CGHA for principal component extraction in the complex domain

Principal component extraction is an efficient statistical tool which is applied to data compression, feature extraction, signal processing, etc. Representative algorithms in the literature can only handle real data. However, in many scenarios such as sensor array signal processing, complex data are encountered. In this paper, the complex domain generalized Hebbian algorithm (CGHA) is presented for complex principal component extraction. It extends the real domain generalized Hebbian algorithm (GHA) proposed by Sanger (1992). Convergence of CGHA is analyzed. Like GHA, CGHA can be implemented by a single-layer linear neural network with simple computation. An example is given where CGHA is utilized in direction-of-arrival estimation of multiple narrowband plane waves received by a sensor array.