A Data-Cleaning Approach to Robust Multisensor Detection of Improper Signals

We consider the problem of detecting the presence of an improper complex-valued signal, common among two or more sensors (channels), in the presence of spatially independent, colored improper noise and additive outliers. A source of improper noise is in-phase/quadrature-phase imbalance during down-conversion of bandpass noise to baseband at the receiver. For clean data (i.e., known to be outlier free), a nonparametric binary hypothesis testing formulation in frequency-domain, utilizing the discrete Fourier transform of an augmented measurement sequence, has been proposed in the literature, and it results in a generalized likelihood ratio test (GLRT). In this paper we robustify this approach against additive outliers in the data, using a data-cleaning approach. Using some existing robust estimators of multivariate scatter, we first detect the outliers, and subsequently remove and replace them using vector median filtering to yield cleaned data. The existing GLRT is then applied to the cleaned data. The approach is illustrated via simulations. The considered problem has applications in diverse areas including spectrum sensing for cognitive radio.