Array mapping for the SESAM system: Optimal transformation matrix design

Mapping of the data output vector from an existing antenna array onto the data vector of an imaginary array of more suitable configuration is well known in array signal processing. By mapping onto an array manifold of lower dimension or uniform structure f. ex., processing speed can be improved. Conditions for the retaining of DOA estimate variance under such mapping have been formulated by several authors but the equally important systematic mapping errors, the bias, has been less treated to date. This paper uses a geometrical interpretation of a Taylor expansion of the DOA estimator cost function to derive an alternative design of the mapping matrix that almost completely removes the bias. The key feature of the proposed design is that it takes the orthogonality between the manifold mapping errors and certain gradients of the estimator cost function into account. Verifying simulations are given which show that mapping bias can be reduced by a factor of 100 or more especially in difficult situations involving a near ambiguous real array. A multi step procedure is proposed which in addition gives optimal variance performance.