Nominal direction and direction spread estimation for slightly distributed scatterers using the SAGE algorithm

In this paper, the SAGE (subspace-alternating generalized expectation-maximization) algorithm is derived using the generalized array manifold (GAM) model proposed in Asztely et al. (1997) (GAM-SAGE) to estimate the nominal directions, i.e. azimuths and elevations of slightly distributed scatterers (SDS). As byproducts estimates of the azimuth spreads (AS), elevation spreads (ES), and the azimuth-elevation correlation coefficients (AECC) of the SDS can be computed from the estimates of the GAM parameters. These parameters determine with close accuracy the direction spreads of SDS. Simulation studies show that in a single-SDS scenario, the GAM-SAGE algorithm outperforms the Spread-ESPRIT technique, and both of them outperform the SAGE algorithm derived with the conventional specular-scatterer (SS) model (SS-SAGE) when the output signal-to-noise ratio (SNR) is beyond a certain threshold which depends on the AS and ES of the SDS. In a two-SDS scenario with strong power imbalance between the SDS, provided the direction spacing between the SDS equals twice the intrinsic azimuth or elevation resolution of the array, the GAM-SAGE algorithm can estimate the nominal direction of the SDS with weakest power with tolerably small errors. The SS-SAGE algorithm returns high root mean squared estimation error (RMSEE) regardless of the direction separation. We also found that the AECC estimator needs to operate in high SNR in order for its bias and RMSEE to be tolerably small. The performance of the AECC estimator, as well as the AS and ES estimators can be improved by applying an array-size selection technique proposed in Yin et al. (2005).