arXiv subjects

Subhrakanti Dey

Publications and source records attributed to Subhrakanti Dey.

At least 55 records · Page 3Linked to original sources

arXiv2018

Sequential Detection of Deception Attacks in Networked Control Systems with Watermarking

In this paper, we investigate the role of a physical watermarking signal in quickest detection of a deception attack in a scalar linear control system where the sensor measurements can be replaced by an arbitrary stationary signal generated by an attacker. By adding a random watermarking signal to the control action, the controller designs a sequential test based on a Cumulative Sum (CUSUM) method that accumulates the log-likelihood ratio of the joint distribution of the residue and the watermarking signal (under attack) and the joint distribution of the innovations and the watermarking signal under no attack. As the average detection delay in such tests is asymptotically (as the false alarm rate goes to zero) upper bounded by a quantity inversely proportional to the Kullback-Leibler divergence(KLD) measure between the two joint distributions mentioned above, we analyze the effect of the watermarking signal variance on the above KLD. We also analyze the increase in the LQG control cost due to the watermarking signal, and show that there is a tradeoff between quick detection of attacks and the penalty in the control cost. It is shown that by considering a sequential detection test based on the joint distributions of residue/innovations and the watermarking signal, as opposed to the distributions of the residue/innovations only, we can achieve a higher KLD, thus resulting in a reduced average detection delay. Numerical results are provided to support our claims.

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arXiv2017

Stochastic Game in Remote Estimation under DoS Attacks

This paper studies remote state estimation under denial-of-service (DoS) attacks. A sensor transmits its local estimate of an underlying physical process to a remote estimator via a wireless communication channel. A DoS attacker is capable to interfere the channel and degrades the remote estimation accuracy. Considering the tactical jamming strategies played by the attacker, the sensor adjusts its transmission power. This interactive process between the sensor and the attacker is studied in the framework of a zero-sum stochastic game. To derive their optimal power schemes, we first discuss the existence of stationary Nash equilibrium (SNE) for this game. We then present the monotone structure of the optimal strategies, which helps reduce the computational complexity of the stochastic game algorithm. Numerical examples are provided to illustrate the obtained results.

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arXiv2017

Optimal Scheduling of Multiple Sensors with Packet Length Constraint

This paper considers the problem of sensory data scheduling of multiple processes. There are $n$ independent linear time-invariant processes and a remote estimator monitoring all the processes. Each process is measured by a sensor, which sends its local state estimate to the remote estimator. The sizes of the packets are different due to different dimensions of each process, and thus it may take different lengths of time steps for the sensors to send their data. Because of bandwidth limitation, only a portion of all the sensors are allowed to transmit. Our goal is to minimize the average of estimation error covariance of the whole system at the remote estimator. The problem is formulated as a Markov decision process (MDP) with average cost over an infinite time horizon. We prove the existence of a deterministic and stationary policy for the problem. We also find that the optimal policy has a consistent behavior and threshold type structure. A numerical example is provided to illustrate our main results.

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arXiv2017

Multi-sensor Transmission Management for Remote State Estimation under Coordination

This paper considers the remote state estimation in a cyber-physical system (CPS) using multiple sensors. The measurements of each sensor are transmitted to a remote estimator over a shared channel, where simultaneous transmissions from other sensors are regarded as interference signals. In such a competitive environment, each sensor needs to choose its transmission power for sending data packets taking into account of other sensors' behavior. To model this interactive decision-making process among the sensors, we introduce a multi-player non-cooperative game framework. To overcome the inefficiency arising from the Nash equilibrium (NE) solution, we propose a correlation policy, along with the notion of correlation equilibrium (CE). An analytical comparison of the game value between the NE and the CE is provided, with/without the power expenditure constraints for each sensor. Also, numerical simulations demonstrate the comparison results.

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arXiv2017

Decentralized Transmission Policies for Energy Harvesting Devices

The problem of finding decentralized transmission policies in a wireless communication network with energy harvesting constraints is formulated and solved using the decentralized Markov decision process framework. The proposed policy defines the transmission probabilities of all devices so as to correctly balance the collision probabilities with the energy constraints. After an initial coordination phase, in which the network parameters are initialized for all devices, every node proceeds in a fully decentralized fashion. We numerically show that, because of the harvesting, a fully orthogonal scheme (e.g., TDMA-like) is sub-optimal in this scenario, and that the optimal trade-off lies between an orthogonal and a completely symmetric system.

