Analysis of the COLD Uniform Linear Array

In this paper, we study the Cocentered Orthogonal Loop and Dipole pairs Uniform Linear Array (COLD-ULA) array which is sensitive to the source polarization in the context of the localization of time-varying narrow-band far-field sources. We derive and analyze nonmatrix expressions of the deterministic Cramer-Rao Bound (CRB) for the direction and the polarization parameters under the assumption that the number of sensors is large. We name this bound ACRB^(COLD). This assumption seems in a first time to be severe but we show that the ACRB^(COLD) is close to the CRB (computed without the large number of sensors assumption) even if the number of sensors is moderate (slightly higher about ten sensors). Our approach has two important advantages: (i) the computational complexity of the proposed closed-form of the bound is very cheap, comparing to the brute force computation of a matrix-based deterministic CRB which needs the inversion of a large Fisher Information Matrix in case of time-varying model parameters and (ii) some useful informations can be deduced from the behaviour of the bound in the situation when the sources are not too closely-spaced. In particular, we prove that the ACRB^(COLD) for the direction parameter is not affected by the knowledge or not of the polarization parameters. Another conclusion is that with a COLD-ULA, more model parameters can be estimated than the uniformly polarized ULA without degrading the estimation accuracy of localization parameter.