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Research

Keywords: blind, broadband arrays, audio, acoustics

R. A. Kennedy, D. Miniutti, X. Ouyang, and M. Ghosh, "United States Patent: US 7,269,216 --- Blind Magnitude Equalizer for Segment Sync-Based Timing Recovery of Receivers", September 2007.
Abstract BibTeX
Official: Link PDF: pat7269216.pdf Google-Scholar: [0]
Abstract: A magnitude only equalizer equalizes a magnitude of a received wireless signal without regard to phase distortions introduced, and transmits the magnitude equalized signal to a timing recovery loop for improved correlation peak detection in a sync based timing recovery scheme. A channel equalizer receiving the output signal from the timing recovery loop equalizes the signal and corrects any phase distortions introduced by the magnitude only equalizer. The magnitude only equalizer includes at least one filter utilizing only real coefficients and constrained such that the direct term of the overall filter structure within the magnitude only equalizer is unity.
@{KennedyP2007a,
    title = {{United States Patent:} {US} 7,269,216 --- Blind Magnitude Equalizer for Segment Sync-Based Timing Recovery of Receivers},
    author = {Kennedy, R. A. and Miniutti, D. and Ouyang, X. and Ghosh, M.},
    month = {September},
    year = {2007}}
R. A. Kennedy and T. D. Abhayapala, "United States Patent: US 7,054,359 --- VSV-MOE Pre-Equalizer for 8-VSB DTV", May 2006.
Abstract BibTeX
Official: Link PDF: pat7054359.pdf Google-Scholar: [1]
Abstract: A vestigial sideband (VSB) modulation minimum output energy (MOE) pre-equalizer operating on a received ATSC 8-VSB DTV signal includes one or more of an adaptive feed-forward filter and an adaptive feedback filter each utilizing only real adaptive coefficients, with the direct term for the overall filter constrained to unity to remove one degree of filter parameterization freedom. Adaptation of the filter(s) is based on minimizing a blind energy cost function, and is independent of adaptation of a conventional adaptive channel equalizer. The pre-equalized signal is passed to the conventional adaptive equalizer for channel equalization utilizing DFE, IIR-CMA, etc., resulting in performance improvements including faster convergence and greater robustness with relatively small implementation costs.
@{KennedyP2006a,
    title = {{United States Patent:} {US} 7,054,359 --- {VSV-MOE} Pre-Equalizer for 8-{VSB DTV}},
    author = {Kennedy, R. A. and Abhayapala, T. D.},
    month = {May},
    year = {2006}}
T. S. Pollock, T. D. Abhayapala, and R. A. Kennedy, "Introducing Space into MIMO Capacity Calculations", Journal on Telecommunications Systems, vol. 24, no. 2, pp. 415-436, October 2003.
Abstract BibTeX
Official: Link DOI: 10.1023/A:1026143603179 PDF: KennedyJ2003a.pdf Google-Scholar: [21]
Abstract: The large spectral efficiencies promised for multiple-input multiple-output (MIMO) wireless fading channels are derived under certain conditions which do not fully take into account the spatial aspects of the channel. Spatial correlation, due to limited angular spread or insufficient antenna spacing, significantly reduces the performance of MIMO systems. In this paper we explore the effects of spatially selective channels on the capacity of MIMO systems via a new capacity expression which is more general and realistic than previous expressions. By including spatial information we derive a closed-form expression for ergodic capacity which uses the physics of signal propagation combined with the statistics of the scattering environment. This expression gives the capacity of a MIMO system in terms of antenna placement and scattering environment and leads to valuable insights into the factors determining capacity for a wide range of scattering models.
@article{KennedyJ2003a,
    title = {Introducing Space into {MIMO} Capacity Calculations},
    author = {Pollock, T. S. and Abhayapala, T. D. and Kennedy, R. A.},
    journal = {Journal on Telecommunications Systems},
    volume = {24},
    pages = {415-436},
    month = {October},
    year = {2003}}
P. D. Teal, T. D. Abhayapala, and R. A. Kennedy, "Spatial Correlation for General Distributions of Scatterers", IEEE Signal Processing Letters, vol. 9, no. 10, pp. 305-308, October 2002.
Abstract BibTeX
Official: Link DOI: 10.1109/LSP.2002.804138 PDF: 01043864.pdf Google-Scholar: [35]
Abstract: The well-known results of the spatial correlation function for two-dimensional and three-dimensional diffuse fields of narrowband signals are generalized to the case of general distributions of scatterers. A method is presented that allows closed-form expressions for the correlation function to be obtained for arbitrary scattering distribution functions. These closed-form expressions are derived for a variety of commonly used scattering distribution functions.
@article{KennedyJ2002b,
    title = {Spatial Correlation for General Distributions of Scatterers},
    author = {Teal, P. D. and Abhayapala, T. D. and Kennedy, R. A.},
    journal = {IEEE Signal Processing Letters},
    volume = {9},
    pages = {305-308},
    month = {October},
    year = {2002}}
D. K. Borah, R. A. Kennedy, Z. Ding, and I. Fijalkow, "Sampling and Prefiltering Effects on Blind Equalizer Design", IEEE Trans. Signal Processing, vol. 49, no. 1, pp. 209-218, January 2001.
Abstract BibTeX
Official: Link DOI: 10.1109/78.890364 PDF: 00890364.pdf Google-Scholar: [13]
Abstract: In the development of equalization algorithms for unknown channels, the effects of the sampling rate and the analog receive prefilter prior to discretization of the received signal are often overlooked. In this paper, these effects are investigated. The relationship between the fractionally spaced output samples of a noise-limiting prefilter and the symbol spaced output samples of a matched filter is studied for both the time-invariant and the time-varying channels. It is shown that the prefilter and the sampling rate can have significant effects on blind equalization algorithms. Thus, this paper provides a common framework for comparing different blind algorithms that are studied in the literature with different sampling rates. A case study of the well-known subspace method for blind channel identification is presented. The effects of the noise color due to the prefilter on equalizers is investigated, and the sensitivity of the truncation of the overall channel impulse response in terms of the mean squared error (MSE) performance criterion is investigated through numerical examples.
