Efficient frequency invariant beamforming using virtual arrays

In wideband array processing, frequency invariant beamforming provides a popular means to make the beampattern allpass with respect to frequency. Traditionally, such beampatterns are realized as a two dimensional filter, using tapped delay-line (TDL) filters following each spatial sensor. However it has been recently shown that with the help of a rectangular antenna array, it is possible to generate fixed frequency invariant beampatterns without using filters. In this paper, this concept is generalized to the case of two dimensional arrays with elements on a (possibly nonseparable) lattice. Since performance of the frequency invariant beamformer depends on the number of sensors which could be large for a 2D array of size M × N, a novel approach to beamforming based on the difference co-array of a physical array is also proposed, which avoids use of additional physical sensors. The realization of the frequency invariant beams using second order statistics of the impinging signal with only M + N physical sensors, instead of the two dimensional array of size M×N, is demonstrated. The usefulness of the proposed method is verified through computer simulation.