OVERVIEW

The problem of slow convergence using the LMS or maximum SNR algorithms arises whenever there is a wide spread in the eigenvalues of the input signal correlation matrix. The condition of wide eigenvalue spread occurs if the signal environment includes a very strong source of interference together with other weaker but nevertheless potent interference sources. This condition also obtains if two or more very strong interference sources arrive at the array from closely spaced but not identical directions.

It was shown in Chapter 4 that by appropriately selecting the step size and moving in suitably chosen directions an accelerated gradient procedure offers marked improvement in the convergence rate over that obtained with an algorithm that moves in directions determined by the gradient alone. Another approach for obtaining rapid convergence is to rescale the space in which the minimization is taking place by appropriately transforming the input signal coordinates so that the constant cost contours of the performance surface (which are represented by ellipses in Chapter 4) are approximately spherical and no eigenvalue spread is present in the rescaled space. If such a rescaling can be done, then in principle it would be possible to correct all the error components in a single step by choosing an appropriate step size.

With a method called scaled conjugate gradient descent (SCGD) [1], this philosophy is followed with a procedure that employs a CGD cycle of N iterations and uses the information gained from this cycle to construct a scaling matrix that...