Arjunan Rajeswaran

Capacity of power constrained ad-hoc networks

Throughput capacity is a critical parameter for the design and evaluation of ad-hoc wireless networks. Consider n identical randomly located nodes, on a unit area, forming an ad-hoc wireless network. Assuming a fixed per node transmission capability of T hits per second at a fixed range, it has been shown that the uniform throughput capacity per node r(n) is /spl otimes/(T//spl radic/nlogn). We consider an alternate communication model, with each node constrained to a maximum transmit power P/sub 0/ and capable of utilizing W Hz of bandwidth. Under the limiting case W/spl rarr//spl infin/, such as in ultra wide band networks, the uniform throughput per node is /spl otimes/((nlogn)/sup /spl alpha/-1/2/ (upper bound) and /spl Omega/(n/sup (/spl alpha/-1)/2//(logn)/sup (/spl alpha/+1)/2/) (achievable lower bound). These bounds demonstrate that throughput increases with node density n, in contrast to previously published results. This is the result of the large bandwidth, and the assumed power and rate adaptation, which alleviate interference. Thus, the significance of physical layer properties on the capacity of ad-hoc wireless networks is demonstrated.

RAKE performance for a pulse based UWB system in a realistic UWB indoor channel

The performance of a RAKE receiver for a pulse based ultra-wideband (UWB) communications system is studied in a realistic channel model that is based on an extensive set of indoor channel measurements. The RAKE receiver is shown to contribute to a mitigation of the ISI. In particular, at low input SNR values and small number of RAKE taps, it is shown that employing additional RAKE taps for energy capture is more important to overall system performance than employing equalization to combat the ISI. The performance of the RAKE with some realistic channel estimation errors is also studied.

DoS analysis of reservation based MAC protocols

Reservation based medium access control (MAC) protocols such as the 802.11 distributed coordination function (DCF), are designed to maximize throughput efficiency, by utilizing small control packets. However, this ability to reserve bandwidth makes the protocol susceptible to sophisticated MAC layer denial of service (DoS) attacks. A novel attack on reservation based MAC protocols is described using the example of 802.11 networks. An analysis of the attack demonstrates the catastrophic effect on network throughput of a low power MAC layer jammer. This is in contrast to physical layer jamming, where the loss of throughput is proportional to jammer power. A counter-measure based on modifying the MAC protocol is developed, and shown to limit the intelligent jammers effect. Protections against further attacks on the modified protocol are also discussed.

Scheduling and power adaptation for networks in the ultra wide band regime

The max-min fair scheduling problem in wireless ad hoc networks, in general, is a non-convex optimization problem. However in the limit of infinite bandwidth (W /spl rarr/ /spl infin/), the solution reduces to a simple simultaneous transmission (spread spectrum) of all links. Thus, having a very large bandwidth significantly simplifies the problem of scheduling. In This work, the scheduling problem is considered in the 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. This approximation is applied to the general non-convex scheduling problem to obtain a dual problem, which involves a quadratic optimization sub-problem. A search algorithm is devised to find the optimal solution of the quadratic sub-problem. This solution is utilized to iteratively construct the schedule (sub-band 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. Thus, exploiting the UWB nature of the physical layer simplifies the wireless ad-hoc network scheduling problem.

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.

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

Capacity of Ultra Wide Band Wireless Ad Hoc Networks

Throughput capacity is a critical parameter for the design and evaluation of ad-hoc wireless networks. Assuming a fixed per node transmission capability of T bits per second at a fixed range, it has been shown [1] that the information theoretic uniform throughput capacity per node r(n) is Theta (T/radicn log n), a decreasing function of node density n. However we consider an alternate communication model, with each node constrained to a maximum transmit power P0 and capable of utilizing W Hz of bandwidth. Under the limiting case W rarr infin, such as in ultra wide band (UWB) networks, we show that the uniform throughput per node is O ((n log n)alpha-1/2 (upper bound) and Omega(n(alpha-1)/2(log n(alpha+1)/2) (achievable lower bound). Thus we demonstrate that the throughput increases with node density n, in contrast to previously published results. The capacity problem is also considered from an optimization theoretic perspective. The novel information theoretic capacity bound is compared to the network optimization results, demonstrating its practical applicability to UWB networks. The dramatic effect of the UWB physical layer on the capacity justifies the promise of UWB as a physical layer technology for ad-hoc networks.

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.

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.

PHY-Graph Model for Ad Hoc Wireless MAC

The ad hoc wireless MAC problem is based on a model of interference between links. Prior disk graph models consider pair-wise interference and have been analyzed to provide bounds on MAC performance, through the application of graph theoretic coloring results. The recently developed PHY graph model is based on the physical layer and so is a more realistic model than disk graph models. An initial MAC performance bound based on the PHY graph model has been shown. Here, the model is analyzed in a novel proof resulting in an improved bound on the MAC performance. The accuracy of the PHY graph model, in modelling the ad hoc wireless problem, is explored through detailed simulations. Salient features of the model are utilized to provide a performance improvement.