Constant Modulus Algorithms Using Hyperbolic Givens Rotations
Abstract
We propose two new algorithms to minimize the constant modulus (CM) criterion
in the context of blind source separation. The first algorithm, referred
to as Givens CMA (G-CMA) uses unitary Givens rotations and proceeds in
two stages: prewhitening step, which reduces the channel matrix to a unitary
one followed by a separation step where the resulting unitary matrix
is computed using Givens rotations by minimizing the CM criterion. However,
for small sample sizes, the prewhitening does not make the channel
matrix close enough to unitary and hence applying Givens rotations alone
does not provide satisfactory performance. To remediate to this problem, we
propose to use non-unitary Shear (Hyperbolic) rotations in conjunction with
Givens rotations. This second algorithm referred to as Hyperbolic G-CMA
(HG-CMA) is shown to outperform the G-CMA as well as the Analytical CMA (ACMA) in terms of separation quality. The last part of this paper
is dedicated to an efficient adaptive implementation of the HG-CMA and to
performance assessment through numerical experiments.