@article{KennedyJ2001a,
    title = {Sampling and Prefiltering Effects on Blind Equalizer Design},
    author = {Borah, D. K. and Kennedy, R. A. and Ding, Z. and Fijalkow, I.},
    journal = {IEEE Trans. Signal Processing},
    volume = {49},
    pages = {209-218},
    month = {January},
    year = {2001}}
B. D. Radlović and R. A. Kennedy, "Non-minimum Phase Equalization and its Subjective Importance in Room Acoustics", IEEE Trans. Speech and Audio Processing, vol. 8, no. 6, pp. 728-737, November 2000.
Abstract BibTeX
Official: Link DOI: 10.1109/89.876311 PDF: 00876311.pdf Google-Scholar: [26]
Abstract: This paper investigates the perceptual significance of residual phase distortion due to an approximate equalization of the nonminimum-phase room response from a sound source to a microphone in a reverberant room. It is shown that disrupted phase relationships introduced by a minimum-phase equalization filter may have a detrimental effect on perceived sound quality. The subjective assessment of phase distortion on speech signals is related to an objective error criterion, newly introduced in this paper. An alternative approach to the minimum-phase/all-pass decomposition based on iterative flattening of the room transfer function (RTF) magnitude is also presented, which overcomes potential numerical problems and provides more insight into subjective aspects of magnitude and phase equalization in the reduction of acoustic reverberation. Factors contributing to the results and practical implications for equalization are discussed.
@article{KennedyJ2000c,
    title = {Non-minimum Phase Equalization and its Subjective Importance in Room Acoustics},
    author = {Radlović, B. D. and Kennedy, R. A.},
    journal = {IEEE Trans. Speech and Audio Processing},
    volume = {8},
    pages = {728-737},
    month = {November},
    year = {2000}}
B. D. Radlović, R. C. Williamson, and R. A. Kennedy, "Equalization in an Acoustic Reverberant Environment: Robustness Results", IEEE Trans. Speech and Audio Processing, vol. 8, no. 3, pp. 311-319, May 2000.
Abstract BibTeX
Official: Link DOI: 10.1109/89.841213 PDF: 00841213.pdf Google-Scholar: [35]
Abstract: This paper investigates the robustness of sound equalization using a room response inverse filter with respect to changing or uncertain source or microphone positions. It is shown that due to the variations of the transfer function from point to point in a room, even small changes in the source or microphone position of just a few tenths of the acoustic wavelength can cause large degradations in the equalized room response. The robustness problem is especially acute at high frequencies, which are known to carry some important attributes of the speech signal. The spatial extent of equalization, derived from the statistical-average properties of sound transmission in rooms, is illustrated by computer simulations which corroborate the theoretical results presented.
@article{KennedyJ2000b,
    title = {Equalization in an Acoustic Reverberant Environment: Robustness Results},
    author = {Radlović, B. D. and Williamson, R. C. and Kennedy, R. A.},
    journal = {IEEE Trans. Speech and Audio Processing},
    volume = {8},
    pages = {311-319},
    month = {May},
    year = {2000}}
T. D. Abhayapala, R. A. Kennedy, and R. C. Williamson, "Nearfield Broadband Array Design Using a Radially Invariant Modal Expansion", J. Acoust. Soc. Am., vol. 107, no. 1, pp. 392-403, January 2000.
Abstract BibTeX
Official: Link DOI: 10.1121/1.428311 PDF: KennedyJ2000a.pdf Google-Scholar: [17]
Abstract: This paper introduces an efficient parameterization for the nearfield broadband beamforming problem with a single parameter to focus the beamformer to a desired operating radius and another set of parameters to control the actual broadband beampattern shape. The parameterization is based on an orthogonal basis set of elementary beampatterns by which an arbitrary beampattern can be constructed. A set of elementary beamformers are then designed for each elementary beampattern and the desired beamformer is constructed by summing the elementary beamformers with frequency and source-array distance dependent weights. An important consequence of our result is that the beamformer can be factored into three levels of filtering: (i) beampattern independent elementary beamformers; (ii) beampattern shape dependent filters; and (iii) radial focusing filters where a single parameter can be adjusted to focus the array to a desired radial distance from the array origin. As an illustration the method is applied to the problem of producing a practical array design that achieves a frequency invariant beampattern over the frequency range of 1:10 (which is suitable for speech acquisition using a microphone array), and with the array focused either to farfield or nearfield where at the lowest frequency the radial distance to the source is only three wavelengths.
@article{KennedyJ2000a,
    title = {Nearfield Broadband Array Design Using a Radially Invariant Modal Expansion},
    author = {Abhayapala, T. D. and Kennedy, R. A. and Williamson, R. C.},
    journal = {J. Acoust. Soc. Am.},
    volume = {107},
    pages = {392-403},
    month = {January},
    year = {2000}}
R. A. Kennedy, T. D. Abhayapala, and D. B. Ward, "Broadband Nearfield Beamforming using a Radial Beampattern Transformation", IEEE Trans. Signal Processing, vol. 46, no. 8, pp. 2147-2156, August 1998.
