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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.

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Many problems in multiagent networks can be solved through distributed learning (state estimation) of linear dynamical systems. In this paper, we develop a partial-diffusion Kalman filtering (PDKF) algorithm, as a fully distributed solution for state estimation in the multiagent networks with limited communication resources. In the PDKF algorithm, every agent (node) is allowed to share only a subset of its intermediate estimate vectors with its neighbors at each iteration, reducing the amount of internode communications. We analyze the stability of the PDKF algorithm and show that the algorithm is stable and convergent in both mean and mean-square senses. We also derive a closedform expression for the steady-state mean-square deviation criterion. Furthermore, we show theoretically and by numerical examples that the PDKF algorithm provides a trade-off between the estimation performance and the communication cost that is extremely profitable.

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.

In this paper, we study the effect of noisy channels on the transient performance of diffusion adaptive network with least-mean squares (LMS) learning rule. We first drive the update equation of diffusion LMS which incorporates the effects of noisy channels. Then, using the framework of fundamental weighted energy conservation relation, we derive closed-form expressions for learning curves in terms of mean-square deviation and excess mean-square error. We also find the mean and mean-square stability bounds of step-size for diffusion LMS with noisy channels. We show that although noisy channels affect the performance of the diffusion LMS network, the stability bounds of the step-size are the same form as in the ideal channels case. The derived closed-form expressions are shown to provide a good match with values found by simulation.