Optimum Antenna Arrays for Isotropic Direction Finding

A method is proposed to optimally place the sensors of an ambiguity-free planar antenna array in order to ensure a constant and minimal (mean square) error on the estimated angle of arrival, and so regardless of the source actual direction of arrival (DOA). It is obtained as a simplification, in the case of axis-symmetrical arrays, of a previously proposed systematic-search-based method. The exponential complexity of the technique is drastically reduced by halving the number of unknowns, and large-sized optimal isotropic arrays are computed. They show an increasing (as the number of sensors increases) gain w.r.t. circular arrays, and exhibit a Cramer-Rao bound (CRB) reduced by an asymptotic 29% relatively to their circular counterparts.