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In this paper the authors propose an adaptive estimation algorithm for in-network processing of complex signals over distributed networks. In the proposed algorithm, as the incremental augmented complex least mean square (IAC-LMS) algorithm, nodes of the network are allowed to collaborate via incremental cooperation mode to exploit the spatial dimension; while at the same time are equipped with LMS learning rules to endow the network with adaptation. The authors have extracted closed-form expressions that show how IAC-LMS algorithm performs in the steady-state. The authors further have derived the required conditions for mean and mean-square stability of the proposed algorithm. The authors use both synthetic benchmarks and real world non-circular data to evaluate the performance of the proposed algorithm. Simulation results also reveal that the IAC-LMS algorithm is able to estimate both second order circular (proper) and non-circular (improper) signals. Moreover, IAC-LMS algorithm outperforms the non-cooperative solution.

The article studies the steady-state performance of a diffusion least-mean squares (LMS) adaptive network with imperfect communications where the topology is random (links may fail at random times) and the communication in the channels is corrupted by additive noise. Using the established weighted spatial-temporal energy conservation argument, the authors derive a variance relation which contains moments that represent the effects of noisy links and random topology. The authors evaluate these moments and derive closed-form expressions for the mean-square deviation, excess mean-square error and mean-square error to explain the steady-state performance at each individual node. The mean stability analysis is also provided. The derived theoretical expressions have good match with simulation results. Nevertheless, the important result is that the noisy links are the main factor in performance degradation of a diffusion LMS algorithm running in a network with imperfect communications.

Joint energy consumption and trading management is still a major challenge in smart (micro-) grids. The main goal of solving such problems is to flatten the aggregate power consumption-generation curve and increase the local direct power trading among the participants as much as possible. Here, an inclusive formulation for energy management and trading of a Micro/Nano-grid (M/NG) is proposed. Subsequently, a holistic solution to jointly optimizing the internal energy consumption management and external local energy trading for a smart grid including several M/NGs is provided. As the problem is computationally intractable, the proposed approach involves three hierarchical stages. Firstly, a game-theoretic online stochastic energy management model is provided with a reinforcement learning solution by which the M/NGs can schedule their power consumptions. Secondly, an effective incentive-compatible doubleauction is formulated by which the M/NGs can directly trade with each other. Thirdly, the central controller develops an optimal power allocation program to reduce the power transmission loss and the destructive effects of local energy trading. The simulation results validate the efficiency of the proposed framework.