Multidimensional prewhitening for enhanced signal reconstruction and parameter estimation in colored noise with Kronecker correlation structure

• Two prewhitening algorithms that exploit the structure of Kronecker colored noise are devised.
• With noise-only measurements, prewhitening factors are estimated along different dimensions.
• When noise-only measurements are unavailable, parameter estimation and prewhitening iterate.
• Adaptive convergence thresholds are designed to determine the optimal number of iterations.
• The prewhitening algorithms without and with noise statistics have comparable performance.

Parameter estimation of multidimensional data in the presence of colored noise or interference with a Kronecker product covariance structure, which appears in electroencephalogram/magnetoencephalogram and multiple-input multiple-output applications, is addressed. In order to improve the accuracy of the multidimensional subspace-based estimation techniques designed for white noise, prewhitening algorithms are devised by exploiting the Kronecker structure of the noise covariance matrix. We first contribute to the development of the multidimensional prewhitening (MD-PWT) scheme which assumes that noise-only measurements are available. By applying prewhitening sequentially along various dimensions using the corresponding correlation factors estimated from the noise-only measurements, the MD-PWT significantly improves the performance of the closed-form parallel factor decomposition based parameter estimator (CFP-PE) with a small number of noise-only snapshots. When noise-only measurements are unavailable, an iterative joint estimation of noise and signal parameters and prewhitening algorithm is proposed by iteratively applying the MD-PWT and CFP-PE. Adaptive convergence thresholds are designed as the stopping conditions such that the optimal number of iterations is automatically determined. Simulation results show that the iterative scheme performs nearly the same as the MD-PWT with noise statistics, in all scenarios except for a special one of intermediate signal-to-noise ratios and high noise correlation levels.