  In this paper, the problem of how to optimally and precisely control array
response levels is addressed. By using the concept of the optimal weight vector
from the adaptive array theory and adding virtual interferences one by one, the
change rule of the optimal weight vector is found and a new formulation of the
weight vector update is thus devised. Then, the issue of how to precisely
control the response level of one single direction is investigated. More
specifically, we assign a virtual interference to a direction such that the
response level can be precisely controlled. Moreover, the parameters, such as,
the interference-to-noise ratio (INR), can be figured out according to the
desired level. Additionally, the parameter optimization is carried out to
obtain the maximal array gain. The resulting scheme is called optimal and
precise array response control (OPARC) in this paper. To understand it better,
its properties are given, and its comparison with the existing accurate array
response control ($ {\textrm A}^2\textrm{RC} $) algorithm is provided. Finally,
simulation results are presented to verify the effectiveness and superiority of
the proposed OPARC.
