TABLE OF CONTENTS In many applications the practical usefulness of an adaptive array critically depends on the convergence rate that can be achieved. For example, when adaptive radars require simultaneous rejection of jamming and clutter and provide automatic platform motion compensation, then rapid convergence to steady-state solutions is essential. Adaptive control of sensor arrays with the popular maximum SNR or LMS algorithms may well result in slow adaptive weight vector convergence (depending on the eigenvalues of the noise covariance matrix). When the covariance matrix eigenvalues differ by orders of magnitude, then the algorithm convergence time can be exceedingly long, and in any case it is highly example dependent. One way to speed convergence and circumvent the convergence rate dependence on eigenvalue distribution is to employ a direct method of adaptive weight computation, based on the sample covariance matrix of the signal environment [1] [3].
The signals impinging on the receiving elements of an N-element adaptive array are represented by the N-dimensional signal vector x, whose associated covariance matrix is given by
| (6.1) |  |
When the desired signal is absent, then only noise and interference are present and
| (6.2) |  |
When the desired signal is present, then from Chapter 3 the optimal weight vector solution is given by
| (6.3) |  |
where r xd is the cross-correlation between the random vector x( t) and the reference signal d( t). When the desired signal is absent, then the optimal weight vector solution is given by
