Abhay Karandikar

An on-line learning algorithm for energy efficient delay constrained scheduling over a fading channel

In this paper, we consider the problem of energy efficient scheduling under average delay constraint for a single user fading channel. We propose a new approach for on-line implementation of the optimal packet scheduling algorithm. This approach is based on reformulating the value iteration equation by introducing a virtual state called post-decision state. The resultant value iteration equation becomes amenable to online implementation based on stochastic approximation. This approach has an advantage that an explicit knowledge of the probability distribution of the channel state as well as the arrivals is not required for the implementation. We prove that the on-line algorithm indeed converges to the optimal policy.

Quantitative assessment of TV white space in India

Licensed but unutilized television (TV) band spectrum is called as TV white space in the literature. Ultra high frequency (UHF) TV band spectrum has very good wireless radio propagation characteristics. The amount of TV white space in the UHF TV band in India is of interest. Comprehensive quantitative assessment and estimates for the TV white space in the 470-590 MHz band for four zones of India (all except north) are presented in this work. This is the first effort in India to estimate TV white spaces in a comprehensive manner. The average available TV white space per unit area in these four zones is calculated using two methods: (i) the primary (licensed) user and secondary (unlicensed) user point of views; and, (ii) the regulations of Federal Communications Commission in the United States. By both methods, the average available TV white space in the UHF TV band is shown to be more than 100 MHz! A TV transmitter frequency reassignment algorithm is also described. Based on spatial-reuse ideas, a TV channel frequency allocation scheme is presented which results in insignificant interference to the TV receivers while using the smallest bandwidth for existing transmission across the four zones. In the proposed reassignment, it is found that four TV band channels (or 32 MHz) are sufficient to provide the existing UHF TV band coverage in India.

Scheduling with limited information in wireless systems

Opportunistic scheduling is a key mechanism for improving the performance of wireless systems. However, this mechanism requires that transmitters are aware of channel conditions (or CSI, Channel State Information) to the various possible receivers. CSI is not automatically available at the transmitters, rather it has to be acquired. Acquiring CSI consumes resources, and only the remaining resources can be used for actual data transmissions. We explore the resulting trade-off between acquiring CSI and exploiting channel diversity to the various receivers. Specifically, we consider a system consisting of a transmitter and a fixed number of receivers/users. An infinite buffer is associated to each receiver, and packets arrive in this buffer according to some stochastic process with fixed intensity. We study the impact of limited channel information on the stability of the system. We characterize its stability region, and show that an adaptive queue length-based policy can achieve stability whenever doing so is possible. We formulate a Markov Decision Process problem to characterize this queue length-based policy. In certain specific and yet relevant cases, we explicitly compute the optimal policy. In general case, we provide a scheduling policy that achieves a fixed fraction of the systems stability region. Scheduling with limited information is a problem that naturally arises in cognitive radio systems, and our results can be used in these systems.

Structural Properties of Optimal Transmission Policies Over a Randomly Varying Channel

We consider the problem of transmitting packets over a randomly varying point to point channel with the objective of minimizing the expected power consumption subject to a constraint on the average packet delay. By casting it as a constrained Markov decision process in discrete time with time-averaged costs, we prove structural results about the dependence of the optimal policy on buffer occupancy, number of packet arrivals in the previous slot and the channel fading state for both i.i.d. and Markov arrivals and channel fading. The techniques we use to establish such results: convexity, stochastic dominance, decreasing-differences, are among the standard ones for the purpose. Our main contribution, however, is the passage to the average cost case, a notoriously difficult problem for which rather limited results are available. The novel proof techniques used here are likely to have utility in other stochastic control problems well beyond their immediate application considered here.

Explicit congestion notification (ECN) in TCP over wireless network

Reliable transport protocols like the transmission control protocol (TCP) are tuned to perform well in traditional wireline networks where packet losses occur mostly because of congestion. However, networks with wireless and lossy links also suffer from significant packet losses due to random losses and handoffs. TCP responds to all the packet losses by invoking a congestion control algorithm and this results in degraded end-to-end performance in wireless and lossy links. In this paper, we suggest a strategy to determine the cause of packet drops in a wireless network running the TCP protocol. Our method is based on modification of explicit congestion notification (ECN) in TCP for wireless networks.

