American Journal of Signal Processing

p-ISSN: 2165-9354    e-ISSN: 2165-9362

2015;  5(2A)

doi:10.5923/s.ajsp.201501

Complex Domain Adaptive Filtering: Algorithms, Implementations and Applications

Copyright © 2015 Scientific & Academic Publishing. All Rights Reserved.

Adaptive filters are known as powerful algorithms in statistical signal processing that are used in a wide range of signal processing applications such as channel equalization, noise cancellation, system modeling. Initially, the adaptive filters have been derived for real-value signals. The complex domain provides a natural processing framework for signals with intensity and direction components. Statistical signal processing in complex domain has traditionally been viewed as a straightforward extension of the corresponding algorithms in the real domain. However, recent developments in augmented complex statistics show that they do not make full use of the algebraic structure of the complex domain. For example, it was shown that the covariance matrix is not sufficient to model the statistics of noncircular signals and it is necessary to introduce the pseudo-covariance matrix to fully capture the relation between the real and imaginary components of random vectors. It is also shown that the standard linear model is only sufficient for modeling proper signals, whereas an optimal model for 'improper' signals is provided by a widely linear model. Given these challenges, the complex-valued adaptive signal processing and filtering opportunities arise.
This special issue aims to provide a venue for ongoing research in novel complex domain adaptive filters, as well as new applications and performance analysis. Two papers in this issue focus on developing adaptive algorithms for processing of three and four-dimensional processes collaboratively. Such signals appear in body sensor measurements, color images, wind and renewable energy. In order to deal with three and four dimensional, Quaternion domain is introduced and can be regarded as a non-commutative extension of complex domain. The algorithms are developed based on the incremental and diffusion strategies. The proposed algorithms employ both the covariance and pseudo-covariance terms within their update equations, and can, therefore cater for non-circularly symmetric quaternion data. The results show the superior performance of the proposed algorithms in comparison with non-cooperative solutions.
The next paper proposes a modified technique for frequency estimation in unbalanced three-phase power systems. The algorithm is based on the widely linear complex-valued signal modeling derived from three-phase voltages by Clark transformation under unbalanced conditions. It contains two update equations, like ACLMS, together with normalized time variant step size, thus its promising in increasing and enhancing both convergence rate and accuracy.
In the final paper a robust adaptive CFO estimation algorithm for OFDM system has been proposed which is able to provide accurate estimate of CFO even in the presence of impulsive noise. The algorithm relies on the maximum correntropy criterion (MCC) which is a robust optimality criterion for impulsive noise. The proposed algorithm has computational complexity similar to the popular least mean-square (LMS), while it is robust against the impulsive signal because of using higher order moments beyond just second order moments. The performance of the proposed algorithm is evaluated under different conditions, including the Gaussian noise, impulsive noise, and time-varying CFO, where simulation results reveal the effectiveness of the proposed algorithm.