On the surface characteristics of a mixed constant modulus and cross-correlation criterion for the blind equalization of a MIMO channel

The surface characteristics of a recently proposed constant modulus (CM) and cross-correlation (CC)-based cost function for simultaneous (blind) reconstruction of multiple sources are studied. We explicitly derive the gradient and the Hessian of the CM-CC cost function for binary phase shift keying (BPSK) sources. These analyses show that the parameter which mixes the CM and CC criterion has to be greater than 4/3 to avoid undesirable local minima in the error surface. We further show that some saddle points (due to previous estimated sources) coincide with the origin when the mixing parameter is greater than or equal to 2, hence this is the desirable parameter range as it might reduce the possibility of slow convergence due to the attraction of saddles. Our analytical results are supported by simulations, and provide very good insight into the behaviour of the algorithm, particularly for the selection of a suitable mixing parameter. (C) 1999 Elsevier Science B.V. All rights reserved.