Optimal relay placement for cellular coverage extension

In this paper, we address the problem of optimal relay placement in cellular networks for maximum extension of coverage area. We present a novel definition of the coverage radius after the introduction of relays. Using this, we determine the optimal relay positions to maximize the coverage radius and estimate the number of relays required per cell. We also analyze relay placement in the multi-cell scenario, which takes into account inter-cell interference, a dominant factor in the next generation cellular Orthogonal Frequency Division Multiple Access (OFDMA) systems. Considering inter-cell interference in the multi-cell scenario, leads to an interesting iterative algorithm which is used to determine the optimal relay station (RS) positions.

Link Scheduling Algorithms for Wireless Mesh Networks

Wireless Mesh Networks (WMNs) have the potential of being a cost effective solution to provide connectivity and coverage in both urban and rural areas. Typically, a WMN is a backbone network that carries high data rate traffic and employs Time Division Multiple Access (TDMA) like access mechanisms. For a WMN to provide high throughput, the design of an efficient link scheduling algorithm is of paramount importance. Towards this end, we provide an overview of link scheduling algorithms in Spatial TDMA wireless mesh networks. These algorithms can be classified into three categories: those based only on a communication graph model of the network, those based on a communication graph model and Signal to Interference and Noise Ratio (SINR) threshold conditions at receivers and those based on an SINR graph model of the network. We first outline a framework for modeling STDMA networks. We review representative research works and provide the description of an algorithm from each of these classes. We describe the relative merits and demerits of each class of algorithms and compare their performance via simulations. We conclude with a discussion on practical implementation of these algorithms and open research problems.

A Stable Online Algorithm for Energy-Efficient Multiuser Scheduling

In this paper, we consider the problem of energy-efficient uplink scheduling with delay constraint for a multiuser wireless system. We address this problem within the framework of constrained Markov decision processes (CMDPs) wherein one seeks to minimize one cost (average power) subject to a hard constraint on another (average delay). We do not assume the arrival and channel statistics to be known. To handle state-space explosion and informational constraints, we split the problem into individual CMDPs for the users, coupled through their Lagrange multipliers; and a user selection problem at the base station. To address the issue of unknown channel and arrival statistics, we propose a reinforcement learning algorithm. The users use this learning algorithm to determine the rate at which they wish to transmit in a slot and communicate this to the base station. The base station then schedules the user with the highest rate in a slot. We analyze convergence, stability, and optimality properties of the algorithm. We also demonstrate the efficacy of the algorithm through simulations within IEEE 802.16 system.

Robust Active Queue Management for Wireless Networks

Active Queue Management (AQM) algorithms have been extensively studied in the literature in the context of wired networks. In this paper, we study AQM for wireless networks. Unlike a wired link, which is assumed to have a fixed capacity, a wireless link has a capacity that is time-varying due to fading. Thus, the controller is required to meet performance objectives in the presence of these capacity variations. We propose a robust controller design that maintains the queue length close to an operating point. We treat capacity variations as an external disturbance and design a robust controller using H∞ control techniques. We also consider the effect of round-trip time in our model. Our method of incorporating the delay into the discretized model simplifies controller design by allowing direct use of systematic controller design methods and/or design packages. We demonstrate the robustness of the controller to changes in the load condition and in the round-trip time through ns-2 simulations.

On High Spatial Reuse Link Scheduling in STDMA Wireless Ad Hoc Networks

We consider the point-to-point link scheduling problem in Spatial Time Division Multiple Access (STDMA) wireless ad hoc networks, motivate the use of spatial reuse as performance metric and provide an explicit characterization of spatial reuse. We assume uniform transmission power at all nodes and propose an algorithm based on a graph model of the network as well as Signal to Interference and Noise Ratio (SINR) computations. Our algorithm achieves higher spatial reuse than existing algorithms, without compromising on computational complexity.