Modelling and estimation of carrier frequency and phase uncertainties in large aperture arrays

This paper is concerned with the modelling and estimation of frequency and phase carrier uncertainties in an array system where its elements are distributed over a large area and consequently forming large aperture arrays with massive inter-element spacings. In this situation, it is practically impossible to have a common carrier (common local oscillator - LO) in order to form a fully coherent array system, as in the case of small aperture arrays where the array elements are in the vicinity of each other. Instead, each of the receiving array elements has its own independent carrier which will have slightly different frequencies and phases, even if the local oscillators are using similar hardware or even if each local oscillator is using a GPS reference clock for locking. These discrepancies will introduce frequency and phase uncertainties in the array which must be removed to achieve a coherent array system. In this paper, these uncertainties are mathematically modelled, their effect on the performance of an array system is examined and a simple method is proposed to estimate and eliminate these uncertainties. This work is supported by computer simulation studies and experimental results using a software defined radio (SDR) array testbed.