Analysis of an over-constrained adaptive array

In antenna arrays, the number of nulls that can be formed independently is equal to or less than the number of array elements minus one. Therefore, if the number of interferences exceeds the number of freedom for pattern synthesis in adaptive arrays, nulls in the radiation pattern can not be steered toward each interference direction. To clarify the behavior of the adaptive array in such an environment, an analysis is made for the case where two interferences are impinging on the two-element directionally constrained adaptive array. As a result, it is proved that the adaptive array acts to reduce the undesired noise power at the array output. However, improvement in output signal-to-noise ratio is insufficient because of the limitation in null formation.