Efficient Covariance Matrix Reconstruction with Iterative Spatial
  Spectrum Sampling
S. Mohammadzadeh V. H. Nascimento R. C. de Lamare O. Kukrer
This work presents a cost-effective technique for designing robust adaptive
beamforming algorithms based on efficient covariance matrix reconstruction with
iterative spatial power spectrum (CMR-ISPS). The proposed CMR-ISPS approach
reconstructs the interference-plus-noise covariance (INC) matrix based on a
simplified maximum entropy power spectral density function that can be used to
shape the directional response of the beamformer. Firstly, we estimate the
directions of arrival (DoAs) of the interfering sources with the available
snapshots. We then develop an algorithm to reconstruct the INC matrix using a
weighted sum of outer products of steering vectors whose coefficients can be
estimated in the vicinity of the DoAs of the interferences which lie in a small
angular sector. We also devise a cost-effective adaptive algorithm based on
conjugate gradient techniques to update the beamforming weights and a method to
obtain estimates of the signal of interest (SOI) steering vector from the
spatial power spectrum. The proposed CMR-ISPS beamformer can suppress
interferers close to the direction of the SOI by producing notches in the
directional response of the array with sufficient depths. Simulation results
are provided to confirm the validity of the proposed method and make a
comparison to existing approaches