Arindam Kumar Das

Analysis of the contention access period of IEEE 802.15.4 MAC

The recent ratification of IEEE 802.15.4 PHY-MAC specifications for low-rate wireless personal area networks represents a significant milestone in promoting deployment of wireless sensor networks (WSNs) for a variety of commercial uses. The 15.4 specifications specifically target wireless networking among low-rate, low-power and low-cost devices that is expected to be a key market segment for a large number of WSN applications. In this article, we first analyze the performance of the contention access period specified in the IEEE 802.15.4 standard in terms of throughput and energy consumption. This analysis is facilitated by a modeling of the contention access period as nonpersistent CSMA with backoff. We show that, in certain applications in which having an inactive period in the superframe may not be desirable due to delay constraints, shutting down the radio between transmissions provides significant savings in power without significantly compromising the throughput. We also propose and analyze the performance of a modification to the specification which could be used for applications in which MAC-level acknowledgements are not used. Extensive ns-2 simulations are used to verify the analysis.

Optimization models for fixed channel assignment in wireless mesh networks with multiple radios

The combination of multiple radio nodes in conjunction with a suitably structured multi-hop or mesh architecture has the potential to solve some of the key limitations of present day wireless access networks that are based on single-radio nodes. This paper ad- dresses the channel assignment problem for multi-channel multi-interface (radio) wireless mesh networks. We focus on static wireless mesh networks where multiple non- overlapping channels are available for each wireless inter- face. In this network environment, our objective is to find a fixed channel assignment which maximizes the number of bidirectional links that can be activated simultaneously, subject to interference constraints. We present two mixed integer linear programming models for solving the fixed channel assignment problem with multiple radios. Detailed computational results on various grid topologies are also presented and discussed.

Minimum power broadcast trees for wireless networks: integer programming formulations

Wireless multicast/broadcast sessions, unlike wired networks, inherently reach several nodes with a single transmission. For omnidirectional wireless broadcast to a node, all nodes closer will also be reached. Heuristic algorithms for constructing the minimum power tree in wireless networks have been proposed by Wieselthier et al. and Stojmenovic et al. Recently, an evolutionary search procedure has been proposed by Marks et al. In this paper, we present three different integer programming models which can be used for an optimal solution of the minimum power broadcast/multicast problem in wireless networks. The models assume complete knowledge of the distance matrix and is therefore most suited for networks where the locations of the nodes are fixed.

r-shrink: a heuristic for improving minimum power broadcast trees in wireless networks

Broadcasting in wireless networks, unlike wired networks, inherently reaches several nodes with a single transmission. For omni-directional wireless broadcast to a node, all nodes closer will also be reached. This property can be used to compute routing trees which minimize the sum of the transmitter powers. It has been shown that this problem is NP-complete. In this paper, we present the r-shrink procedure, a heuristic for improving the solutions obtained using fast sub-optimal algorithms. Specifically, we focus on the low-complexity BIP algorithm and Prims minimum spanning tree algorithm and show through extensive simulations that better solutions are obtained almost always, with considerably lower tree power, if the proposed procedure is used to improve the trees generated using these algorithms.

Agreement in presence of noise: pseudogradients on random geometric networks

We consider the agreement problem over realizations of a (Poisson) random geometric network with noisy interconnections. The vertices of random geometric networks are assumed to be uniformly distributed on the unit square; an edge exists between a pair of vertices if the distance between them is less than or equal to a given threshold. Our treatment of the agreement problem in such a setting relies upon notions from stochastic stability. In this venue, we show that the noisy agreement protocol has a guaranteed convergence with probability one, provided that an embedded step size parameter meets certain constraints. These constraints turn out to closely related to the spectra of the underlying graph Laplacian. Moreover, we point out the ramifications of having noisy networks by establishing connections between rate of convergence of the protocol and the range threshold in random geometric graphs.

WLC30-4: Static Channel Assignment in Multi-radio Multi-Channel 802.11 Wireless Mesh Networks: Issues, Metrics and Algorithms

The combination of multiple radio nodes in con junction with a suitably structured multi-hop or mesh architecture has the potential to solve some of the key limitations of present day wireless access networks that are based on single-radio nodes. This paper addresses the static channel assignment problem for multi-channel multi-radio static wireless mesh networks. We present four metrics based on which mesh channel assignments can be obtained. In particular, we focus on minimization of the average and maximum collision domain sizes and show that these problems are closely related to problems in combinatorial optimization such as MAX k-CUT and MIN k- PARTITION. We also present heuristic algorithms for solving the channel assignment problems using the above two metrics.

The minimum power broadcast problem in wireless networks: a simulated annealing approach

Broadcasting in wireless networks, unlike wired networks, inherently reaches several nodes with a single transmission. For an omnidirectional wireless broadcast to a node, all nodes closer to the transmitting node are also reached. This property can be used to compute routing trees which minimize the sum of the transmitter powers. We present a mixed integer programming formulation and a simulated annealing algorithm for the problem. Extensive experimental results for the heuristic approach are presented. They show that the proposed algorithm is capable of improving the results of state-of-the-art algorithms for most of the problems considered. The solutions provided by the simulated annealing algorithm can be improved by applying a very fast post-optimization procedure. This leads to the best known mean results for the problems considered.

MDLT: a polynomial time optimal algorithm for maximization of time-to-first- failure in energy constrained wireless broadcast networks

We consider the problem of maximizing the time-to-first-failure, defined as the time till the first node in the network runs out of battery energy, in energy constrained broadcast wireless networks. We discuss a greedy algorithm and prove that it solves the problem optimally for a broadcast application, in polynomial time, provided the complete power matrix and the battery residual capacities are known.

Distributed Linear Parameter Estimation in Sensor Networks based on Laplacian Dynamics Consensus Algorithm

In this paper, we consider the problem of distributed linear parameter estimation in static and dynamic sensor networks. We propose iterative averaging algorithms based on Laplacian dynamics which converge to the centralized least squares solution asymptotically. In the first part of this paper, we consider the case of unclustered (flat architecture) sensor networks and analyze convergence of the iterative algorithm, for both static and dynamic topologies. Subsequently, we extend our analysis to static but clustered sensor networks with pulsed inter-cluster updates. In this scheme, we assume that all inter-cluster communications occur every H time steps, H > 1, and the corresponding updates are held till the next update instant. Depending on the sensor locations and the topology formation algorithm used, it may be the case that inter-cluster communications require higher transmitter power support than intra-cluster communications. From a power efficiency (or alternately, network lifetime) point of view, it may therefore be beneficial to limit the extent of inter-cluster communication, without significantly enhancing the convergence time of the distributed estimation algorithm. We anticipate that a pulsed inter-cluster update scheme will also be beneficial for applications such as military sensor networks, where low probability of detection and interception is essential. Our analysis provides sufficient conditions under which the distributed algorithm operating on a pulsed inter-cluster update scheme converges. Simulation results are provided which illustrate the dependence of the convergence rate of the algorithm on H

Power controlled minimum frame length scheduling in TDMA wireless networks with sectored antennas

We consider the problem of power controlled minimum frame length scheduling for TDMA wireless networks. Given a set of one-hop transmission requests, our objective is to schedule them in a minimum number of time slots, so that each slot schedule is free of self-interferences and meets desired SINR constraints. Additionally, the transmit power vector corresponding to each slot schedule should be minimal. We consider two different versions of the problem, a per-slot version and a per-frame version, and develop mixed integer linear programming models which can be used for solving the problems optimally. In addition, we propose a heuristic algorithm for the per-slot version.