Design of low rank estimators for higher-order statistics based on the second-order statistics

Higher-order statistics (HOS) are well known for their robustness to additive Gaussian noise and their ability to preserve phase. HOS estimates on the other hand, have been criticised for high complexity and the need of long data in order to maintain low variance. Rank reduction offers a general principle for reduction of estimator variance and complexity. In this paper we consider the problem of designing low-rank estimators for third-order statistics (TOS). We propose a method for choosing the rank reduced transformation matrix based on the second-order statistics of the signal. Results indicate that the proposed approach significantly reduces the mean square error associated with the TOS estimates. Simulation results are presented to also demonstrate the advantages of using low rank TOS estimates for blind system estimation.