Title :
Mean and Mean-Square Analysis of the Complex LMS Algorithm for Non-Circular Gaussian Signals
Author :
Douglas, Scott C. ; Mandic, Danilo P.
Author_Institution :
Dept. of Electr. Eng., Southern Methodist Univ., Dallas, TX
Abstract :
The least-mean-square (LMS) algorithm is a useful and popular procedure for adaptive signal processing of both real-valued and complex-valued signals. Past analysis of the complex LMS algorithm has assumed that the input signal vector is circularly-distributed, such that the pseudo-covariance matrix of the input signal is zero. In this paper, we relax this assumption, providing a complete mean and mean-square analysis of the complex LMS algorithm for non-circular Gaussian signals. Our analysis unifies the statistical descriptions of the conventional (real-valued) LMS and complex LMS algorithms as specific cases of our more-general behavioral description, negating the need for a distinction between these two procedures. Simulations indicate that our analysis more-accurately predicts the behavior of complex LMS for non-circular signals as compared to existing analyses in the scientific literature.
Keywords :
covariance matrices; least mean squares methods; signal processing; adaptive signal processing; least-mean-square algorithm; mean analysis; mean-square analysis; noncircular Gaussian signals; pseudocovariance matrix; Adaptive signal processing; Algorithm design and analysis; Analytical models; Covariance matrix; Least squares approximation; Predictive models; Signal analysis; Signal processing; Signal processing algorithms; Statistics;
Conference_Titel :
Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, 2009. DSP/SPE 2009. IEEE 13th
Conference_Location :
Marco Island, FL
Print_ISBN :
978-1-4244-3677-4
Electronic_ISBN :
978-1-4244-3677-4
DOI :
10.1109/DSP.2009.4785903
