Robust Multichannel Decorrelation via Tensor Einstein Product

Decorrelation of multichannel signals has played a crucial preprocessing role (in prewhitening and orthogonalization) for many signal processing applications. Classical decorrelation techniques can only be applied for signal vectors. Nonetheless, many emerging big-data and sensor-network applications involve signal tensors (signal samples required to be arranged in a tensor form of arbitrary orders). Meanwhile, the existing tensor-decorrelation methods have serious limitations. First, the correlation-tensors have to be of certain particular orders. Second, the unrealistic assumption of the specific signal-tensor form, namely the canonical polyadic (CP) form, is made. Third, the correlation-tensor has to be full-rank or an extra preprocessor based on principal component analysis is required for any non-full-rank correlation tensor. To remove the aforementioned impractical limitations, we propose a novel robust approach for high-dimensional multichannel decorrelation, which can accommodate signal tensors of arbitrary orders, forms, and ranks without any need of extra preprocessor. In this work, we introduce two new tensor-decorrelation algorithms. Our first new algorithm is designed to tackle full-rank correlation-tensors and our second new algorithm is designed to tackle non-full-rank correlation-tensors. Meanwhile, we also propose a new parallel-computing paradigm to accelerate our proposed new tensor-decorrelation algorithms. To demonstrate the applicability of our proposed new scheme, we also apply our proposed new tensor-decorrelation approach to pre-whiten the tensor signals and analyze the corresponding convergence-speed and misadjustment performances of the tensor least-mean-squares (TLMS) filter. Finally, we assess the computational- and memory-complexities of our proposed new algorithms by simulations over both artificial and real data. Simulation results show that our proposed new multichannel-decorrelation algorithms outperform the existing tensor-decorrelation methods in terms of convergence speed, eigenspread, normalized mean square error (NRMSE), and estimation accuracy.