Quiescent pattern control in linearly constrained adaptive arrays

When an adaptive array operates in the presence of white noise only, the resulting beam pattern is referred to as the quiescent response. Typically, these patterns have mainlobe and sidelobe shapes differing from those designed for use in deterministic, nonadaptive arrays. This paper describes a simple method which allows nearly arbitrary specification of the quiescent response in a linearly constrained power minimization adaptation array. The only restriction on the quiescent is that it must meet the constraints defined for the adaptive array. Since many well-known deterministic designs such as Chebychev are not likely to meet the linear constraint conditions used in adaptive arrays for mainlobe and other pattern control functions, a procedure is presented which modifies the deterministic design to force it to meet the linear constraints in a least-squares manner. Once this has been accomplished, the methods outlined in this paper can be used to cause the modified deterministic design to become the quiescent response of the adaptive array. As a result, the adaptive array can be configured to closely resemble a deterministic array when the noise is white. Under conditions of correlated interference, or jamming, however, the response changes so as to effectively steer nulls in the appropriate directions. The method is based on the use of a generalized side-lobe canceller and requires one additional linear constraint for both narrow-band and broad-band arrays.