Abstract BibTeX
Official: Link DOI: 10.1109/78.705426 PDF: 00705426.pdf Google-Scholar: [50]
Abstract: This paper presents a new method of designing a beamformer having a desired nearfield broadband beampattern. The methodology uses the spherical harmonic solution to the wave equation to transform the desired nearfield beampattern to an equivalent farfield beampattern. A farfield beamformer is then designed for a transformed farfield beampattern that, if achieved, gives the desired nearfield pattern exactly. Salient features of the new method are as follows. (i) The nearfield patterns can be achieved for all angles, not just the primary look direction. (ii) There is no theoretical restriction on the bandwidth. (iii) General array geometries may be used. As an illustration, we apply the method to the problem of producing a practical array design that achieves a nearfield beampattern that is frequency invariant over an octave bandwidth, where at the lowest frequency, the array-source separation is three wavelengths.
@article{KennedyJ1998e,
    title = {Broadband Nearfield Beamforming using a Radial Beampattern Transformation},
    author = {Kennedy, R. A. and Abhayapala, T. D. and Ward, D. B.},
    journal = {IEEE Trans. Signal Processing},
    volume = {46},
    pages = {2147-2156},
    month = {August},
    year = {1998}}
N. C. McGinty, R. A. Kennedy, and P. Hoeher, "Parallel Trellis Viterbi Algorithm for Sparse Channels", IEEE Commun. Lett., vol. 2, no. 5, pp. 143-145, May 1998.
Abstract BibTeX
Official: Link DOI: 10.1109/4234.673661 PDF: 00673661.pdf Google-Scholar: [19]
Abstract: The Viterbi algorithm (VA), which normally operates using a single trellis, can be optimally reformulated into a set of independent trellises for a special class of sparse intersymbol interference (ISI) channels. These independent trellises operate in parallel and have less overall complexity than a single trellis. This trellis decomposition can be applied to a more general class of sparse channels approximately resulting in a suboptimal reduced complexity equalizer.
@article{KennedyJ1998d,
    title = {Parallel Trellis {V}iterbi Algorithm for Sparse Channels},
    author = {McGinty, N. C. and Kennedy, R. A. and Hoeher, P.},
    journal = {IEEE Commun. Lett.},
    volume = {2},
    pages = {143-145},
    month = {May},
    year = {1998}}
D. B. Ward, Z. Ding, and R. A. Kennedy, "Broadband DOA Estimation Using Frequency Invariant Beamforming", IEEE Trans. Signal Processing, vol. 46, no. 5, pp. 1463-1469, May 1998.
Abstract BibTeX
Official: Link DOI: 10.1109/78.668812 PDF: 00668812.pdf Google-Scholar: [41]
Abstract: A new method of direction-of-arrival (DOA) estimation for multiple broadband farfield signals is presented. The technique uses a beamspace preprocessing structure based on frequency invariant beamforming. Specifically, a set of beam-shaping filters focus the received array data in the time domain, thereby avoiding the need for frequency decomposition. Hence, the proposed method is conceptually different from most other broadband DOA estimators, which require frequency decomposition. Numerical results are presented to demonstrate the use of the new method and compare it with conventional coherent signal subspace methods.
@article{KennedyJ1998c,
    title = {Broadband {DOA} Estimation Using Frequency Invariant Beamforming},
    author = {Ward, D. B. and Ding, Z. and Kennedy, R. A.},
    journal = {IEEE Trans. Signal Processing},
    volume = {46},
    pages = {1463-1469},
    month = {May},
    year = {1998}}
K. Doğançay and R. A. Kennedy, "Blind detection of equalization errors in communication systems", IEEE Trans. Inform. Theory, vol. 43, no. 2, pp. 469-482, March 1997.
Abstract BibTeX
Official: Link DOI: 10.1109/18.556106 PDF: 00556106.pdf Google-Scholar: [17]
Abstract: In adaptive channel equalization, transmitted symbol estimates at the equalizer output may be in error because of excessive channel noise, convergence of the equalizer to a "closed-eye" local minimum, or error propagation if the equalizer has a decision feedback structure. This paper is concerned with the detection of equalization errors (i.e., errors in transmitted symbol estimates) in a blindfolded manner whereby no direct access to the channel input is required. The detection problem is cast into a binary hypothesis testing framework. Assuming a linear communication channel that is time-invariant during the test interval, a relationship between the presence of equalization errors and time variations in the underlying linear model taking the transmitted symbol estimates to the equalizer input is established. Based on this relationship, a uniformly most powerful test is constructed to detect the presence of equalization errors in finite- length observations. Finite sample size and asymptotic detection performance of the test is studied. A method for estimating the equalization delay without direct access to the channel input is developed. The effectiveness of the test is illustrated by way of computer simulations.
@article{KennedyJ1997c,
    title = {Blind detection of equalization errors in communication systems},
    author = {Doğançay, K. and Kennedy, R. A.},
    journal = {IEEE Trans. Inform. Theory},
    volume = {43},
    pages = {469-482},
    month = {March},
    year = {1997}}
D. B. Ward, R. A. Kennedy, and R. C. Williamson, "FIR Filter Design for Frequency Invariant Beamformers", IEEE Signal Processing Lett., vol. 3, no. 3, pp. 69-71, March 1996.
Abstract BibTeX
Official: Link DOI: 10.1109/97.481158 PDF: 00481158.pdf Google-Scholar: [42]
Abstract: Two methods of implementing FIR filters for a frequency invariant beamformer are presented. Each of these methods uses a single underlying set of filter coefficients obtained directly from the desired beamformer response. One method uses multirate processing, and the other is based on a single sampling rate.
