presented.