Norm and coefficient constraints for robust adaptive beamforming

Norm-constrained and coefficient-constrained adaptive filters are often used in robust adaptive beamforming to mitigate the target-signal cancellation problem caused by DOA (direction of arrival) mismatch. The norm and coefficient constraints are usually selected numerically based on computer simulations or real-time experiments, which is not enough for theoretical analysis that requires explicit mathematical expressions. This paper analytically derives these constraints using the Taylor series expansion of the array correlation matrix. The constraints that are expressed in terms of maximal DOA mismatch agree well with the simulation results, and most importantly they are quite useful in practical beamformer design and performance analysis.