Esa Ollila and Visa Koivunen
Helsinki University of Technology, Espoo, Finland
In this chapter we address the problem of multichannel signal processing of complex-valued signals in cases where the underlying ideal assumptions on signal and noise models are not necessarily true. In signal processing applications we are typically interested in second-order statistics of the signal and noise. We will focus on departures from two key assumptions: circularity of the signal and/or noise as well as the Gaussianity of the noise distribution. Circularity imposes an additional restriction on the correlation structure of the complex random vector. We will develop signal processing algorithms that take into account the complete second-order statistics of the signals and are robust in the face of heavy-tailed, impulsive noise. Robust techniques are close to optimal when the nominal assumptions hold and produce highly reliable estimates otherwise. Maximum likelihood estimators (MLEs) derived under complex normal (Gaussian) assumptions on noise models may suffer from drastic degradation in performance in the face of heavy-tailed noise and highly deviating observations called outliers.
Many man-made complex-valued signals encountered in wireless communication and array signal-processing applications possess circular symmetry properties. Moreover, additive sensor noise present in the observed data is commonly modeled ...