OPARC: Optimal and Precise Array Response Control Algorithm—Part I: Fundamentals

Abstract

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 interferenceto-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 (A 2 RC) algorithm is provided. Finally, simulation results are presented to verify the effectiveness and superiority of the proposed OPARC.Index Terms-Array response control, adaptive array theory, array pattern synthesis, array signal processing.

OPARC: Optimal and Precise Array Response Control Algorithm—Part II: Multi-Points and Applications

“…The OPARC algorithm, developed in the companion paper [1], is able to optimally and precisely adjust one-point response level at a time. Thus, we may apply it to the M kpoint OPARC problem (14) as follows.…”

“…In the mth step, OPARC is to realize L(θ k,m , θ 0 ) = ρ k,m , m = 1, · · · , M k . Unfortunately, OPARC brings inevitable pattern variations on the previous controlled angles as we have discussed in [1]. More specifically, the response levels of θ k,i , i = 1, · · · , m−1, vary after accurately controlling the response level of θ k,m to its desired level ρ k,m , 2 ≤ m ≤ M k .…”

“…Note that a multi-point accurate array response control (MA 2 RC) algorithm has been recently developed in [2]. Nevertheless, since it is built on the basis of the accurate array response control (A 2 RC) algorithm [3], the MA 2 RC suffers from the similar drawbacks to A 2 RC, i.e., a solution is empirically adopted and hence a satisfactory performance cannot be always guaranteed as analyzed in details in [1]. In this paper, we first carry out a careful investigation on the change rule of the optimal beamformer when multiple virtual interferences are simultaneously assigned.…”

“…Then, a generalized methodology of the weight vector update is observed and utilized for the realization of the multi-point array response control. Similar to the OPARC in [1], we formulate a constrained optimization problem such that the array response levels of multiple points can be optimally (in the sense of array gain) and precisely controlled. Then, two different solvers, by either taking advantage of the OPARC algorithm or employing the recently developed consensus alternating direction method of multipliers (C-ADMM) approach in [4], are provided to find an approximate solution of the established optimization problem.…”

“…Notations: The same as [1], we use bold upper-case and lower-case letters to represent matrices and vectors, respectively. In particular, we use I to denote the identity matrix.…”