Steady State and Transient Performance Analysis of Adaptive Array Antennas

The performance assessments of array antennas with N antenna elements is generally undertaken by using N-dimensional linear matrix algebra irrespective of the number K of received signals. However, the fundamental dimension (rank) of these problems does not exceed the minimum of K and N. Therefore, for antennas with a large number of antenna elements and in situations when K << N, there is a great advantage to reduce the problem to K dimensions. Yet, the success of this approach rests on having both explicit and simple linear operators (matrices) to partition the problem into its principal domain and orthogonal complement. In this paper, we will employ this approach to both steady state and transient analysis of adaptive array antennas and show its power to provide a complete solution to these problems. The approach has general applicability and can easily be extended to arbitrary large number of antenna elements including, in the limit, continuous antenna apertures that may appear in optical systems.