Concave functions play a central role in optimization. So-called exponentially concave functions are of similar importance in information theory. In this paper, we comprehensively discuss mathematical properties of the class of exponentially concave functions, like closedness under linear and convex combination and relations to quasi-, Jensen-and Schur-concavity. Information theoretic quantities such as self-information and (scaled) entropy are shown to be exponentially concave. Furthermore, new inequalities for the Kullback-Leibler divergence, for the entropy of mixture distributions, and for mutual information are derived.

In the present work, we investigate the power allocation problem in distributed sensor networks that are used for passive radar applications. The signal emitted by a target is observed by the sensor nodes independently. Since these local observations are noisy and are thus unreliable, they are fused together as a single reliable observation at a remotely located fusion center in order to increase the overall system performance. The fusion center uses the best linear unbiased estimator in order to estimate the present target signal accurately. By using the proposed system model, fusion rule and objective function we are able to optimize the power allocation analytically and can hence present a closed-form solution to the power allocation problem. Since the power allocation problem can be subject to different power constraints, three different cases of power constraints are discussed and compared with each other. Furthermore, we demonstrate that all considered constraints lead to signomial optimization problems which are in general quite hard to solve. The main applications of the proposed results are issues concerning the sensor selection and energy efficiency in passive sensor networks.Index Terms-Analytical power allocation, energy-efficient optimization, distributed radar, network resource management, information fusion.

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In this paper, we investigate the power allocation problem in distributed sensor networks and give a sensitivity analysis for perfect and imperfect knowledge of system parameters. As it is common for sensors with weak power-supplies, constraints by sum and individual power-range limitations are imposed. The power allocation problem leads to a signomial program, and is analytically solved by a Lagrangian setup. Typical examples of such networks are passive radar systems with multiple nodes, whose aim is to detect and classify target signals. For each sensor node, an amplify-and-forward strategy for the received target signal is proposed. This per-node information is transmitted over a communication channel and combined at a fusion center. The fusion center carries out the final decision about the type of the target signal by a best linear unbiased estimator and a subsequent classification. In contrast to approaches in the literature, which combine discrete local decisions into a single global one, the approach in this paper offers many advantages, ranging from the simplicity of its implementation to the achievement of an optimal solution in closed-form. In addition, it allows for a sensitivity analysis of the whole sensor network under variations of different system parameters.Index Terms-Closed-form optimization, energy-efficient system-design, distributed radar, network resource management, information fusion.

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The ultimate goal of the present paper is to provide mathematical tools for dealing with the complicated average error probability (AEP) in Nakagami fading channels. This is useful for analytical investigations as well as alleviating computational effort in simulations or on-line computations. We hence thoroughly analyze the mathematical structure of the AEP over Nakagami fading channels. First, the AEP is re-parameterized to obtain a mathematically concise form. The main contributions are then as follows. An ordinary differential equation is set up, which has the AEP as a solution. By this approach, a new representation of the AEP is found, which merely needs integration over a broken rational function. This paves the way to numerous amazing relations of the AEP, e.g., to the Gaussian hypergeometric and the incomplete beta function. Moreover, monotonicity and logconvexity are demonstrated. Finally, asymptotic expansions of the AEP are given.

Smart grids evolve rapidly towards a system that includes components from different domains, which makes interdisciplinary modelling and analysis indispensable. In this paper, we present a cosimulation architecture for smart grids together with a comprehensive data model for the holistic representation of the power system, the communication network, and the energy market. Cosimulation is preferred over a monolithic approach since it allows leveraging the capabilities of existing, well-established domainspecific software. The challenges that arise in a multidomain smart grid cosimulation are identified for typical use cases through a discussion of the recent literature. Based on the identified requirements and use cases, a joint representation of the smart grid ecosystem is facilitated by a comprehensive data model. The proposed data model is then integrated in a software architecture, where the domain-specific simulators for the power grid, the communication network, and the market mechanisms are combined in a cosimulation framework. The details of the software architecture and its implementation are presented. Finally, the implemented framework is used for the cosimulation of a virtual power plant, where battery storages are controlled by a novel peak-shaving algorithm, and the battery storages and the market entity are interfaced through a communication network.