Sundeep Prabhakar Chepuri

Sparsity-Promoting Sensor Selection for Non-Linear Measurement Models

The problem of choosing the best subset of sensors that guarantees a certain estimation performance is referred to as sensor selection. In this paper, we focus on observations that are related to a general non-linear model. The proposed framework is valid as long as the observations are independent, and its likelihood satisfies the regularity conditions. We use several functions of the Cramér-Rao bound (CRB) as a performance measure. We formulate the sensor selection problem as the design of a sparse vector, which in its original form is a nonconvex ℓ0-(quasi) norm optimization problem. We present relaxed sensor selection solvers that can be efficiently solved in polynomial time. The proposed solvers result in sparse sensing techniques. We also propose a projected subgradient algorithm that is attractive for large-scale problems. The developed theory is applied to sensor placement for localization.

Optimization of hard fusion based spectrum sensing for energy-constrained cognitive radio networks

a b s t r a c t The detection reliability of a cognitive radio network improves by employing a cooperative spectrum sensing scheme. However, increasing the number of cognitive radios entails a growth in the cooperation overhead of the system. Such an overhead leads to a throughput degradation of the cognitive radio network. Since current cognitive radio networks consist of low-power radios, the energy consumption is another critical issue. In this paper, throughput optimization of the hard fusion based sensing using the k-out-of-N rule is considered. We maximize the throughput of the cognitive radio network subject to a constraint on the probability of detection and energy consumption per cognitive radio in order to derive the optimal number of users, the optimal k and the best probability of false alarm. The simulation results based on the IEEE 802.15.4/ZigBee standard, show that the majority rule is either optimal or almost optimal in terms of the network throughput.

Energy and throughput efficient strategies for cooperative spectrum sensing in cognitive radios

An efficient cooperative spectrum sensing based cognitive radio network employs a certain number of secondary users to sense the spectrum while satisfying a constraint on the detection performance. We derive the optimal number of cognitive radios under two scenarios: an energy efficient and a throughput optimization setup. In the energy efficient setup, the number of cooperating cognitive radios is minimized for a k-out-of-N fusion rule with a constraint on the probability of detection and false alarm while in the throughput optimization setup, we maximize the throughput of the cognitive radio network, by deriving the optimal reporting time in a sensing time frame which is proportional to the number of cognitive users, subject to a constraint on the probability of detection. It is shown that both problems can be simplified to line search problems. The simulation results show that the OR and the majority rule outperform the AND rule in terms of energy efficiency and that the OR rule gives a higher throughput than the AND rule with a smaller number of users.

Sensor Selection for Estimation with Correlated Measurement Noise

In this paper, we consider the problem of sensor selection for parameter estimation with correlated measurement noise. We seek optimal sensor activations by formulating an optimization problem, in which the estimation error, given by the trace of the inverse of the Bayesian Fisher information matrix, is minimized subject to energy constraints. Fisher information has been widely used as an effective sensor selection criterion. However, existing information-based sensor selection methods are limited to the case of uncorrelated noise or weakly correlated noise due to the use of approximate metrics. By contrast, here we derive the closed form of the Fisher information matrix with respect to sensor selection variables that is valid for any arbitrary noise correlation regime and develop both a convex relaxation approach and a greedy algorithm to find near-optimal solutions. We further extend our framework of sensor selection to solve the problem of sensor scheduling, where a greedy algorithm is proposed to determine non-myopic (multi-time step ahead) sensor schedules. Lastly, numerical results are provided to illustrate the effectiveness of our approach, and to reveal the effect of noise correlation on estimation performance.

Joint Clock Synchronization and Ranging: Asymmetrical Time-Stamping and Passive Listening

A fully asynchronous network with one sensor and M anchors (nodes with known locations) is considered in this letter. We propose a novel asymmetrical time-stamping and passive listening (ATPL) protocol for joint clock synchronization and ranging. The ATPL protocol exploits broadcast to not only reduce the number of active transmissions between the nodes, but also to obtain more information. This is used in a simple estimator based on least-squares (LS) to jointly estimate all the unknown clock-skews, clock-offsets, and pairwise distances of the sensor to each anchor. The Cramér-Rao lower bound (CRLB) is derived for the considered problem. The proposed estimator is shown to be asymptotically efficient, meets the CRLB, and also performs better than the available clock synchronization algorithms.

