  This paper proposes a reduced-rank scheme for adaptive beamforming based on
the constrained joint iterative optimization of filters. We employ this scheme
to devise two novel reduced-rank adaptive algorithms according to the constant
modulus (CM) criterion with different constraints. The first devised algorithm
is formulated as a constrained joint iterative optimization of a projection
matrix and a reduced-rank filter with respect to the CM criterion subject to a
constraint on the array response. The constrained constant modulus (CCM)
expressions for the projection matrix and the reduced-rank weight vector are
derived, and a low-complexity adaptive algorithm is presented to jointly
estimate them for implementation. The second proposed algorithm is extended
from the first one and implemented according to the CM criterion subject to a
constraint on the array response and an orthogonal constraint on the projection
matrix. The Gram-Schmidt (GS) technique is employed to achieve this orthogonal
constraint and improve the performance. Simulation results are given to show
superior performance of the proposed algorithms in comparison with existing
methods.
