IMPLEMENTATION AND CONVERGENCE CONSIDERATIONS OF A LINEARLY CONSTRAINED ADAPTIVE ARRAY

Frost introduced a linearly constrained optimization algorithm such that certain mainbeam properties are preserved while attaining good cancellation. An open-loop implementation of this algorithm is developed here. This implementation is shown to be equivalent to the technique developed by Jim, Griffiths, and Buckley whereby the constrained problem is reduced to an unconstrained problem. In addition, analytical results are presented for the convergence rate when the sampled matrix inversion (SMI) or Gram-Schmidt (GS) algorithm are employed. It has been previously shown that the steady-state solution for the optimal weights is identical for both constrained and reduced unconstrained problems. It is shown here that if the SMI or GS algorithms are employed, then the transient weighting vector solution for the constrained problem is identical to the equivalent transient weighting vector solution for the reduced unconstrained implementation. © 1990 IEEE