blind research

Papers dealing with blind equalization and related areas.

Keywords: blind equalization, CMA, Sato Algorithm, ill-convergence, Godard

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: [129]
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}}
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: [49]
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}}
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: [39]
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}}
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: [31]
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: [22]
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}}
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}}
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: [13]
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}}
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: [10]
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}}
R. A. Kennedy, G. W. Pulford, B. D. O. Anderson, and R. R. Bitmead, "When has a Decision Directed Equalizer Converged?", IEEE Trans. Commun., vol. 37, no. 8, pp. 879-884, August 1989.
Abstract BibTeX
Official: Link DOI: 10.1109/26.31188 PDF: 00031188.pdf Google-Scholar: [9]
Abstract: Adaptive decision-directed equalizers can become locked for long periods onto incorrect equilibria. A test involving data available at the equalizer output is proposed for determining whether an equilibrium is correct or not, up to a fixed overall delay. If an independent sequence of random variables taking values $\pm$1 is the input to a finite impulse response filter, and the output of the filter is passed through a slicer, then the slicer output is uncorrelated if and only if it is a delayed version of the filter input. An analogous result for M-ary rather than binary data is outlined.
@article{KennedyJ1989b,
    title = {When has a Decision Directed Equalizer Converged?},
    author = {Kennedy, R. A. and Pulford, G. W. and Anderson, B. D. O. and Bitmead, R. R.},
    journal = {IEEE Trans. Commun.},
    volume = {37},
    pages = {879-884},
    month = {August},
    year = {1989}}