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arXiv2017

Remote State Estimation over Packet Dropping Links in the Presence of an Eavesdropper

This paper studies remote state estimation in the presence of an eavesdropper. A sensor transmits local state estimates over a packet dropping link to a remote estimator, while an eavesdropper can successfully overhear each sensor transmission with a certain probability. The objective is to determine when the sensor should transmit, in order to minimize the estimation error covariance at the remote estimator, while trying to keep the eavesdropper error covariance above a certain level. This is done by solving an optimization problem that minimizes a linear combination of the expected estimation error covariance and the negative of the expected eavesdropper error covariance. Structural results on the optimal transmission policy are derived, and shown to exhibit thresholding behaviour in the estimation error covariances. In the infinite horizon situation, it is shown that with unstable systems one can keep the expected estimation error covariance bounded while the expected eavesdropper error covariance becomes unbounded. An alternative measure of security, constraining the amount of information revealed to the eavesdropper, is also considered, and similar structural results on the optimal transmission policy are derived. In the infinite horizon situation with unstable systems, it is now shown that for any transmission policy which keeps the expected estimation error covariance bounded, the expected amount of information revealed to the eavesdropper is always lower bounded away from zero. An extension of our results to the transmission of measurements is also presented.

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arXiv2017

A Decentralized Optimization Framework for Energy Harvesting Devices

Designing decentralized policies for wireless communication networks is a crucial problem, which has only been partially solved in the literature so far. In this paper, we propose the Decentralized Markov Decision Process (Dec-MDP) framework to analyze a wireless sensor network with multiple users which access a common wireless channel. We consider devices with energy harvesting capabilities, so that they aim at balancing the energy arrivals with the data departures and with the probability of colliding with other nodes. Randomly over time, an access point triggers a SYNC slot, wherein it recomputes the optimal transmission parameters of the whole network, and distributes this information. Every node receives its own policy, which specifies how it should access the channel in the future, and, thereafter, proceeds in a fully decentralized fashion, without interacting with other entities in the network. We propose a multi-layer Markov model, where an external MDP manages the jumps between SYNC slots, and an internal Dec-MDP computes the optimal policy in the near future. We numerically show that, because of the harvesting, a fully orthogonal scheme (e.g., TDMA-like) is suboptimal in energy harvesting scenarios, and the optimal trade-off lies between an orthogonal and a random access system.

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arXiv2016

Attack Allocation on Remote State Estimation in Multi-Systems: Structural Results and Asymptotic Solution

This paper considers optimal attack attention allocation on remote state estimation in multi-systems. Suppose there are $\mathtt{M}$ independent systems, each of which has a remote sensor monitoring the system and sending its local estimates to a fusion center over a packet-dropping channel. An attacker may generate noises to exacerbate the communication channels between sensors and the fusion center. Due to capacity limitation, at each time the attacker can exacerbate at most $\mathtt{N}$ of the $\mathtt{M}$ channels. The goal of the attacker side is to seek an optimal policy maximizing the estimation error at the fusion center. The problem is formulated as a Markov decision process (MDP) problem, and the existence of an optimal deterministic and stationary policy is proved. We further show that the optimal policy has a threshold structure, by which the computational complexity is reduced significantly. Based on the threshold structure, a myopic policy is proposed for homogeneous models and its optimality is established. To overcome the curse of dimensionality of MDP algorithms for general heterogeneous models, we further provide an asymptotically (as $\mathtt{M}$ and $\mathtt{N}$ go to infinity) optimal solution, which is easy to compute and implement. Numerical examples are given to illustrate the main results.

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arXiv2016

Sensor Scheduling in Variance Based Event Triggered Estimation with Packet Drops

This paper considers a remote state estimation problem with multiple sensors observing a dynamical process, where sensors transmit local state estimates over an independent and identically distributed (i.i.d.) packet dropping channel to a remote estimator. At every discrete time instant, the remote estimator decides whether each sensor should transmit or not, with each sensor transmission incurring a fixed energy cost. The channel is shared such that collisions will occur if more than one sensor transmits at a time. Performance is quantified via an optimization problem that minimizes a convex combination of the expected estimation error covariance at the remote estimator and expected energy usage across the sensors. For transmission schedules dependent only on the estimation error covariance at the remote estimator, this work establishes structural results on the optimal scheduling which show that 1) for unstable systems, if the error covariance is large then a sensor will always be scheduled to transmit, and 2) there is a threshold-type behaviour in switching from one sensor transmitting to another. Specializing to the single sensor case, these structural results demonstrate that a threshold policy (i.e. transmit if the error covariance exceeds a certain threshold and don't transmit otherwise) is optimal. We also consider the situation where sensors transmit measurements instead of state estimates, and establish structural results including the optimality of threshold policies for the single sensor, scalar case. These results provide a theoretical justification for the use of such threshold policies in variance based event triggered estimation. Numerical studies confirm the qualitative behaviour predicted by our structural results. An extension of the structural results to Markovian packet drops is also outlined.

