On the concentrated stochastic likelihood function in array signal processing (Q1902518)

The paper deals with the problem of stochastic likelihood function [(STO)LF] association with narrowband array signal processing. The problem is considered taking into account the signal covariance matrix elements and the noise power. A simple, complete proof of the concentrated (STO)LF formula is provided. It is assumed that the array is calibrated so that the functional form of array output is known, and also that the array is unambiguous so that the rank of the functional form is \(n\). Another assumption is that the snapshots are independent and identically distributed complex Gaussian random variables with zero mean. The likelihood function is called (STO)LF because it corresponds to the assumption that the signals are stochastic. A theorem is proven and a derivation of the concentrated (STO)LF result is made. The result of the theorem proven can be readily extended to a fairly general class of unknown (parameterized) noise covariance matrices. The paper can be of interest for specialists engaged in signal detection algorithms development.