  The direction of arrival (DOA) estimation of sound sources has been a popular
signal processing research topic due to its widespread applications. Using
spherical microphone arrays (SMA), DOA estimation can be applied in the
spherical harmonic (SH) domain without any spatial ambiguity. However, the
environment reverberation and noise can degrade the estimation performance. In
this paper, we propose a new expectation maximization (EM) algorithm for
deterministic maximum likelihood (ML) DOA estimation of L sound sources in the
presence of spatially nonuniform noise in the SH domain. Furthermore a new
closed-form Cramer-Rao bound (CRB) for the deterministic ML DOA estimation is
derived for the signal model in the SH domain. The main idea of the proposed
algorithm is considering the general model of the received signal in the SH
domain, we reduce the complexity of the ML estimation by breaking it down into
two steps: expectation and maximization steps. The proposed algorithm reduces
the complexity from 2L-dimensional space to L 2-dimensional space. Simulation
results indicate that the proposed algorithm shows at least an improvement of
6dB in robustness in terms of root mean square error (RMSE). Moreover, the RMSE
of the proposed algorithm is very close to the CRB compared to the recent
methods in reverberant and noisy environments in the large range of signal to
noise ratio.
