Order estimation of 2-dimensional complex superimposed exponential signal model using exponentially embedded family (EEF) rule: large sample consistency properties

In this paper, we consider the order estimation problem of a 2-dimensional complex superimposed exponential signal model in presence of additive white noise. We use the recently proposed exponentially embedded family (EEF) rule (see Stoica and Babu in IEEE Signal Process Lett 19(9):551–554, 2012 ; Kay in IEEE Trans Aerosp Electron Syst 41(1):333–345, 2005 ) for estimating the order of the 2-dimensional signal model and prove that the EEF rule based estimator is consistent in large sample scenario. Extensive simulations are performed to ascertain the performance of the order estimation rule and also to compare the finite sample performance of EEF rule based estimator with other popular order selection rules using simulation examples.