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This paper proposes a parametric-based network architecture for joint channel estimation and data detection in communications systems with hardware impairments. This architecture is composed of a data-augmented layer, a custom soft thresholding function, and several linear layers modeling the effect of channel effects and hardware impairments. In the proposed network, the soft thresholding function softly constrains the detected data to be within the considered constellation. The latter depends only on one one parameter that is optimized during training. The benefit of the proposed approach is illustrated through a communication chain corrupted by multiple impairments and noises.

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.

This paper introduces a new algorithm to approximate non orthogonal joint diagonalization (NOJD) of a set of complex matrices. This algorithm is based on the Frobenius norm formulation of the JD problem and takes advantage from combining Givens and Shear rotations to attempt the approximate joint diagonalization (JD). It represents a non trivial generalization of the JDi (Joint Diagonalization) algorithm (Souloumiac 2009) to the complex case. The JDi is first slightly modified then generalized to the CJDi (i.e. Complex JDi) using complex to real matrix transformation. Also, since several methods exist already in the literature, we propose herein a brief overview of existing NOJD algorithms then we provide an extensive comparative study to illustrate the effectiveness and stability of the CJDi w.r.t. various system parameters and application contexts., Comment: 13 pages, 18 figures