COMM-7.1

A Stochastic Subspace Algorithm for Blind Channel Identification in Noise Fields with Unknown Spatial Color
Piet Vandaele, Marc Moonen (K. Mercierlaan 94, 3001 Heverlee, Belgium)

In this paper, the blind channel identification problem is formulated in a stochastic state space framework. Starting from a state space model we present a preprocessing step based on two orthogonal subspace projections. Using these orthogonal projections, we derive an algorithm for blind channel estimation which is insensitive to the spatial color of the noise. The performance of this new algorithm is demonstrated through simulation examples.

COMM-7.2

Fixed Window Constant Modulus Algorithms
Xiang-yang Zhuang, A. Lee Swindlehurst (Brigham Young University)

We propose two batch versions of the constant modulus algorithm in which a fixed block of samples is iteratively re-used. The convergence rate of the algorithms is shown to be very fast. The delay to which the algorithms converge can be determined if the peak position of the initialized global channel/equalizer response is known. These fixed window CM algorithms are data efficient, computationally inexpensive and no step-size tuning is required. The effect of noise and the relationship between the converging delay and noise enhancement are analyzed as well.

COMM-7.3

On the capacity of linear time-varying channels
Sergio Barbarossa, Anna Scaglione (University of Rome "La Sapienza")

Linear time-varying (LTV) channels are often encountered in mobile communications but, as opposed to the linear time-invariant (LTI) channels case, there is no a well established theory for computing the channel capacity, or providing simple bounds to the maximum information rate based only on the channel impulse response, or predicting the structure of the channel eigenfunctions. In this paper, we provide: i) a method for computing the mutual information between blocks of transmitted and received sequences, for any finite block length; ii) the optimal precoding (decoding) strategy to achieve the maximum information rate; iii) an upper bound for the channel capacity based only on the channel time-varying transfer function; iv) a time-frequency representation of the channel eigenfunctions, revealing a rather intriguing, but nonetheless intuitively justifiable, bubble structure.

COMM-7.4

On the performance of the Viterbi decoder with trained and semi-blind channel estimators
Alexei Gorokhov (CNRS-LSS, Ecole Superieure d'Electricite)

Maximum-likelihood sequence estimation is often used to recover digital signals transmitted over finite memory convolutive channels when an estimate of the channel is available. In this letter, we study the impact of channel estimation errors on the quality of sequence detection. The general case of single input multiple output (SIMO) channels is considered. An asymptotic upper bound for the symbol error rate is presented which allows to treat channel estimation errors as equivalent losses in signal-to-noise ratio (SNR). This relationship is studied and numerically validated for the standard least squares channel estimate and for the semi-blind estimator which makes use of the empirical subspace of the observed data.

COMM-7.5

Non-Data Aided Joint Estimation of Carrier Frequency Offset and Channel using Periodic Modulation Precoders: Performance Analysis
Erchin Serpedin (University of Virginia, Dept. of Electrical Engineering, Charlottesville, VA 22903), Antoine Chevreuil (Universite de Marne-la-Valle, UF SPI 2, Rue de la Butte Verte, 93166 Noisy-le-Grand, France), Georgios B Giannakis (University of Virginia, Dept. of Electrical Engineering, Charlottesville, VA 22903), Philippe Loubaton (Universite de Marne-la-Valle, UF SPI 2, Rue de la Butte Verte, 93166 Noisy-le-Grand, France)

Recent results have shown that blind channel estimators, which are robust to the location of channel zeros and channel order overestimation errors, can be derived for communication channels equipped with Transmitted Induced Cyclostationarity (TIC) precoders. This paper addresses the problem of joint estimation of the unknown InterSymbol Interference (ISI) and carrier frequency offset using TIC-based set-ups. First, it is shown that the second-order cyclic statistics of the output allow recovery of the channel taps under a scaling factor ambiguity dependent on the unknown carrier offset frequency. Next, a carrier frequency estimator is proposed, and its asymptotic (large sample) performance is analyzed. It is shown that the asymptotic performance of the frequency estimator improves in the presence of a channel equalizer for high SNR's. Finally, numerical simulations are presented to colloborate the performance of proposed algorithms.

COMM-7.6

Recursive Blind Channel Identification and Equalization By ULV Decomposition
Xiaohua Li, Howard Fan (University of Cincinnati)

Most eigenstructure-based blind channel identification and equalization algorithms with second-order statistics need SVD or EVD of the correlation matrix of the output signal. In this paper, we show new algorithms based on QR factorization of the output data directly. A recursive algorithm is developed by updating a rank-revealing ULV decomposition. Compared with existing algorithms in the same category, our algorithm is computationally more efficient and numerically (potentially) more robust. The computation in each recursion of the recursive algorithm can be reduced to the order of $O(m^2)$ under some simplifications, where $m$ is the dimension of the received signal vector. Numerical simulations demonstrate the performance of the proposed algorithm.

COMM-7.7

On the equivalence between the super-exponential algorithm and a gradient search method
Mamadou Mboup (UFR Math-Info, University Rene Descartes), Phillip A Regalia (Institut National des Telecommunications)

This paper reviews the Super-exponential algorithm proposed by Shalvi and Weinstein for blind channel equalization. We show that the algorithm coincides with a gradient search of a maximum of a cost function, which belongs to a family of functions very relevant in blind channel equalization. This family traces back to Donoho's work on minimum entropy deconvolution, and also underlies the Godard (or Constant Modulus) and the Shalvi-Weinstein algorithms. Using this gradient search interpretation, we give a simple proof of convergence for the Super-exponential algorithm. Finally, we show that the gradient step-size choice giving rise to the super-exponential algorithm is optimal.

COMM-7.8

The Fractionally Spaced Vector Constant Modulus Algorithm
Mark A Haun, Douglas L Jones (Dept. of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign)

The vector constant modulus algorithm (VCMA) was recently introduced as an extension of CMA which can equalize data from shaped sources having nearly Gaussian marginal distributions. Some simple changes in the structure of VCMA allow it to be used in fractionally-spaced equalizers with their attendant benefits. Althoughj developed with shell mapping in mind, VCMA can also equalize data from other shaping methods such as trellis shaping. Furthermore, the vector modulus concept from VCMA can be successfully applied to other algorithms based on constant modulus criteria, including RCA and MMA. Simulations have verified all of these results.

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Last Update: February 4, 1999 Ingo Höntsch