Pre-steering derivative constraints for robust broadband antenna arrays

The weights of an optimum PB (Pre-steered broadband) antenna array processor are often obtained by solving a LCMV (linearly constrained minimum variance) problem. The objective function is the mean output power (variance) and the constraints space is a set of linear equations which ensure a constant gain in a fixed direction known as the look direction. However, errors in a practical scenario could degrade the performance of the LCMV processor significantly, namely, mismatches between the look direction and the actual DOA (direction of arrival) of the desired signal, positional errors in the sensors and quantization errors in the pre-steered front end of the broadband processor. The main contribution of this paper is the derivation of a new set of constraints, referred to as the Pre-steering derivative constraints, which is able to maintain the processor robustness in the general 3D (three dimensional) space scenario with all the errors mentioned above.