Premkumar Karumbu

Abstract: We consider a small extent sensor network for event detection, in which nodes take samples periodically and then contend over a {\em random access network} to transmit their measurement packets to the fusion center. We consider two procedures at the fusion center to process the measurements. The Bayesian setting is assumed; i.e., the fusion center has a prior distribution on the change time. In the first procedure, the decision algorithm at the fusion center is \emph{network-oblivious} and makes a decision only when a complete vector of measurements taken at a sampling instant is available. In the second procedure, the decision algorithm at the fusion center is \emph{network-aware} and processes measurements as they arrive, but in a time causal order. In this case, the decision statistic depends on the network delays as well, whereas in the network-oblivious case, the decision statistic does not depend on the network delays. This yields a Bayesian change detection problem with a tradeoff between the random network delay and the decision delay; a higher sampling rate reduces the decision delay but increases the random access delay. Under periodic sampling, in the network--oblivious case, the structure of the optimal stopping rule is the same as that without the network, and the optimal change detection delay decouples into the network delay and the optimal decision delay without the network. In the network--aware case, the optimal stopping problem is analysed as a partially observable Markov decision process, in which the states of the queues and delays in the network need to be maintained. A sufficient statistic for decision is found to be the network-state and the posterior probability of change having occurred given the measurements received and the state of the network. The optimal regimes are studied using simulation.

Abstract: In this paper we report on the outcomes of a research and demonstration project on human intrusion detection in a large secure space using an ad hoc wireless sensor network. This project has been a unique experience in collaborative research, involving ten investigators (with expertise in areas such as sensors, circuits, computer systems, communication and networking, signal processing and security) to execute a large funded project that spanned three to four years. In this paper we report on the speci�c engineering solution that was developed: the various architectural choices and the associated speci�c designs. In addition to developing a demonstrable system, the various problems that arose have given rise to a large amount of basic research in areas such as geographical packet routing, distributed statistical detection, sensors and associated circuits, a low power adaptive micro-radio, and power optimising embedded systems software. We provide an overview of the research results obtained.

Abstract: In this paper, we analyze optimal (in space and time) adaptive power transmission policies for fading channels when the channel-state information (CSI) at the transmitter (CSIT) and the receiver (CSIR) is available. The transmitter has a long-term (time) average power constraint. There can be multiple antennas at the transmitter and at the receiver. The channel experiences Rayleigh fading. We consider beamforming and space-time coded systems with perfect/imperfect CSIT and CSIR. The performance measure is the bit error rate (BER). We show that in both coded and uncoded systems, our power allocation policy provides exponential diversity order if perfect CSIT is available. We also show that, if the quality of CSIT degrades then the exponential diversity is retained in the low SNR region but we get only polynomial diversity in the high SNR region. Another interesting conclusion is that in case of imperfect CSIT and CSIR, knowledge of CSIT at the receiver is very important. Finally, for the optimal power control policy of the uncoded system we find the error-exponents which provide the rate versus diversity-order tradeoff for this policy. This tradeoff is of an entirely different nature than the well-known Zheng-Tse tradeoff.

Abstract: In this paper, we analyze the performance of various layers of the general packet radio service (GPRS) protocol stack, including radio link control/medium-access control (RLC/MAC) layer and logical link-control (LLC) layer on the uplink. In the GPRS MAC protocol, several time-slotted uplink radio-frequency channels are shared by the mobiles on a request-reservation-based multiple-access scheme. Using the theory of Markov chains, we derive expressions for the average throughput and delay performance of the GPRS MAC protocol. We evaluate the performance of the RLC layer (in acknowledged mode) using block-level retransmission (BLR), as de�ned in the current GPRS standard, and compare it with that of using slot-level retransmission (SLR). We show that SLR at the RLC layer performs signi�cantly better than the BLR, particularly when the channel-error rates are moderate to high. We further investigate the choice of parameters (e.g., number of retransmission attempts) for the automatic repeat request schemes at the RLC and LLC layers. Our results show that it is more bene�cial to do error recovery by allowing more retransmission attempts at the RLC layer than at the LLC layer. We also evaluate the performance of transmission-control protocol with BLR and SLR at the RLC layer.

