Structured covariance matrices and dimensionality reduction in array processing

Data are often passed through rectangular matrix transformations in adaptive beamforming and direction-of-arrival estimation to reduce data dimension and lower computational load. The authors show that the transformation defines a structured model for the full dimension data covariance matrix. Signal processing applied to the reduced dimension data is equivalent to processing the original data while constraining the covariance matrix to have the specified structure. A procedure is given for designing the structure of the covariance matrix to minimize the average error between the true covariance and the structured model. Simulations indicate that this design procedure is very effective and that improved resolution can be obtained with reduced-dimension direction-of-arrival estimates