"An
Efficient Block-Based Addressing Scheme for the Nearly Optimum Shaping of
Multidimensional Signal Spaces", *IEEE Trans. Information Theory*, vol.
41, no. 6, pp. 2026-2031, Nov. 1995.

We introduce an efficient addressing scheme for the nearly
optimum shaping of a multidimensional signal constellation. The 2-D
(two-dimensional) subspaces are partitioned into *K* energy shells of equal
cardinality. The average energy of a 2-D shell can be closely approximated by a
linear function of its index. In an *N*=2*n*-D space, we obtain *K ^{n}*
shaping clusters of equal cardinality. Shaping is achieved by selecting

S. Valaee, B. Champagne, and P. Kabal

"Parametric
Localization of Distributed Sources", *IEEE Trans. Signal Processing*,
vol. 43, no. 9, pp. 2144-2153, Sept. 1995.

Most array processing algorithms are based on the assumption that the signals are generated by point sources. This is a mathematical constraint that is not satisfied in many applications. In this paper, we consider situations where the sources are distributed in space with a parametric angular cross-correlation kernel. We propose an algorithm that estimates the parameters of this model using a generalization of the MUSIC algorithm. The method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors. We study two particular cases: coherent and incoherent spatial source distributions. The spatial correlation function for a uniformly distributed signal is derived. From this, we find the array gain and show that (in contrast to point sources) it does not increase linearly with the number of sources. We compare our method to the conventional (point source) MUSIC algorithm. The simulation studies show that the new method outperforms the MUSIC algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources. It is also shown that the threshold signal-to-noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method.

A. K. Khandani, P. Kabal, and E. Dubois

"Computing
the Weight Distribution of a Set of Points Obtained by Scaling, Shifting, and
Truncating a Lattice", *IEEE Trans. Information Theory, vol. 41,
no. 5, pp. 1480-1482, Sept. 1995.*

A method is developed to compute the weight distribution of a set of points obtained from a lattice. The lattice is scaled (with possibly nonequal factors) along different dimensions, is shifted to an arbitrary point, and its lower dimensional subspaces are truncated within given shaping regions. Each branch in the lattice trellis diagram is labeled by the weight distribution of the corresponding coset incorporating the effects of scaling, shifting, and truncation. The weight distribution is obtained by multiplying the weight distribution of the serial branches and then adding the result over parallel paths.

"Auditory
Distortion Measure for Speech Coder Evaluation - Hidden Markovian Approach",
*Speech Communication*, vol. 17, no. 1-2, pp. 39-57, Aug. 1995.

This article introduces a methodology for quantifying the distortion introduced by a low or medium bit-rate speech coder. Since the perceptual acuity of a human being determines the precision with which speech data must be processed, the speech signal is transformed onto a perceptual-domain (PD). This is done using Lyon's cochlear (auditory) model whose output provides the probability-of-firing information in the neural channels at different clock times. In our present approach, we use a hidden Markov model to describe the basic firing/non-firing process operative in the auditory pathway. We consider a two-state fully-connected model of order one for each neural channel; the two states of the model correspond to the firing and non-firing events. Assuming that the models are stationary over a fixed duration, the model parameters are determined from the PD observations corresponding to the original signal. Then, the PD representations of the coded speech are passed through the respective models and the corresponding likelihood probabilities are calculated. These probability scores are used to define a cochlear hidden Markovian (CHM) distortion measure. This methodology considers the temporal ordering in the neural firing patterns. The CHM measure which utilizes the contextual information present in the firing pattern shows robustness against coder delays.

"Wideband
Array Processing Using a Two-Sided Correlation Transformation", *IEEE
Trans. Signal Processing*, vol. 43, no. 1, pp. 160-172, Jan. 1995.

A new method for broadband array processing is proposed. The method is based on unitary, transformation of the signal subspaces. We apply a two-sided transformation on the correlation matrices of the array. It is shown that the two-sided correlation transformation (TCT) has a smaller subspace fitting error than the coherent signal-subspace method (CSM). It is also shown that unlike CSM, the TCT algorithm can generate unbiased estimates of the directions-of-arrival, regardless of the bandwidth of the signals. The capability of the TCT and CSM methods for resolving two closely spaced sources is compared. The resolution threshold for the new technique is much smaller than that for CSM.

Q.-G. Liu, B. Champagne, and P. Kabal

"Room
Speech Dereverberation via Minimum-Phase and All-Pass Component Processing of
Multi-Microphone Signals", *Proc. IEEE Pacific Rim Conf. Commun.,
Computers, Signal Processing* (Victoria, BC), pp. 571-574, May 1995.

In this paper, a new microphone array processing technique is proposed for blind dereverberation of speech signals affected by room acoustics. It is based on the separate processing of the minimum-phase and all-pass components of multi-microphone signals. The underlying motivation for the new processor is to use spatio-temporal processing of a single set of synchronous speech segments from several microphones to reconstruct the source speech, such that it is applicable to practical time-variant acoustic environments. Simulated room impulse responses are used to evaluate the new processor and to compare it to a conventional beamformer. A significant improvement in array gain and a reduction of reverberation in listening tests are observed.

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