A novel covariance model for MIMO sensing systems and its identification from measurements

• Published in: Signal processing 2022-08, Vol.197, p.108542, Article 108542
• Main Authors: Häfner, Stephan, Dürr, André, Waldschmidt, Christian, Thomä, Reiner
• Format: Article
• Language: English
• Subjects: Channel sounding; Covariance matrices; Iterative optimisation; Maximum-likelihood estimation; MIMO sensing; Radar; Simultaneous diagonalisation
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2022.108542

•A covariance matrix model for data sets gathered by MIMO sensing systems is presented.•A ML estimator is proposed to estimate the model parameters, which gives a non-convex cost function.•Generalised eigenvalue decomposition is used to efficiently calculate the inverse and log-determinant of the covariance matrix.•Gradient-based optimisation using an approximate Fisher matrix is proposed for numerical efficient optimisation of the ML cost function.•MIMO FMCW radar measurements are used to demonstrate the performance of the novel covariance model. A novel model for the covariance matrix of sampled observations by multiple-input-multiple-output (MIMO) sensing systems with parallel receiver channels will be presented. The model is of shifted Kronecker structure and accounts for two mutually independent noise processes: a coloured and a white one. The maximum-likelihood (ML) estimator is applied to identify this covariance model from observations. The ML estimator gives rise to a non-convex optimisation problem. Since no closed-form solution is available, an iterative, space-alternating Gauss–Newton algorithm is proposed to solve the optimisation problem. This approach repeatedly requires the evaluation of the ML cost function. Since the cost function composes of the inverse and determinant of the covariance matrix, its evaluation can be memory exhaustive, numerically unstable and computationally complex. A computational method is developed to overcome these issues, using the simultaneous matrix diagonalisation and exploiting the properties of the Kronecker product. Measurements by a MIMO radar are used to identify the covariance model and to demonstrate its benefits. The identified covariance model is used to whiten the measurements. The whitening reduces interfering, noise-like components, which enhances the signal-to-interference ratio and hence facilitates the target detection.