Adaptive arrays—An introduction

Adaptive array antenna systems are currently the subject of intense interest and investigation/development for radar and communications applications. The principal reason for the interest is their ability to automatically steer nulls onto undesired sources of interference, thereby reducing output noise and enhancing the detection of desired signals. These systems usually consist of an array of antenna elements and a real-time adaptive receiver-processor which has feedback control over the element weights. This paper provides a tutorial introduction to adaptive arrays from the viewpoint of antenna beam-forming and null steering. The particular vehicle chosen for discussion is the Howells-Applebaum analog servo-control-loop processor. This processor derives feedback control error signals from the correlations between element signals, i.e., on the basis of the covariance matrix of the set of system inputs. A simple two-element array with a single adaptive control loop is addressed first, in order to set the stage for analysis of a basic K-element linear array with K adaptive control loops. The set of linear differential equations associated with the controlloop network can be solved by a Q-matrix transformation into orthonormal eigenvector space. The purely mathematical Q-matrix is interpreted in terms of orthogonal beam-forming networks, similar in principle to a Butler matrix beam-forming network. The Q-matrix network produces a set of K orthogonal normalized eigenvector beams whose output powers are proportional to the eigenvalues of the covariance matrix. These beams are utilized in a convenient expression for calculating the time-dependent output pattern function for the array. Performance characteristics have been calculated for different distributions of interference sources to demonstrate the effects of power level, source location with respect to the quiescent beam pattern, source spacing in terms of array resolution, source bandwidth, continuous source distributions, and the array "degrees of freedom" captured. Two modifications of the basic system are also included: the addition of a hard-limiter in the control loops, and a change in the antenna aperture element arrangement to a circular array with an omni "mainbeam."