Performance of cumulant-based rank reduction estimator in presence of unexpected modeling errors

Abstract

Compared with the rank reduction estimator (RARE) based on second-order statistics (called SOS-RARE), the RARE based on fourth-order cumulants (referred to as FOC-RARE) can handle more sources and restrain the negative impacts of the Gaussian colored noise. However, the unexpected modeling errors appearing in practice are known to significantly degrade the performance of the RARE. Therefore, the direction-of-arrival (DOA) estimation performance of the FOC-RARE is quantitatively derived. The explicit expression for direction-finding (DF) error is derived via the first-order perturbation analysis, and then the theoretical formula for the mean square error (MSE) is given. Simulation results demonstrate the validation of the theoretical analysis and reveal that the FOC-RARE is more robust to the unexpected modeling errors than the SOS-RARE.

Keywords

fourth-order cumulants (FOC) / rank reduction estimator (RARE) / modeling error / mean square error (MSE)

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