@article{KennedyJ1996b,
    title = {{FIR} Filter Design for Frequency Invariant Beamformers},
    author = {Ward, D. B. and Kennedy, R. A. and Williamson, R. C.},
    journal = {IEEE Signal Processing Lett.},
    volume = {3},
    pages = {69-71},
    month = {March},
    year = {1996}}
D. B. Ward, R. A. Kennedy, and R. C. Williamson, "Theory and design of broadband sensor arrays with frequency invariant far-field beam patterns", J. Acoust. Soc. Am., vol. 97, no. 2, pp. 1023-1034, February 1995.
Abstract BibTeX
Official: Link DOI: 10.1121/1.412215 PDF: KennedyJ1995b.pdf Google-Scholar: [104]
Abstract: The theory and design of a broadband array of sensors with a frequency invariant far-field beam pattern over an arbitrarily wide design bandwidth is presented. The frequency invariant beam pattern property is defined in terms of a continuously distributed sensor, and the problem of designing a practical sensor array is then treated as an approximation to this continuous sensor using a discrete set of filtered broadband omnidirectional array elements. The design methodology is suitable for one-, two-, and three-dimensional sensor arrays; it imposes no restrictions on the desired aperture distribution (beam shape), and can cope with arbitrarily wide bandwidths. An important consequence of the results is that the frequency response of the filter applied to the output of each sensor can be factored into two components: One component is related to a slice of the desired aperture distribution, and the other is sensor independent. The results also indicate that the locations of the sensors are not a crucial design consideration, although it is shown that nonuniform spacings simultaneously avoid spatial aliasing and minimize the number of sensors. An example design which covers a 10:1 frequency range (which is suitable for speech acquisition using a microphone array) illustrates the utility of the method. Finally, the theory is generalized to cover a parameterized class of arrays in which the frequency dependence of the beam pattern can be controlled in a continuous manner from a classical single-frequency design to a frequency invariant design.
@article{KennedyJ1995b,
    title = {Theory and design of broadband sensor arrays with frequency invariant far-field beam patterns},
    author = {Ward, D. B. and Kennedy, R. A. and Williamson, R. C.},
    journal = {J. Acoust. Soc. Am.},
    volume = {97},
    pages = {1023-1034},
    month = {February},
    year = {1995}}
S. Vembu, S. Verdú, R. A. Kennedy, and W. Sethares, "Convex cost functions in blind equalization", IEEE Trans. Signal Processing, vol. 42, no. 8, pp. 1952-1960, August 1994.
Abstract BibTeX
Official: Link DOI: 10.1109/78.301833 PDF: 00301833.pdf Google-Scholar: [36]
Abstract: Existing blind adaptive equalizers that use nonconvex cost functions and stochastic gradient descent suffer from lack of global convergence to an equalizer setup that removes sufficient ISI when an FIR equalizer is used. The authors impose convexity on the cost function and anchoring of the equalizer away from the all-zero setup. They establish that there exists a globally convergent blind equalization strategy for 1D pulse amplitude modulation (PAM) systems with bounded input data (discrete or continuous) even when the equalizer is truncated. The resulting cost function is a constrained l1 norm of the joint impulse response of the channel and the equalizer. The results apply to arbitrary linear channels (provided there are no unit circle zeros) and apply regardless of the initial ISI (that is whether the eye is initially open or closed). They also show a globally convergent stochastic gradient scheme based on an implementable approximation of the l1 cost function.
@article{KennedyJ1994d,
    title = {Convex cost functions in blind equalization},
    author = {Vembu, S. and Verdú, S. and Kennedy, R. A. and Sethares, W.},
    journal = {IEEE Trans. Signal Processing},
    volume = {42},
    pages = {1952-1960},
    month = {August},
    year = {1994}}
R. A. Kennedy, B. D. O. Anderson, and R. R. Bitmead, "Blind adaptation of decision feedback equalizers: Gross convergence properties", Int. J. of Adapt. Contr. and Signal Processing, vol. 7, no. 6, pp. 497-524, November 1993.
Abstract BibTeX
PDF: KennedyJ1993c.pdf Google-Scholar: [24]
Abstract: An analysis of the stochastic dynamics of the blind adaptation of decision feedback equalizers is presented. The analysis accounts for the presence of decision errors which, under feedback, are propagated. A number of blind algorithms are presented and a theory is developed to explain gross convergence properties observed through simulations. The possibility of and mechanism behind undesirable local minima are highlighted and a detailed case study is given. The potential capture by local minima shows the importance of good initialization. These results superficially resemble those obtained for blind adaptation applied to linear equalizers.for blind adaptation applied to linear equalizer.
@article{KennedyJ1993c,
    title = {Blind adaptation of decision feedback equalizers: {G}ross convergence properties},
    author = {Kennedy, R. A. and Anderson, B. D. O. and Bitmead, R. R.},
    journal = {Int. J. of Adapt. Contr. and Signal Processing},
    volume = {7},
    pages = {497-524},
    month = {November},
    year = {1993}}
S. Verdú, B. D. O. Anderson, and R. A. Kennedy, "Blind equalization without gain identification", IEEE Trans. Inform. Theory, vol. 39, no. 1, pp. 292-297, January 1993.
Abstract BibTeX
Official: Link DOI: 10.1109/18.179377 PDF: 00179377.pdf Google-Scholar: [25]
Abstract: Blind equalization up to a constant gain of linear time-invariant channels is studied. Dropping the requirement of gain identification allows equalizer anchoring. This results in the elimination of a degree of freedom that causes ill-convergence of conventional blind equalizers, and affords the possibility of using simple update rules based on the stochastic approximation of output energy. Unlike conventional blind equalizers, truncations of the nonrecursive infinite-dimensional realizations of those equalizers inherit the convergence properties of their infinitely parametrized counterparts. A globally convergent blind recursive equalizer for channels without all-pass sections is obtained based on the exact equalization of the minimum-phase part of the channel and the identification of its nonminimum-phase zeros.
