Derivation and analysis of incremental augmented complex least mean square algorithm

Abstract

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.

Cooperative spectrum estimation over large‐scale cognitive radio networks

“…Hence, cooperation should be limited to secondary users that pertain to a similar cluster. In distributed learning problems [30][31][32][33][34][35], nodes of network know their neighbourhoods but they do not know which subsets of their neighbours are interested into the same cluster. In order to derive a method for solving multitask learning problem, we define the N × N optimal neighbourhood matrix A o , where the entry a lk o will be set to a non-zero number if secondary user k discovers that its adjacent secondary user l belongs to the same cluster…”

“…In this section, we investigate the performance of the proposed algorithm (30) and (31) with correntropy cooperation policy (39) for multitask learning problem that was summarised in Table 1. For initial iterations (i < T s ) the algorithm performs in a noncooperative manner, and thus each secondary user k of the network tracks its optimum vector w k o without any cooperation…”

“…The main contributions of our work are: (i) the extension of distributed learning algorithm with a fixed combination matrix [29] to a distributed learning algorithm with a time-varying combination matrix that was derived from correntropy function stated in [30][31][32][33][34]; (ii) the implementation of the proposed algorithm for the problem of multiple-spectrum estimation in large-scale cognitive networks [13]; and (iii) the analysis of the stability and the meansquare performance of the proposed distributed algorithm employed for the multitask spectrum estimation problem.…”

A robust variable step size fractional least mean square (RVSS-FLMS) algorithm

“…The statistics in the LMS are estimated continuously, therefore it is an adaptive filter belonging to the group of stochastic gradient methods. Extensive research is done towards optimization of the LMS algorithm by numerous researchers [9,18,19,20,21]. LMS is applied in diversified applications such as plant identification [8], noise cancellation [22], echo cancellation [23], ECG signal analysis [24], time series prediction [25] etc.…”

A Robust Diffusion Adaptive Network Based on the Maximum Correntropy Criterion

“…As we can see from (9), correntropy can be interpreted as a generalized correlation function between two random variables X and Y which shows how similar two random variables are, within a small neighborhood determined by the kernel width σ.…”