ROBUST ESTIMATION TECHNIQUES FOR COMPLEX-VALUED RANDOM VECTORS - Adaptive Signal Processing: Next Generation Solutions - page 87

2
ROBUST ESTIMATION
TECHNIQUES FOR
COMPLEX-VALUED
RANDOM VECTORS
Esa Ollila and Visa Koivunen
Helsinki University of Technology, Espoo, Finland
2.1 INTRODUCTION
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 depar-
tures 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 tech-
niques 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.