@article{KennedyJ1993b,
    title = {Blind equalization without gain identification},
    author = {Verdú, S. and Anderson, B. D. O. and Kennedy, R. A.},
    journal = {IEEE Trans. Inform. Theory},
    volume = {39},
    pages = {292-297},
    month = {January},
    year = {1993}}
Z. Ding, R. A. Kennedy, B. D. O. Anderson, and C. R. Johnson Jr, "Local convergence of Sato blind algorithm and generalizations under practical constraints", IEEE Trans. Inform. Theory, vol. 39, no. 1, pp. 129-144, January 1993.
Abstract BibTeX
Official: Link DOI: 10.1109/18.179350 PDF: 00179350.pdf Google-Scholar: [23]
Abstract: An early use of recursive identification in blind adaptive channel equalization is an algorithm developed by Y. Sato (1975). An important generalization of the Sato algorithm with extensive analysis appears in the work of A. Benveniste et al. (1980). These generalized algorithms have been shown to possess a desirable global convergence property under two idealized conditions. The convergence properties of this class of blind algorithms under practical constraints common to a variety of channel equalization applications that violate these idealized conditions are studied. Results show that, in practice, when the equalizer is finite-dimensional and/or the input is discrete (as in digital communications) the equalizer parameters may converge to parameter settings that fail to achieve the objective of approximating the channel inverse. It is also shown that a center spike initialization is insufficient to guarantee avoiding such ill-convergence. Simulations verify the analytical results.
@article{KennedyJ1993a,
    title = {Local convergence of {Sato} blind algorithm and generalizations under practical constraints},
    author = {Ding, Z. and Kennedy, R. A. and Anderson, B. D. O. and Johnson Jr, C. R.},
    journal = {IEEE Trans. Inform. Theory},
    volume = {39},
    pages = {129-144},
    month = {January},
    year = {1993}}
Z. Ding, C. R. Johnson Jr, and R. A. Kennedy, "On the (non)-existence of undesirable equilibria of Godard blind equalizers", IEEE Trans. Signal Processing, vol. 40, no. 10, pp. 2425-2432, October 1992.
Abstract BibTeX
Official: Link DOI: 10.1109/78.157287 PDF: 00157287.pdf Google-Scholar: [50]
Abstract: Existing results in the literature have proved that particular blind equalization algorithms, including Godard algorithms, are globally convergent in an ideal and nonimplementable setting where a doubly infinite dimensional equalizer is available for adaptation. Contrary to popular conjectures, it is shown that implementable finite dimensional equalizers which attempt to approximate the ideal setting generally fail to have global convergence to acceptable equalizer parameter settings without the use of special remedial measures. A theory based on the channel convolution matrix nullspace is proposed to explain the failure of Godard algorithms for such practical blind equalization situations. This nullspace theory is supported by a simple example showing ill convergence of the Godard algorithm.
@article{KennedyJ1992e,
    title = {On the (non)-existence of undesirable equilibria of Godard blind equalizers},
    author = {Ding, Z. and Johnson Jr, C. R. and Kennedy, R. A.},
    journal = {IEEE Trans. Signal Processing},
    volume = {40},
    pages = {2425-2432},
    month = {October},
    year = {1992}}
R. A. Kennedy and Z. Ding, "Blind adaptive equalizers for quadrature amplitude modulated communication systems based on convex cost functions", Opt. Eng., vol. 31, no. 6, pp. 1189-1199, June 1992.
Abstract BibTeX
Official: Link DOI: 10.1117/12.57511 PDF: JOE001189.pdf Google-Scholar: [12]
Abstract: Blind adaptive channel equalizers are important devices to remove channel distortion in high data-rate, bandlimited digital communication systems when the transmission of a training sequence is impractical or very costly. Traditional blind equalization algorithms adapt the equalizer parameters to minimize some specially designed non-MSE cost functions. These algorithms can experience local convergence problems and can thereby result in insufficient or no removal of channel distortion. We present a new quadrature amplitude modulated blind equalization scheme that is globally convergent in the equalizer parameter space to a compact set containing the desired ideal equalizer parameter setting. Our new algorithm is based on a convex cost function and a linear constraint on the equalizer parameters. For a generic class of channels, this new algorithm results in the equalizer parameter convergence to a unique global minimum achieving intersymbol interference suppression and carrier phase error removal. Different implementation approaches are assessed and simulation results are shothe theoretical global convergence of the new algorithm.
@article{KennedyJ1992c,
    title = {Blind adaptive equalizers for quadrature amplitude modulated communication systems based on convex cost functions},
    author = {Kennedy, R. A. and Ding, Z.},
    journal = {Opt. Eng.},
    volume = {31},
    pages = {1189-1199},
    month = {June},
    year = {1992}}
Z. Ding and R. A. Kennedy, "On the whereabouts of local minima for blind adaptive equalizers", IEEE Trans. Circuits Syst., vol. 39, no. 2, pp. 119-123, February 1992.
Abstract BibTeX
Official: Link DOI: 10.1109/82.205817 PDF: 00205817.pdf Google-Scholar: [15]
Abstract: The lack of global convergence of existing blind equalization algorithms prompts the need for studying their mean cost functions and the whereabouts of local and global minima. The authors explore the location of minima for several general families of cost functions for blind equalization. It is shown that minima are unique along any radial direction in the equalizer parameter space. The authors characterize the resident manifold on which all minima and all saddle points of the cost function must reside. This information can be helpful in designing initialization strategies and parameter constraints to avoid convergence under adaptation to undesirable local minima.
