  In this paper, the partial relaxation approach is introduced and applied to
DOA estimation using spectral search. Unlike existing methods like Capon or
MUSIC which can be considered as single source approximations of multi-source
estimation criteria, the proposed approach accounts for the existence of
multiple sources. At each considered direction, the manifold structure of the
remaining interfering signals impinging on the sensor array is relaxed, which
results in closed form estimates for the interference parameters. The
conventional multidimensional optimization problem reduces, thanks to this
relaxation, to a simple spectral search. Following this principle, we propose
estimators based on the Deterministic Maximum Likelihood, Weighted Subspace
Fitting and covariance fitting methods. To calculate the pseudo-spectra
efficiently, an iterative rooting scheme based on the rational function
approximation is applied to the partial relaxation methods. Simulation results
show that the performance of the proposed estimators is superior to the
conventional methods especially in the case of low Signal-to-Noise-Ratio and
low number of snapshots, irrespectively of any specific structure of the sensor
array while maintaining a comparable computational cost as MUSIC.
