Antoine Chevreuil

Blind channel and carrier frequency offset estimation using periodic modulation precoders

Previous results have shown that blind channel estimators, which are resilient to the location of channel zeros, color of additive stationary noise, and channel order overestimation errors, can be developed for communication systems equipped with transmitter-induced cyclostationarity precoders. The present paper extends these blind estimation approaches to the more general problem of estimating the unknown intersymbol interference (ISI) and carrier frequency offset/Doppler effects using such precoders. An all-digital open-loop carrier frequency offset estimator is developed, and its asymptotic (large sample) performance is analyzed and compared to the Cramer-Rao bound (CRB). A subspace-based channel identification approach is proposed for estimating, in closed-form, the unknown channel, regardless of the channel spectral nulls. It is shown that compensating for the carrier frequency offset introduces no penalty in the asymptotic performance of the subspace channel estimator. Simulations are presented to corroborate the performance of the proposed algorithms.

Blind second-order identification of FIR channels: forced cyclostationarity and structured subspace method

We address the problem of blind second-order equalization of scalar-valued polynomial channels. When an almost periodic deterministic function modulates the initial symbol sequence, the observation exhibits second-order cyclostationarity. This property is shown to give rise to a structured spectral factorization problem. The identification of the unknown channel is then always possible via a structured version of the subspace method. No assumption on the channel is required, except the knowledge of a lower bound of the order. The estimate is consistent, and this property remains unchanged in the presence of stationary noise and when the symbols are colored.

MIMO blind second-order equalization method and conjugate cyclostationarity

The blind identification of vector-valued FIR transfer functions using exclusively second-order statistics of the output has become conventional. The so-called subspace method provides a nice and efficient way of solving the problem. However, the extension to the multi-input/multi-output (MIMO) case is not that straightforward, and, for instance, some indetermination drawbacks may occur. We show in this correspondence that the introduction of some cyclostationarity at the input (which still leads to feasible systems) may lead to an algorithm that is far more satisfactory because for both, it is less prone to indetermination problems, and the required assumptions are not too sophisticated.

Blind channel identification and equalization using periodic modulation precoders: performance analysis

The paper deals with blind identification and equalization of communication channels within the so-called modulation induced cyclostationarity (MIC) framework, where the input symbol stream is modulated by a P periodic precoder with the purpose of inducing cyclostationarity in the transmit sequence. By exploiting the cyclostationarity induced by the periodic precoder, a subspace-based channel identification algorithm that is resilient to the location of channel zeros, channel order overestimation errors, and color of additive stationary noise, is developed. The asymptotic performance of the subspace-based identification approach is analyzed and compared with the asymptotic lower bound provided by the nonlinear cyclic correlation matching approach. Criteria for optimally designing the periodic precoder are also presented. The performance of MMSE-FIR and MMSE-DFE equalizers is quantified for the proposed cyclostationarity-induced framework in terms of the MMSE. Although cyclostationarity-inducing transmitters present several advantages relative to their stationary counterparts from a channel estimation viewpoint, it is shown that from an equalization viewpoint, MIC-based systems exhibit a slightly increased MMSE/BER when compared with the stationary case.

Separation of Convolutive Mixtures of Cyclostationary Sources: A Contrast Function Based Approach

Fourth-order cumulants are quite popular in the field of blind separation of convolutive mixtures of stationary sources. Their use in the context of cyclo-stationary sources cannot be taken for granted because consistent estimation of the temporal mean of the fourth-order cumulants needs the knowledge of the cyclic frequencies of the received signal. In this paper, we introduce a cost function whose estimation does not need the knowledge of the cyclic frequencies. We show that under some reasonable sufficient conditions, its maximization allows to separate the sources.

Blind equalization - case of an unknown symbol period

We address the problem of estimating blindly a linearly modulated sequence of unknown rate transmitted over an unknown frequency selective channel. We achieve the goal by extending the concept of deconvolution to a cyclo-stationary context and present a generic class of functionals, the minimization of which achieves the equalization. This defines estimates of the symbol rate: by construction, they are insensitive to a lack of excess bandwidth, bestowing a clear advantage on them over the estimates of the literature.

Blind equalization in the presence of jammers and unknown noise: solutions based on second-order cyclostationary statistics

Addresses the blind identification of a linear time-invariant channel using some second-order cyclostationary statistics. In contrast to other contributions, the case where the second-order statistics of the noise and of the jammers are totally unknown is considered. It is shown that the channel can be identified consistently by adapting the so-called subspace method of Moulines et al. (1995). This adaptation is valid for fractionally spaced systems and, more interestingly, for the general systems exhibiting transmitter induced cyclostationarity introduced by Tsatsanis and Glannakis (1995). The new subspace method is based in both cases on a common tool, i.e., a general spectral factorization algorithm. The identifiability conditions are specified and some simulation examples are given.

Separation of instantaneous mixtures of cyclo-stationary sources

It has been observed that, generally, the Comon algorithm successfully achieves to separate instantaneous mixtures of non-stationary signals, despite it has been designed for stationary environments. We address the theoretical justification of this fact. We provide a tractable condition on the statistics of the sources ensuring that the Comon function is a contrast. This condition is worked out for various digital communication signals. We finally explain why the Comon and JADE algorithms remain strongly connected in a cyclo-stationary context.

A blind source separation framework for detecting CPM sources mixed by a convolutive MIMO filter

This paper deals with blind separation of convolutive mixtures of continuous phase modulated (CPM) sources. The main difficulty lies in the fact that CPM sources are non-linear (and hence non i.i.d.) sources. The problem is addressed through the general formulation of blind source separation (BSS). The separation method consists in iterative constrained optimizations of criteria depending on the fourth-order statistics. We prove the validity of the considered contrast functions for the extraction of one source. A local study then allows us to show that the optimization is free of spurious local maxima at each step and that it is possible to alleviate the error accumulation problem by using an unconstrained post-optimization technique. After separation is achieved, the emitted symbols are estimated, based on recent results concerning CPM equalization. Finally, simulations illustrate the validity of the method.

Performance analysis of blind channel estimators based on non-redundant periodic modulation precoders

Periodic modulation precoders allow blind identification of SISO channels from output second-order cyclic statistics, irrespective of the location of channel zeros, color of additive stationary noise, or the channel order overestimation errors. The performance of blind channel estimators relying on periodic precoders is investigated. Criteria for optimal designs of periodic modulation precoders are also presented.