@article{KennedyJ1992b,
    title = {On the whereabouts of local minima for blind adaptive equalizers},
    author = {Ding, Z. and Kennedy, R. A.},
    journal = {IEEE Trans. Circuits Syst.},
    volume = {39},
    pages = {119-123},
    month = {February},
    year = {1992}}
D. Williamson, R. A. Kennedy, and G. W. Pulford, "Block Decision Feedback Equalization", IEEE Trans. Commun., vol. 40, no. 2, pp. 255-264, February 1992.
Abstract BibTeX
Official: Link DOI: 10.1109/26.129188 PDF: 00129188.pdf Google-Scholar: [55]
Abstract: A natural generalization of the conventional decision feedback equalizer (DFE) based on block processing and maximum a posteriori decisions is presented. This block DFE is indexed by two parameters depending on the block length p and the number of decisions q⩽p made at each iteration. The block DFE emulates: the conventional DFE when p=q=1; the maximum likelihood sequence estimator when p=q?$\,^\circ$; and the maximum symbol-by-symbol a posteriori optimal detector when q=1, p?$\,^\circ$. For more general (p,q) parameter settings, one achieves combinations and simplifications of these classical nonlinear detectors. The authors also recover more recently developed nonlinear equalizer structures based on forward tree search algorithms in the high SNR limit (for q =1). They simulate the equalizer using a standard literature example. The theoretical framework presented accommodates autoregressive moving average (ARMA) channels models. Investigations into the error performance of the block DFE are briefly discussed.
@article{KennedyJ1992a,
    title = {Block Decision Feedback Equalization},
    author = {Williamson, D. and Kennedy, R. A. and Pulford, G. W.},
    journal = {IEEE Trans. Commun.},
    volume = {40},
    pages = {255-264},
    month = {February},
    year = {1992}}
Z. Ding, R. A. Kennedy, B. D. O. Anderson, and C. R. Johnson Jr, "Ill-Convergence of Godard blind equalizers in data communication systems", IEEE Trans. Commun., vol. 39, no. 9, pp. 1313-1327, September 1991.
Abstract BibTeX
Official: Link DOI: 10.1109/26.99137 PDF: 00099137.pdf Google-Scholar: [118]
Abstract: The existence of stable undesirable equilibria for the Godard algorithm is demonstrated through a simple autoregressive (AR) channel model. These undesirable equilibria correspond to local but nonglobal minima of the underlying mean cost function, and thus permit the ill-convergence of the Godard algorithms which are stochastic gradient descent in nature. Simulation results confirm predicted misbehavior. For channel input of constant modulus, it is shown that attaining the global minimum of the mean cost necessarily implies correct equalization. A criterion is also presented for allowing a decision at the equalizer as to whether a global or nonglobal minimum has been reached.
@article{KennedyJ1991a,
    title = {Ill-Convergence of {Godard} blind equalizers in data communication systems},
    author = {Ding, Z. and Kennedy, R. A. and Anderson, B. D. O. and Johnson Jr, C. R.},
    journal = {IEEE Trans. Commun.},
    volume = {39},
    pages = {1313-1327},
    month = {September},
    year = {1991}}
R. A. Kennedy, B. D. O. Anderson, and R. R. Bitmead, "Channels leading to rapid error recovery for decision feedback equalizers", IEEE Trans. Commun., vol. 37, no. 11, pp. 1146-1155, November 1989.
Abstract BibTeX
Official: Link DOI: 10.1109/26.46506 PDF: 00046506.pdf Google-Scholar: [16]
Abstract: When a decision feedback equalizer is used on a channel satisfying a simple passivity constraint (equivalently expressible in terms of gain-phase constraints) the error recovery time is finite, and thus recovery is rapid, regardless of the initial error state and the particular data sequence. This class of nontrivial channels includes cases of practical interest and identifies some channels for which a decision feedback equalizer is a practical option.
@article{KennedyJ1989c,
    title = {Channels leading to rapid error recovery for decision feedback equalizers},
    author = {Kennedy, R. A. and Anderson, B. D. O. and Bitmead, R. R.},
    journal = {IEEE Trans. Commun.},
    volume = {37},
    pages = {1146-1155},
    month = {November},
    year = {1989}}
R. A. Kennedy, B. D. O. Anderson, and R. R. Bitmead, "Tight Bounds on the Error Probabilities of Decision Feedback Equalizers", IEEE Trans. Commun., vol. 35, no. 10, pp. 1022-1029, October 1987.
Abstract BibTeX
Official: Link PDF: 01096679.pdf Google-Scholar: [25]
Abstract: A decision feedback equalizer (DFE) with correct tap weights operating on a noisy channel is considered. We show how the results concerning a noiseless channel can be extended to yield tight bounds on the stationary error probability performance for the noisy case. The effect of noise on DFE performance is classified according to the noise distribution and the channel parameters.
@article{KennedyJ1987d,
    title = {Tight Bounds on the Error Probabilities of Decision Feedback Equalizers},
    author = {Kennedy, R. A. and Anderson, B. D. O. and Bitmead, R. R.},
    journal = {IEEE Trans. Commun.},
    volume = {35},
    pages = {1022-1029},
    month = {October},
    year = {1987}}
R. A. Kennedy and B. D. O. Anderson, "Recovery Times of Decision Feedback Equalizers on Noiseless Channels", IEEE Trans. Commun., vol. 35, no. 10, pp. 1012-1021, October 1987.
Abstract BibTeX
Official: Link PDF: 01096682.pdf Google-Scholar: [34]
Abstract: The performance of decision feedback equalizers (DFE's) working on a noiseless channel with correct tap weights is studied. We show that the space of channel parameters can accordingly be partitioned into a finite number of sets. The error recovery performance of a DFE is the same for all DFE's within one such set, and is determinable. We also discuss some tight bounds for recovery time statistics, which are particularly important when the number of equalizer taps is not small. We argue that minimum phase or near minimum phase character for the channel does not necessarily guarantee short recovery time.
