Robust presteering derivative constraints for broadband antenna arrays

The weights of an optimum presteered broadband (PB) antenna array processor are often obtained by solving a linearly constrained minimum variance (LCMV) problem. The objective function is the mean output power (variance), and the constraint space is a set of linear equations that ensure a constant gain in a specified direction known as the look direction. The LCMV optimization results in a set of weights that attenuate all signals except for the look direction signal. However, it is well known that array calibration errors can degrade the performance of the processor with only look direction constraints. For instance, a slight mismatch between the direction of arrival (DOA) of the desired signal and the calibrated look direction of the processor will cause the optimization process to interpret the signal as interference, causing signal attenuation. To alleviate the directional mismatch problem, the spatial power response of the PB processor in the vicinity of the look direction can be widened by imposing additional constraints known as the derivative constraints on the processor weights. While derivative constraints are effective against directional mismatches, we demonstrate that they are no longer robust when there are additional calibration errors like positional errors in the sensors or quantizational errors in the presteered front end of the broadband processor. The main contribution of this paper is the derivation of a new set of constraints referred to as presteering derivative constraints, which are able to maintain processor robustness despite multiple errors including directional mismatches, positional errors, and quantization errors. It is also demonstrated that the presteering derivative constraints are sufficient conditions for derivative constraints, and hence, the spatial power response of the optimized broadband processor is also maximally flat in the vicinity of the look direction.