Synchronization of GNSS signals with unstructured antenna arrays by a multivariate minimization of the generalized variance

This paper addresses the synchronization problem using an array of antennas in the general framework of global navigation satellite systems (GNSS) receivers. Although the pervasive approach to exploit spatial diversity is based on beamforming, we propose a statistical approach driven by the use of blocks of data, common in software radio receivers, in contrast to a sample-per-sample basis, typical in architectures based on application-specific integrated circuits. The key statistical feature in the noise model is the assumption of an arbitrary and unknown covariance matrix which attempts to capture the statistical behavior of multipath and interferences, while exploits the spatial diversity provided by antenna arrays: all the nuisance signals and noise are gathered together in a Gaussian term assumed temporally white but spatially colored with the intention of modeling multipath and interference nature. We show that the maximum likelihood estimation of the synchronization parameters implies a multivariate minimization of the generalized variance, defined as the determinant of the covariance matrix. A proof of the consistency of the estimator is also provided. The paper follows with an intuitive interpretation of the obtained estimator, and numerical simulations show its robustness to the multipath effect.