@article{KennedyJ1987c,
    title = {Recovery Times of Decision Feedback Equalizers on Noiseless Channels},
    author = {Kennedy, R. A. and Anderson, B. D. O.},
    journal = {IEEE Trans. Commun.},
    volume = {35},
    pages = {1012-1021},
    month = {October},
    year = {1987}}
T. D. Abhayapala, T. S. Pollock, and R. A. Kennedy, "Spatial Decomposition of MIMO Wireless Channels", Proc. Seventh International Symposium on Signal Processing and its Applications, ISSPA'03, vol. 1, pp. 309-312, July 2003.
Abstract BibTeX
Official: Link DOI: 10.1109/ISSPA.2003.1224702 PDF: 01224702.pdf Google-Scholar: [22]
Abstract: In this paper a novel decomposition of spatial channels is developed to provide insight into spatial aspects of multiple antenna communication systems. The underlying physics of the free space propagation is used to model the channel in scatterer free regions around the transmitter and the receiver, and the rest of the complex scattering media is represented by a parametric model. The channel matrix is separated into a product of known and random matrices where the known portion shows the effects of the physical configuration of antenna elements. We use the model to show the intrinsic degrees of freedom in a multiantenna system. Potential applications of the model are briefly discussed.
@inproceedings{KennedyC2003m,
    title = {Spatial Decomposition of {MIMO} Wireless Channels},
    author = {Abhayapala, T. D. and Pollock, T. S. and Kennedy, R. A.},
    booktitle = {Proc. Seventh International Symposium on Signal Processing and its Applications, ISSPA'03},
    volume = {1},
    pages = {309-312},
    month = {July},
    year = {2003}}
T. S. Pollock, T. D. Abhayapala, and R. A. Kennedy, "Antenna Saturation Effects on MIMO Capacity", Proc. International Conference on Communications, ICC'03, vol. 3, pp. 2301-2305, May 2003.
Abstract BibTeX
Official: Link DOI: 10.1109/ICC.2003.1204285 PDF: 01204285.pdf Google-Scholar: [12]
Abstract: A theoretically derived antenna saturation point is shown to exist for MIMO systems, at which the system suffers a capacity growth decrease from linear to logarithmic with increasing antenna numbers. We show this saturation point increases linearly with the radius of the region containing the receiver antennas and is independent of the number of antennas. Using an alternative formulation of capacity for MIMO systems we derive a closed form capacity expression, which uses the physics of signal propagation combined with statistics of the scattering environment. This expression gives the capacity of a MIMO system in terms of antenna placement and scattering environment and show that the saturation effect is due to spatial correlation between receiver antennas.
@inproceedings{KennedyC2003k,
    title = {Antenna Saturation Effects on {MIMO} Capacity},
    author = {Pollock, T. S. and Abhayapala, T. D. and Kennedy, R. A.},
    booktitle = {Proc. International Conference on Communications, ICC'03},
    volume = {3},
    pages = {2301-2305},
    month = {May},
    year = {2003}}
R. A. Kennedy and T. D. Abhayapala, "Spatial Concentration of Wave-Fields: Towards Spatial Information Content in Arbitrary Multipath Scattering", Proc. 4th Australian Communications Theory Workshop, pp. 38-45, February 2003.
Abstract BibTeX
PDF: KennedyC2003b.pdf Google-Scholar: [15]
Abstract: The fundamental limitation of using a spatial channel as an information bearing resource is considered. Such theoretical foundations are largely absent in the development of wireless communication systems which unduly focus on implementation and as a consequence there are a number of misconceptions and mal-implementations of communication systems which employ the MIMO principle. The notion of essential dimensionality of spatial systems is examined in detail for the case of a spherical region in three dimensional space in a nearfield scattering environment as a pointer to a more general theory nearing completion. A non-trivial but tight analogy is drawn with the classical work on time-frequency concentration and the dimensionality of essentially time- and band-limited signals by Slepian, Landau and Pollack. 
@inproceedings{KennedyC2003b,
    title = {Spatial Concentration of Wave-Fields: Towards Spatial Information Content in Arbitrary Multipath Scattering},
    author = {Kennedy, R. A. and Abhayapala, T. D.},
    booktitle = {Proc. 4th Australian Communications Theory Workshop},
    pages = {38-45},
    month = {February},
    year = {2003}}
T. S. Pollock, T. D. Abhayapala, and R. A. Kennedy, "Fundamental Limits of MIMO Capacity for Spatially Constrained Arrays", Proc. 4th Australian Communications Theory Workshop, pp. 7-12, February 2003.
Abstract BibTeX
PDF: KennedyC2003a.pdf Google-Scholar: [11]
Abstract: In this paper we investigate the capacity behavior of spatial constrained multiple-antenna array communications. By increasing the number of antennas within a fixed region of space the antenna array becomes dense and spatial correlation inhibits capacity growth. Using a novel spatial channel model we show that the underlying physics of wave propagation limits the capacity of constrained arrays. A theoretically derived antenna saturation point is shown to exist for dense array MIMO systems, at which there is no capacity growth with increasing antenna numbers. We show this saturation point increases linearly with the radius of the region, and that it naturally lends itself to a definition for the theoretical maximum capacity for a fixed region of space. 
@inproceedings{KennedyC2003a,
    title = {Fundamental Limits of {MIMO} Capacity for Spatially Constrained Arrays},
    author = {Pollock, T. S. and Abhayapala, T. D. and Kennedy, R. A.},
    booktitle = {Proc. 4th Australian Communications Theory Workshop},
    pages = {7-12},
    month = {February},
    year = {2003}}
H. M. Jones, R. A. Kennedy, and T. D. Abhayapala, "On Dimensionality of Multipath Fields: Spatial Extent and Richness", Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, ICASSP'2002, vol. III, pp. 2837-2840, May 2002.
