Principal component analysis for noncircular signals in the presence of circular white gaussian noise

The commonly used principal component analysis (PCA) assumes circular Gaussian distribution for the observed complex random variables. This paper extends PCA to the general case where the signals can be noncircular, and introduces a new PCA method called the noncircular PCA (ncPCA). We study the properties of ncPCA and propose an efficient algorithm for its implementation. Numerical results are presented to demonstrate its advantages in signal detection and subspace estimation, in particular when the circularity assumptions on data do not hold.