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arXiv2016

Sensing Throughput Optimization in Fading Cognitive Multiple Access Channels With Energy Harvesting Secondary Transmitters

The paper investigates the problem of maximizing expected sum throughput in a fading multiple access cognitive radio network when secondary user (SU) transmitters have energy harvesting capability, and perform cooperative spectrum sensing. We formulate the problem as maximization of sum-capacity of the cognitive multiple access network over a finite time horizon subject to a time averaged interference constraint at the primary user (PU) and almost sure energy causality constraints at the SUs. The problem is a mixed integer non-linear program with respect to two decision variables namely spectrum access decision and spectrum sensing decision, and the continuous variables sensing time and transmission power. In general, this problem is known to be NP hard. For optimization over these two decision variables, we use an exhaustive search policy when the length of the time horizon is small, and a heuristic policy for longer horizons. For given values of the decision variables, the problem simplifies into a joint optimization on SU \textit{transmission power} and \textit{sensing time}, which is non-convex in nature. We solve the resulting optimization problem as an alternating convex optimization problem for both non-causal and causal channel state information and harvested energy information patterns at the SU base station (SBS) or fusion center (FC). We present an analytic solution for the non-causal scenario with infinite battery capacity for a general finite horizon problem.We formulate the problem with causal information and finite battery capacity as a stochastic control problem and solve it using the technique of dynamic programming. Numerical results are presented to illustrate the performance of the various algorithms.

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arXiv2015

Multiuser Diversity for the Cognitive Uplink with Generalized Fading and Reduced Primary's Cooperation

In cognitive multiple access networks, feedback is an important mechanism to convey secondary transmitter primary base station (STPB) channel gains from the primary base station (PBS) to the secondary base station (SBS). This paper investigates the optimal sum-rate capacity scaling laws for cognitive multiple access networks in feedback limited communication scenarios. First, an efficient feedback protocol called $K$-smallest channel gains ($K$-SCGs) feedback protocol is proposed in which the PBS feeds back the $\K$ smallest out of $N$ STPB channel gains to the SBS. Second, the sum-rate performance of the $K$-SCG feedback protocol is studied for three network types when transmission powers of secondary users (SUs) are optimally allocated. The network types considered are total-power-and-interference-limited (TPIL), interference-limited (IL) and individual-power-and-interference-limited (IPIL) networks. For each network type studied, we provide a sufficient condition on $\K$ such that the $K$-SCG feedback protocol is {\em asymptotically} optimal in the sense that the secondary network sum-rate scaling behavior under the $K$-SCG feedback protocol is the same with that under the full-feedback protocol. We allow distributions of secondary-transmitter-secondary-base-station (STSB), and STPB channel power gains to belong to a fairly general class of distributions called class $\mathcal{C}$-distributions that includes commonly used fading models.

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arXiv2015

Power-Constrained Sparse Gaussian Linear Dimensionality Reduction over Noisy Channels

In this paper, we investigate power-constrained sensing matrix design in a sparse Gaussian linear dimensionality reduction framework. Our study is carried out in a single--terminal setup as well as in a multi--terminal setup consisting of orthogonal or coherent multiple access channels (MAC). We adopt the mean square error (MSE) performance criterion for sparse source reconstruction in a system where source-to-sensor channel(s) and sensor-to-decoder communication channel(s) are noisy. Our proposed sensing matrix design procedure relies upon minimizing a lower-bound on the MSE in single-- and multiple--terminal setups. We propose a three-stage sensing matrix optimization scheme that combines semi-definite relaxation (SDR) programming, a low-rank approximation problem and power-rescaling. Under certain conditions, we derive closed-form solutions to the proposed optimization procedure. Through numerical experiments, by applying practical sparse reconstruction algorithms, we show the superiority of the proposed scheme by comparing it with other relevant methods. This performance improvement is achieved at the price of higher computational complexity. Hence, in order to address the complexity burden, we present an equivalent stochastic optimization method to the problem of interest that can be solved approximately, while still providing a superior performance over the popular methods.

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arXiv2015

Fake-Acknowledgment Attack on ACK-based Sensor Power Schedule for Remote State Estimation

We consider a class of malicious attacks against remote state estimation. A sensor with limited resources adopts an acknowledgement (ACK)-based online power schedule to improve the remote state estimation performance. A malicious attacker can modify the ACKs from the remote estimator and convey fake information to the sensor. When the capability of the attacker is limited, we propose an attack strategy for the attacker and analyze the corresponding effect on the estimation performance. The possible responses of the sensor are studied and a condition for the sensor to discard ACKs and switch from online schedule to offline schedule is provided.

