Efficient calculation of sensor utility and sensor removal in wireless sensor networks for adaptive signal estimation and beamforming

Wireless sensor networks are often deployed over a large area of interest and therefore the quality of the sensor signals may vary significantly across the different sensors. In this case, it is useful to have a measure for the importance or the so-called "utility" of each sensor, e.g., for sensor subset selection, resource allocation or topology selection. In this paper, we consider the efficient calculation of sensor utility measures for four different signal estimation or beamforming algorithms in an adaptive context. We use the definition of sensor utility as the increase in cost (e.g., mean-squared error) when the sensor is removed from the estimation procedure. Since each possible sensor removal corresponds to a new estimation problem (involving less sensors), calculating the sensor utilities would require a continuous updating of different signal estimators (where is the number of sensors), increasing computational complexity and memory usage by a factor. However, we derive formulas to efficiently calculate all sensor utilities with hardly any increase in memory usage and computational complexity compared to the signal estimation algorithm already in place. When applied in adaptive signal estimation algorithms, this allows for on-line tracking of all the sensor utilities at almost no additional cost. Furthermore, we derive efficient formulas for sensor removal, i.e., for updating the signal estimator coefficients when a sensor is removed, e.g., due to a failure in the wireless link or when its utility is too low. We provide a complexity evaluation of the derived formulas, and demonstrate the significant reduction in computational complexity compared to straightforward implementations

Sensor selection for hypothesis testing in wireless sensor networks: a Kullback-Leibler based approach

Abstract — We consider the problem of selecting a subset of p out of n sensors for the purpose of event detection, in a wireless sensor network (WSN). Occurrence or not of the event of interest is modeled as a binary Gaussian hypothesis test. In this case sensor selection consists of finding, among all ( n) p combinations, the one maximizing the Kullback-Leibler (KL) distance between the induced p-dimensional distributions under the two hypotheses. An exhaustive search is impractical if n and p are large, as the resulting optimization problem is combinatorial. We propose a suboptimal approach with computational complexity of order O(n3 p). This consists of relaxing the 0/1 constraint on the entries of the selection matrices to let the optimization problem search over the set of Stiefel matrices. Although finding the Stiefel matrix is a nonconvex problem, we provide an algorithm that guarantees to produce a global optimum for p = 1, through a series of judicious problem reformulations. The case p> 1 is tackled by an incremental, greedy approach. The obtained Stiefel matrix is then used to determine the sensor selection matrix which best approximates its range space. Extensive simulations are used to assess near optimality of the proposed approach. They also show how the proposed approach performs better than exhaustive searches once an upper bound on the computation time is set. I

Optimal Adaptive Random Multiaccess in Energy Harvesting Wireless Sensor Networks

Wireless sensors can integrate rechargeable batteries and energy-harvesting (EH) devices to enable long-term, autonomous operation, thus requiring intelligent energy management to limit the adverse impact of energy outages. This work considers a network of EH wireless sensors, which report packets with a random utility value to a fusion center (FC) over a shared wireless channel. Decentralized access schemes are designed, where each node performs a local decision to transmit/discard a packet, based on an estimate of the packet's utility, its own energy level, and the scenario state of the EH process, with the objective to maximize the average long-term aggregate utility of the packets received at the FC. Due to the non-convex structure of the problem, an approximate optimization is developed by resorting to a mathematical artifice based on a game theoretic formulation of the multiaccess scheme, where the nodes do not behave strategically, but rather attempt to maximize a \emph{common} network utility with respect to their own policy. The symmetric Nash equilibrium (SNE) is characterized, where all nodes employ the same policy; its uniqueness is proved, and it is shown to be a local maximum of the original problem. An algorithm to compute the SNE is presented, and a heuristic scheme is proposed, which is optimal for large battery capacity. It is shown numerically that the SNE typically achieves near-optimal performance, within 3% of the optimal policy, at a fraction of the complexity, and two operational regimes of EH-networks are identified and analyzed: an energy-limited scenario, where energy is scarce and the channel is under-utilized, and a network-limited scenario, where energy is abundant and the shared wireless channel represents the bottleneck of the system.Comment: IEEE Transactions on Communication