Model order selection in sensor array response modeling

In this paper, a method for order selection needed in array response modeling using calibration data is proposed. It allows finding the optimal number of basis functions for describing array steering vectors, according to the manifold separation principle. The proposed solution does not require heuristic design parameters and achieves asymptotically optimal (in the MSE sense) modeling of array nonidealities from calibration measurements. The normalized minimum description length (nMDL) is extended to complex-valued data and employed to choosing the optimal number of modes in the orthogonal decomposition of the array steering vector. Bayesian information criterion (BIC) and the more recent exponentially embedded family (EEF) rules are employed as well, along with convenient expressions to the problem at hand. Extensive simulations using a real-world antenna array are included and the various order selection rules are compared. The results illustrate that the nMDL is a consistent estimator of the optimal number of modes and has a performance close to the minimum mean-squared error.