Abstract: We investigate sequential event detection problems arising in Wireless Sensor Networks (WSNs). A number of battery�powered sensor nodes of the same sensing modality are deployed in a region of interest (ROI). By an event we mean a random time (and, for spatial events, a random location) after which the random process being observed by the sensor �eld experiences a change in its probability law. The sensors make measurements at periodic time instants, perform some computations, and then communicate the results of their computations to the fusion centre. The decision making algorithm in the fusion centre employs a procedure that makes a decision on whether the event has occurred or not based on the information it has received until the current decision instant. We seek event detection algorithms in various scenarios, that are optimal in the sense that the mean detection delay (delay between the event occurrence time and the alarm time) is minimum under certain detection error constraints. In the �rst part of the thesis, we study event detection problems in a small extent network where the sensing coverage of any sensor includes the ROI. In particular, we are interested in the following problems: 1) quickest event detection with optimal control of the number of sensors that make observations (while the others sleep), 2) quickest event detection on wireless ad hoc networks, and 3) optimal transient change detection. In the second part of the thesis, we study the problem of quickest detection and isolation of an event in a large extent sensor network where the sensing coverage of any sensor is only a small portion of the ROI. One of the major applications envisioned for WSNs is detecting any abnormal activity or intrusions in the ROI. An intrusion is typically a rare event, and hence, much of the energy of sensors gets drained away in the pre�intrusion period. Hence, keeping all the sensors in the awake state is wasteful of resources and reduces the lifetime of the WSN. This motivates us to consider the problem of sleep�wake scheduling of sensors along with quickest event detection. We formulate the Bayesian quickest event detection problem with the objective of minimising the expected total cost due to i) the detection delay and ii) the usage of sensors, subject to the constraint that the probability of false alarm is upper bounded by α. We obtain optimal event detection procedures, along with optimal closed loop and open loop control for the sleep�wake scheduling of sensors. In the classical change detection problem, at each sampling instant, a batch of n samples (where n is the number of sensors deployed in the ROI) is generated at the sensors and reaches the fusion centre instantaneously. However, in practice, the communication between the sensors and the fusion centre is facilitated by a wireless ad hoc network based on a random access mechanism such as in IEEE 802.11 or IEEE 802.15.4. Because of the medium access control (MAC) protocol of the wireless network employed, di�erent samples of the same batch reach the fusion centre after random delays. The problem is to detect the occurrence of an event as early as possible subject to a false alarm constraint. In this more realistic situation, we consider a design in which the fusion centre comprises a sequencer followed by a decision maker. In earlier work from our research group, a Network Oblivious Decision Making (NODM) was considered. In NODM, the decision maker in the fusion centre is presented with complete batches of observations as if the network was not present and makes a decision only at instants at which these batches are presented. In this thesis, we consider the design in which the decision maker makes a decision at all time instants based on the samples of all the complete batches received thus far, and the samples, if any, that it has received from the next (partial) batch. We show that for optimal decision making the network�state is required by the decision maker. Hence, we call this setting Network Aware Decision Making (NADM). Also, we obtain a mean delay optimal NADM procedure, and show that it is a network�state dependent threshold rule on the a posteriori probability of change. In the classical change detection problem, the change is persistent, i.e., after the change�point, the state of nature remains in the in�change state for ever. However, in applications like intrusion detection, the event which causes the change disappears after a �nite time, and the system goes to an out�of�change state. The distribution of observations in the out�of�change state is the same as that in the pre�change state. We call this short�lived change a transient change. We are interested in detecting whether a change has occurred, even after the change has disappeared at the time of detection. We model the transient change and formulate the problem of quickest transient change detection under the constraint that the probability of false alarm is bounded by α. We also formulate a change detection problem which maximises the probability of detection (i.e., probability of stopping in the in�change state) subject to the probability of false alarm being bounded by α. We obtain optimal detection rules and show that they are threshold rules on the a posteriori probability of pre�change, where the threshold depends on the a posteriori probabilities of pre�change, in�change, and out�of�change states. Finally, we consider the problem of detecting an event in a large extent WSN, where the event in�uences the observations of sensors only in the vicinity of where it occurs. Thus, in addition to the problem of event detection, we are faced with the problem of locating the event, also called the isolation problem. Since the distance of the sensor from the event a�ects the mean signal level that the sensor node senses, we consider a realistic signal propagation model in which the signal strength decays with distance. Thus, the post�change mean of the distribution of observations across sensors is di�erent, and is unknown as the location of the event is unknown, making the problem highly challenging. Also, for a large extent WSN, a distributed solution is desirable. Thus, we are interested in obtaining distributed detection/isolation procedures which are detection delay optimal subject to false alarm and false isolation constraints. For this problem, we propose the following local decision rules, MAX, HALL, and ALL, which are based on the CUSUM statistic, at each of the sensor nodes. We identify corroborating sets of sensor nodes for event location, and propose a global rule for detection/isolation based on the local decisions of sensors in the corroborating sets. Also, we show the minimax detection delay optimality of the procedures HALL and ALL.

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