Sparse Sensing for Distributed Detection

An offline sampling design problem for distributed detection is considered in this paper. To reduce the sensing, storage, transmission, and processing costs, the natural choice for the sampler is the sparsest one that results in a desired global error probability. Since the numerical optimization of the error probabilities is difficult, we adopt simpler costs related to distance measures between the conditional distributions of the sensor observations. We design sparse samplers for the Bayesian as well as the Neyman-Pearson setting. The developed theory can be applied to sensor placement/selection, sample selection, and fully decentralized data compression. For conditionally independent observations, we give an explicit solution, which is optimal in terms of the error exponents. More specifically, the best subset of sensors is the one with the smallest local average root-likelihood ratio and largest local average log-likelihood ratio in the Bayesian and Neyman-Pearson setting, respectively. We supplement the proposed framework with a thorough analysis for Gaussian observations, including the case when the sensors are conditionally dependent, and also provide examples for other observation distributions. One of the results shows that, for nonidentical Gaussian sensor observations with uncommon means and common covariances under both hypotheses, the number of sensors required to achieve a desired detection performance reduces significantly as the sensors become more coherent.

Optimal hard fusion strategies for cognitive radio networks

Optimization of hard fusion spectrum sensing using the k-out-of-N rule is considered. Two different setups are used to derive the optimal k. A throughput optimization setup is defined by minimizing the probability of false alarm subject to a probability of detection constraint representing the interference of a cognitive radio with the primary user, and an interference management setup is considered by maximizing the probability of detection subject to a false alarm rate constraint. It is shown that the underlying problems can be simplified to equality constrained optimization problems and an algorithm to solve them is presented. We show the throughput optimization and interference management setups are dual. The simulation results show the majority rule is optimal or near optimal for the desirable range of false alarm and detection rates for a cognitive radio network. Furthermore, an energy efficient setup is considered where the number of cognitive radios is to be minimized for the AND and the OR rule and a certain probability of detection and false alarm constraint. The simulation results show that the OR rule outperforms the AND rule in terms of energy efficiency.

Continuous Sensor Placement

Existing solutions to the sensor placement problem are based on sensor selection, in which the best subset of available sampling locations is chosen such that a desired estimation accuracy is achieved. However, the achievable estimation accuracy of sensor placement via sensor selection is limited to the initial set of sampling locations, which are typically obtained by gridding the continuous sampling domain. To circumvent this issue, we propose a framework of continuous sensor placement. A continuous variable is augmented to the grid-based model, which allows for off-the-grid sensor placement. The proposed offline design problem can be solved using readily available convex optimization solvers.

SPARSITY-PROMOTING ADAPTIVE SENSOR SELECTION FOR NON-LINEAR FILTERING

Sensor selection is an important design task in sensor networks. We consider the problem of adaptive sensor selection for applications in which the observations follow a non-linear model, e.g., target/bearing tracking. In adaptive sensor selection, based on the dynamical state model and the state estimate from the previous time step, the most informative sensors are selected to acquire the measurements for the next time step. This is done via the design of a sparse selection vector. Additionally, we model the evolution of the selection vector over time to ensure a smooth transition between the selected sensors of subsequent time steps. The original non-convex optimization problem is relaxed to a semi-definite programming problem that can be solved efficiently in polynomial time.

Sparsity-enforcing sensor selection for DOA estimation

The sensitivity of direction-of-arrival (DOA) estimation to different array geometries motivates the design of optimal sensor constellations. We propose a framework for array geometry design for a linear array with fixed aperture and fixed inter-element spacing, where the array geometry design is formulated as a sensor selection problem. The sensor selection is performed such that it achieves a desired Cramér-Rao bound (CRB) for estimating the DOA of a single source. The nonuniformity of the sensor selection typically results in sidelobes. These sidelobes are suppressed in a specified angular sector again via sensor selection. The aforementioned problems are jointly casted as a semidefinite programming (SDP) problem which can be efficiently solved in polynomial time. Simulations exhibit the trade-offs among the number of selected sensors, sidelobe minimization, and CRB of the DOA estimates.