Abstract BibTeX
Official: Link DOI: 10.1109/ICASSP.2002.1005277 PDF: 01005277.pdf Google-Scholar: [47]
Abstract: We establish that an arbitrary narrowband multipath field in any circular region in two dimensional space has an intrinsic functional dimensionality of (/spl pi/e)R//spl lambda/, /spl ap/8.54R//spl lambda/, that scales only linearly with radius R/spl bsol//spl lambda/ in wavelengths. This result implies that there is no such thing as an arbitrarily complicated multipath field. That is, a field generated by any number of nearfield and farfield, specular and diffuse, multipath reflections is no more complicated than a field generated by a limited number of plane waves. As such, there are limits on how rich multipath can be. This result has significant implications including: i) means to determine a parsimonious parameterization for arbitrary multipath fields; ii) means of synthesizing arbitrary multipath fields with arbitrarily located nearfield or farfield, spatially discrete or continuous sources. We give examples of multipath field analysis and synthesis.
@inproceedings{KennedyC2002g,
    title = {On Dimensionality of Multipath Fields: Spatial Extent and Richness},
    author = {Jones, H. M. and Kennedy, R. A. and Abhayapala, T. D.},
    booktitle = {Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, ICASSP'2002},
    volume = {III},
    pages = {2837-2840},
    month = {May},
    year = {2002}}
R. A. Kennedy, T. D. Abhayapala, D. B. Ward, and R. C. Williamson, "Nearfield Broadband Frequency Invariant Beamforming", Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, ICASSP'96, vol. 2, pp. 909-912, May 1996.
Abstract BibTeX
Official: Link DOI: 10.1109/ICASSP.1996.543268 PDF: 00543268.pdf Google-Scholar: [12]
Abstract: This paper presents a method for nearfield frequency invariant broadband array beamforming. This means that we can design an array with associated signal processing to achieve a desired frequency invariant beam pattern (as a function of direction) at any nominal finite distance over an arbitrarily wide range of frequencies. The challenge here is to compensate accurately for the nearfield distortions (both magnitude and phase) which are more acute at the lower frequencies of the operating bandwidth than the higher frequencies. The methodology uses spherical harmonics to transform the nearfield broadband frequency invariant beampattern specification to an equivalent farfield frequency varying beampattern specification. A simulation example is presented to demonstrate the effectiveness of this method in producing a nearfield beam pattern which is frequency invariant over an octave bandwidth.
@inproceedings{KennedyC1996a,
    title = {Nearfield Broadband Frequency Invariant Beamforming},
    author = {Kennedy, R. A. and Abhayapala, T. D. and Ward, D. B. and Williamson, R. C.},
    booktitle = {Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, ICASSP'96},
    volume = {2},
    pages = {909-912},
    month = {May},
    year = {1996}}
R. A. Kennedy and R. J. Evans, "Digital redesign of a continuous controller based on closed loop performance", Proc. IEEE Conf. Decision and Contr., CDC'90, pp. 1898-1901, December 1990.
Abstract BibTeX
Official: Link DOI: 10.1109/CDC.1990.203950 PDF: 00203950.pdf Google-Scholar: [19]
Abstract: The authors present a digital controller redesign philosophy which attempts to match the closed-loop performance of a nominal continuous-time controller using a model-following design setting. The requirement of excessive sampling rates necessary with a number of popular existing techniques (e.g. the prewarped bilinear transform redesign) is largely obviated. Sampling rates close to twice the closed-loop bandwidth (Nyquist rate) give good performance with the proposed technique. It is concluded that the proposed model can be used as is for an analog-to-digital redesign which appears to work favorably at low sampling rates, or it can be used as a starting point for further pole-zero placement.
@inproceedings{KennedyC1990m,
    title = {Digital redesign of a continuous controller based on closed loop performance},
    author = {Kennedy, R. A. and Evans, R. J.},
    booktitle = {Proc. IEEE Conf. Decision and Contr., CDC'90},
    pages = {1898-1901},
    month = {December},
    year = {1990}}
D. B. Ward, R. A. Kennedy, and R. C. Williamson, "Constant Directivity Beamforming", Microphone Arrays, pp. 3-17, 2001.
Abstract BibTeX
PDF: KennedyBC2001c.pdf Google-Scholar: [14]
Abstract: Beamforming, or spatial filtering, is one of the simplest methods for discriminating between different signals based on the physical location of the sources. Because speech is a very wideband signal, covering some four octaves, traditional narrowband beamforming techniques are inappropriate for hands-free speech acquisition. One class of broadband beamformers, called constant directivity beamformers, aim to produce a constant spatial response over a broad frequency range. In this chapter we review such beamformers, and discuss implementation issues related to their use in microphone arrays.
@inproceedings{KennedyBC2001c,
    title = {Constant Directivity Beamforming},
    author = {Ward, D. B. and Kennedy, R. A. and Williamson, R. C.},
    booktitle = {Microphone Arrays},
    pages = {3-17},
    year = {2001}}
Z. Ding, C. R. Johnson Jr, and R. A. Kennedy, "Global Convergence Issues with Linear Blind Adaptive Equalizers", Blind Deconvolution, pp. 60-120, 1994.
Abstract BibTeX
Google-Scholar: [12] 
@inproceedings{KennedyBC1994a,
    title = {Global Convergence Issues with Linear Blind Adaptive Equalizers},
    author = {Ding, Z. and Johnson Jr, C. R. and Kennedy, R. A.},
    booktitle = {Blind Deconvolution},
    pages = {60-120},
    year = {1994}}