A note on most favorable array geometries for DOA estimation and array interpolation

Given an n-element linear array with the fixed positions x(1) and x(n) of the leftmost and rightmost array sensors, it is shown that the stochastic Cramer-Rao bound (CRB) and MUSIC performance depend on positions of the remaining n-2 sensors within the interval [x(1), x(n)]. The asymptotic performance of interpolated array approach shows similar dependence. The most favorable geometries are unrealizable for q < n-1 because the array sensors tend to form q+1 point clusters, where q is the number of sources. An interesting consequence of these facts is that for certain realizable nonuniform linear array (NULA) geometries, interpolated root-MUSIC with virtual uniform linear array (ULA) of the length x(n)-x(1) has better asymptotic performance than conventional root-MUSIC applied to the real ULA of the same length.