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arXiv2014

Optimized Compressed Sensing Matrix Design for Noisy Communication Channels

We investigate a power-constrained sensing matrix design problem for a compressed sensing framework. We adopt a mean square error (MSE) performance criterion for sparse source reconstruction in a system where the source-to-sensor channel and the sensor-to-decoder communication channel are noisy. Our proposed sensing matrix design procedure relies upon minimizing a lower-bound on the MSE. Under certain conditions, we derive closed-form solutions to the optimization problem. Through numerical experiments, by applying practical sparse reconstruction algorithms, we show the strength of the proposed scheme by comparing it with other relevant methods. We discuss the computational complexity of our design method, and develop an equivalent stochastic optimization method to the problem of interest that can be solved approximately with a significantly less computational burden. We illustrate that the low-complexity method still outperforms the popular competing methods.

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arXiv2014

Optimal Energy Allocation for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgments and Energy Harvesting Constraints

This paper presents a design methodology for optimal transmission energy allocation at a sensor equipped with energy harvesting technology for remote state estimation of linear stochastic dynamical systems. In this framework, the sensor measurements as noisy versions of the system states are sent to the receiver over a packet dropping communication channel. The packet dropout probabilities of the channel depend on both the sensor's transmission energies and time varying wireless fading channel gains. The sensor has access to an energy harvesting source which is an everlasting but unreliable energy source compared to conventional batteries with fixed energy storages. The receiver performs optimal state estimation with random packet dropouts to minimize the estimation error covariances based on received measurements. The receiver also sends packet receipt acknowledgments to the sensor via an erroneous feedback communication channel which is itself packet dropping. The objective is to design optimal transmission energy allocation at the energy harvesting sensor to minimize either a finite-time horizon sum or a long term average (infinite-time horizon) of the trace of the expected estimation error covariance of the receiver's Kalman filter. These problems are formulated as Markov decision processes with imperfect state information. The optimal transmission energy allocation policies are obtained by the use of dynamic programming techniques. Using the concept of submodularity, the structure of the optimal transmission energy policies are studied. Suboptimal solutions are also discussed which are far less computationally intensive than optimal solutions. Numerical simulation results are presented illustrating the performance of the energy allocation algorithms.

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arXiv2014

An Optimal Transmission Strategy for Kalman Filtering over Packet Dropping Links with Imperfect Acknowledgements

This paper presents a novel design methodology for optimal transmission policies at a smart sensor to remotely estimate the state of a stable linear stochastic dynamical system. The sensor makes measurements of the process and forms estimates of the state using a local Kalman filter. The sensor transmits quantized information over a packet dropping link to the remote receiver. The receiver sends packet receipt acknowledgments back to the sensor via an erroneous feedback communication channel which is itself packet dropping. The key novelty of this formulation is that the smart sensor decides, at each discrete time instant, whether to transmit a quantized version of either its local state estimate or its local innovation. The objective is to design optimal transmission policies in order to minimize a long term average cost function as a convex combination of the receiver's expected estimation error covariance and the energy needed to transmit the packets. The optimal transmission policy is obtained by the use of dynamic programming techniques. Using the concept of submodularity, the optimality of a threshold policy in the case of scalar systems with perfect packet receipt acknowledgments is proved. Suboptimal solutions and their structural results are also discussed. Numerical results are presented illustrating the performance of the optimal and suboptimal transmission policies.

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arXiv2014

Transmission Power Scheduling for Energy Harvesting Sensor in Remote State Estimation

We study remote estimation in a wireless sensor network. Instead of using a conventional battery-powered sensor, a sensor equipped with an energy harvester which can obtain energy from the external environment is utilized. We formulate this problem into an infinite time-horizon Markov decision process and provide the optimal sensor transmission power control strategy. In addition, a sub-optimal strategy which is easier to implement and requires less computation is presented. A numerical example is provided to illustrate the implementation of the sub-optimal policy and evaluation of its estimation performance.

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arXiv2013

Distributed Cognitive Multiple Access Networks: Power Control, Scheduling and Multiuser Diversity

This paper studies optimal distributed power allocation and scheduling policies (DPASPs) for distributed total power and interference limited (DTPIL) cognitive multiple access networks in which secondary users (SU) independently perform power allocation and scheduling tasks using their local knowledge of secondary transmitter secondary base-station (STSB) and secondary transmitter primary base-station (STPB) channel gains. In such networks, transmission powers of SUs are limited by an average total transmission power constraint and by a constraint on the average interference power that SUs cause to the primary base-station. We first establish the joint optimality of water-filling power allocation and threshold-based scheduling policies for DTPIL networks. We then show that the secondary network throughput under the optimal DPASP scales according to $\frac{1}{\e{}n_h}\log\logp{N}$, where $n_h$ is a parameter obtained from the distribution of STSB channel power gains and $N$ is the total number of SUs. From a practical point of view, our results signify the fact that distributed cognitive multiple access networks are capable of harvesting multiuser diversity gains without employing centralized schedulers and feedback links as well as without disrupting primary's quality-of-service (QoS)

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