Maximum likelihood based direction estimation for noncircular signals

Abstract

In the direction estimation for the signals incident on a sensor array, maximum likelihood (ML) based methods can provide superior performance than subspace based ones such as the multiple signal classification (MUSIC). When the incoming signals are noncircular the exploitation of the property can allow us to improve estimation performance. Based on the deterministic ML criterion, a direction estimation method for strictly noncircular signals is proposed that can outperform the conventional alternating maximization (AM) with no use of noncircularity. Using a generalized Gaussian probability density function, we approach the ML estimation, which is formulated as a nonlinear multidimensional problem. The application of the alternating projection to the multidimensional problem leads to the maximization of an objective function of two variables associated with the direction and the initial phase of a noncircular signal. Theoretically optimizing the phase variable, we obtain the maximum through one-dimensional search with respect to the direction variable only. The complexity of the proposed noncircular AM (NC-AM) is far less than that of the existing ML based method, noncircular decoupled maximization (NC-DM). Moreover, simulation results demonstrate that NC-AM outperforms NC-DM as well as the noncircular MUSIC.