Chair: J.P. Cardoso, Telecom Paris, CNRS (FRANCE)
Chong-Yung Chi, National Tsing Hua University (REPUBLIC OF CHINA)
Mei-Chyn Wu, National Tsing Hua University (REPUBLIC OF CHINA)
Cumulant (higher-order statistics) based inverse filter criteria maximizing J_r,m = |C_m|^r / |C_r| ^m, where m not-equal-to r and C_m (C_r) denotes the mth-order (rth-order) cumulant of the inverse filter output, have been proposed for blind deconvolution and equalization with only non-Gaussian output measurements of an unknown linear time-invariant (LTI) system. This paper shows that the maximum of J_r,m, associated with the true inverse filter of the unknown LTI system, exists only for r to be even and m > r, otherwise, J_r,m is unbounded. The admissible values for (r,m) =(2s,l+s) where l > s greater-or-equal-to 1 include (2,3), (2,4) and (4,6) proposed by Tugnait, Wiggins, Shalvi and Weinstein in addition to more new ones such as (2,5), (2,6) and (4,5). Some simulation results for the inverse filter criteria J_r,m with the proposed admissible values of (r,m) are then provided. Finally, we draw some conclusions.
Dirk T. M. Slock, Institute EURECOM (FRANCE)
Constantinos B. Padias, Institute EURECOM (FRANCE)
In previous work, we have shown that in the case of multiple antennas and/or oversampling, FIR ZF equalizers exist for FIR channels and can be obtained from the noise-free linear prediction (LP) problem. The LP problem also lead to a minimal parameterization of the noise subspace, which was used to solve the deterministic maximum likelihood (DML) channel estimation problem. Here we present further contributions along two lines. One is a number of blind equalization techniques of the adaptive filtering type. We also present some robustifying modifications of the DML problem.
K. Abed Meraim, Telecom Paris
P. Duhamel, Telecom Paris
D. Gesbert, France Telecom
P. Loubaton, Telecom Paris
S. Mayrargue, France Telecom
E. Moulines, Telecom Paris
D. Slock, Institute EURECOM (FRANCE)
Blind channel indentification methods based on the oversampled channel output is a problem of current theoretical and practical interest. In this contribution, it is first demonstrated that the subspace methods developped in [1] are not robust to errors in the determination of the model order. An alternative solution is then proposed, based on a linear prediction approach. The effect of overestimating the channel order is investigated by simulations: it is demonstrated that the prediction erro method is "robust" to over-determination, in contrast to most of the schemes suggested to date.
Georgios B. Giannakis, University of Virginia (USA)
Steven D. Halford, University of Virginia (USA)
Blind Fractionally Spaced (FS) equalizers only require output samples taken at rates higher than the symbol rate to estimate the channel or the equalizer. Methods for finding FIR zero forcing equalizers directly from the observations are described and adaptive versions are developed. In contrast, most current methods require channel estimation as a first step to estimating the equalizer. For the noisy channel, the FIR equalizer is shown to be minimum mean-square error. FS equalizers are not unique, thereby allowing optimum zero-forcing parametric FIR or nonparametric IIR equalizers to be derived such that in addition to being zero-forcing, they also minimize the noise power at the output. These optimum equalizers do not depend on the input distribution and are also valid for deterministic inputs. Finally, if the additive noise is white, they do not depend on the SNR.
Jitendra K. Tugnait, Auburn University (USA)
The problem of fractionally-spaced (FS) blind adaptive equalization under symbol-timing-phase offsets is considered. It is well-known that in the case of trained (non-blind) equalizers, the performance of FS equalizers is independent of the timing-phase unlike that of baud-rate equalizers. Moreover, trained FS equalizers synthesize optimal filters in MMSE sense, hence are superior to baud-rate trained equalizers. These advantages of trained FS equalizers have not been shown to be true for blind equalizers, rather they have been simply assumed. We present a simulation example where such advantages do not materialize. Then we present a solution based upon a parallel, multimodel Godard adaptive filter bank approach which yields a performance almost invariant w.r.t. symbol-timing-phase. An illustrative simulation example 16-QAM (V22 source) signal is presented where effect of symbol-timing-phase offset is studied via computer simulations.
Mouad Boumahdi, CEPHAG (FRANCE)
Jean-Louis Lacoume, CEPHAG (FRANCE)
In this paper we present a method to estimate non-minimum phase AR or ARMA systems based on maximum kurtosis properties. First the Spectrally Equivalent Minimum Phase (SEMP) filter is estimated from output statistics, then the kurtosis allows us to localise the zeros of the associated transfer function from the zeros of its SEMP filter. Combining kurtosis properties and Singular Value Decomposition (SVD) properties we propose a new ARMA orders determination method. On field seismic data we compare the proposed method to Gianakis- Mendel's algorithm and Tugnait's algorithm's. On field underwater explosions data we present a new results showing the interest of estimating a non-causal AR filter to modelise the secondary waves. The results obtained on short length of data (128 samples) confirm the robustness of the proposed method.
K.M. Cheung, Hong Kong University of Science & Technology (HONG KONG)
S.F. Yau, Hong Kong University of Science & Technology (HONG KONG)
The problem of determining the unknown responses of a system which is continuously excited by cyclostationary signals is considered. By exploiting the periodicity of the input impulses, an approach based on array signal processing techniques is proposed to estimate the system responses. This method generalizes Bresler's idea of resolving overlapping echoes by partitioning the signals into portions which fit the mathematical formulation as in Bresler's paper. A compensating algorithm is also devised to compensate the random uncertainties and perturbations of the system and the signals. Once the system responses are determined, standard methods can be used to find the positions and amplitudes of the impulses. Prospective and promising simulation results are obtained.
I. Fijalkow, ENSEA (FRANCE)
J.R. Treichler, Applied Science Technology Inc.
C.R. Johnson Jr., Cornell University (USA)
Under certain conditions on the equalizer length and on the channel dynamics, temporal or spatial diversity allows one to achieve blind equalization perfectly by means of second-order statistics only. Loss of channel disparity causes perfect equalization to be no longer achievable. The achievable channel-equalizer combination then depends only on the part of the multichannel transfer function lacking disparity. We show that the Fractionally Spaced Equalizer adapted by the Constant Modulus Algorithm (FSE-CMA) still achieves "reasonable" equalization. Its performance equals that of the non-fractional CMA, with a slightly shorter baud-length equalizer than the FSE, applied to the part of the channel lacking disparity.
Xinyu Ma, University of Southern California (USA)
Chrysostomos L. Nikias, University of Southern California (USA)
New methods for parameter estimation and blind system identification for impulsive signal environments are presented. The data are modeled as stable processes. First, methods for estimating the parameters (characteristic exponent and dispersion) of a symmetric stable distribution are presented. The fractional lower-order moments, both positive and negative order, and their applications are introduced. Then a new algorithm for blind channel identification based on fractional lower-order moments is proposed. The Alpha-Spectrum, a spectral representation for impulsive environments, is developed. Conditions for blind identifiability of non-minimum phase FIR channels are established using the properties of the Alpha-Spectrum.
Zhi Ding, Auburn University (USA)
Z. Mao, Auburn University (USA)
Blind channel identification has been a popular research subject in recent years. In this paper, we introduce the concept of knowledge-based blind channel identification. By relying on known information such as the pulse shaping filter and the anti-aliasing filter responses, the performance of channel identification and equalization can be significantly enhanced in digital communication systems. We present two simple methods: one in time-domain and one in frequency domain. Our simulation results will demonstrate the performance of these two approaches.