Derivation and analysis of incremental augmented complex least mean square algorithm

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.