Optimal dimension reduction for sensor array signal processing

The computational complexity for direction-of-arrival estimation using sensor arrays increases very rapidly with the number of sensors in the array. One way to lower the amount of computations is to employ some kind of reduction of the data dimension. This is usually accomplished by employing linear transformations for mapping full-dimension data into a lower-dimensional space. In the present work, a transformation matrix is derived, that makes it possible to attain the full-dimension Cramer-Rao bound also in the reduced space. A bound on the dimension of the reduced data set is given, above which it is always possible to obtain the same accuracy for the lower-dimension estimates of the source localizations as that achievable by using the full-dimension data. Furthermore, a method is devised for designing the transformation matrix