Analysis of Blind Decision Feedback Equalizer Convergence: Interest of a Soft Decision
In this paper the behavior of the decision feedback
equalizers (DFEs) adapted by the decision-directed or the constant
modulus blind algorithms is presented. An analysis of the error
surface of the corresponding criterion cost functions is first
developed. With the intention of avoiding the ill-convergence of the
algorithm, the paper proposes to modify the shape of the cost
function error surface by using a soft decision instead of the hard
one. This was shown to reduce the influence of false decisions and to
smooth the undesirable minima. Modified algorithms using the soft
decision during a pseudo-training phase with an automatic switch to
the properly tracking phase are then derived. Computer simulations
show that these modified algorithms present better ability to avoid
local minima than conventional ones.
[1] Z. Ding, Y. Li, and K. D. Ding, "Blind Equalization and
Identification.,-- Marcel Dekker, 2001.
[2] K. Pahlavan and A. Levesque, "Wireless Information Networks,-- John
Wiley & Sons, 1995.
[3] A. Benveniste, M. Goursat, and G. Ruget, "Robust identification of a
nonminimum phase system : Blind adjustment of a linear equalizer in
data communications," IEEE Transactions on Automatic Control, vol.
25, no. 3, pp. 385-398, June 1980.
[4] O. Macchi and E. Eweda, "Convergence analysis of self-adaptive
equalizers," IEEE Transactions on Information Theory, vol. 30, no. 3,
pp. 161-176, Mar. 1984.
[5] O. Macchi and A. Hachicha, "Self-adaptive equalization based on a
prediction principle," in IEEE Global Telecommunication Conference,
Dec. 1986, pp. 1641-1645.
[6] E. Bai and Z. Ding, "Blind decision feedback equalization of
timevarying channels with DPSK inputs," IEEE Transactions on Signal
Processing, vol. 49, no. 7, pp. 1533-1542, July 2001.
[7] A. Rontogiannis and K. Berberidis, "Efficient decision feedback
equalization for sparse wireless channels," Efficient Decision Feedback
Equalization for Sparse Wireless Channels, vol. 2, no. 3, pp. 570-581,
May 2003.
[8] Y. Li and Z. Ding, "Global convergence of fractionally spaced godard
adaptive equalizers," 28th Asilomar COnference on Signals, Systems and
Computers, pp. 617-621, Nov. 1994.
[9] I. Fijalkow, C. E. Manlove, and J. C. R. Johnson, "Adaptive fractionally
spaced blind cma equalization: Excess mse," IEEE Transactions on
Signal Processing, vol. 46, no. 1, pp. 227-231, Jan. 1998.
[10] Z. Ding, R. Kennedy, B. Anderson, and C. Johnson, "Local convergence
of the sato blind equalizer and generalizations under practical
constraints," IEEE Transactions on Information Theory, vol. 39, no. 1,
pp. 129-144, Jan. 1993.
[11] R. Kennedy, B. Anderson, and R. Bitmead, "Blind adaptation of decision
feedback equalizers : Gross convergence properties," International
Journal of Adaptive Control and Signal Processing, vol. 7, pp. 497-523,
1993.
[12] D. Godard, "Self-recovering equalization and carrier tracking in
twodimensional data communication systems," IEEE Transactions on
Communications, vol. 28, no. 11, pp. 1867-1875, Nov. 1980.
[13] R. Kennedy and B. Anderson, "Recovery times of decision feedback
equalizers on noiseless channels," IEEE Transactions on
Communications, vol. 35, no. 10, pp. 1012-1021, Oct. 1987.
[14] P. Feintuch, "An adaptive recursive LMS filter," Proc. IEEE, pp. 1622-
1624, 1976.
[15] J. Proakis, "Digital Communications,-- McGraw-Hill, 2000.
[1] Z. Ding, Y. Li, and K. D. Ding, "Blind Equalization and
Identification.,-- Marcel Dekker, 2001.
[2] K. Pahlavan and A. Levesque, "Wireless Information Networks,-- John
Wiley & Sons, 1995.
[3] A. Benveniste, M. Goursat, and G. Ruget, "Robust identification of a
nonminimum phase system : Blind adjustment of a linear equalizer in
data communications," IEEE Transactions on Automatic Control, vol.
25, no. 3, pp. 385-398, June 1980.
[4] O. Macchi and E. Eweda, "Convergence analysis of self-adaptive
equalizers," IEEE Transactions on Information Theory, vol. 30, no. 3,
pp. 161-176, Mar. 1984.
[5] O. Macchi and A. Hachicha, "Self-adaptive equalization based on a
prediction principle," in IEEE Global Telecommunication Conference,
Dec. 1986, pp. 1641-1645.
[6] E. Bai and Z. Ding, "Blind decision feedback equalization of
timevarying channels with DPSK inputs," IEEE Transactions on Signal
Processing, vol. 49, no. 7, pp. 1533-1542, July 2001.
[7] A. Rontogiannis and K. Berberidis, "Efficient decision feedback
equalization for sparse wireless channels," Efficient Decision Feedback
Equalization for Sparse Wireless Channels, vol. 2, no. 3, pp. 570-581,
May 2003.
[8] Y. Li and Z. Ding, "Global convergence of fractionally spaced godard
adaptive equalizers," 28th Asilomar COnference on Signals, Systems and
Computers, pp. 617-621, Nov. 1994.
[9] I. Fijalkow, C. E. Manlove, and J. C. R. Johnson, "Adaptive fractionally
spaced blind cma equalization: Excess mse," IEEE Transactions on
Signal Processing, vol. 46, no. 1, pp. 227-231, Jan. 1998.
[10] Z. Ding, R. Kennedy, B. Anderson, and C. Johnson, "Local convergence
of the sato blind equalizer and generalizations under practical
constraints," IEEE Transactions on Information Theory, vol. 39, no. 1,
pp. 129-144, Jan. 1993.
[11] R. Kennedy, B. Anderson, and R. Bitmead, "Blind adaptation of decision
feedback equalizers : Gross convergence properties," International
Journal of Adaptive Control and Signal Processing, vol. 7, pp. 497-523,
1993.
[12] D. Godard, "Self-recovering equalization and carrier tracking in
twodimensional data communication systems," IEEE Transactions on
Communications, vol. 28, no. 11, pp. 1867-1875, Nov. 1980.
[13] R. Kennedy and B. Anderson, "Recovery times of decision feedback
equalizers on noiseless channels," IEEE Transactions on
Communications, vol. 35, no. 10, pp. 1012-1021, Oct. 1987.
[14] P. Feintuch, "An adaptive recursive LMS filter," Proc. IEEE, pp. 1622-
1624, 1976.
[15] J. Proakis, "Digital Communications,-- McGraw-Hill, 2000.
@article{"International Journal of Electrical, Electronic and Communication Sciences:60276", author = "S. Cherif and S. Marcos and M. Jaidane", title = "Analysis of Blind Decision Feedback Equalizer Convergence: Interest of a Soft Decision", abstract = "In this paper the behavior of the decision feedback
equalizers (DFEs) adapted by the decision-directed or the constant
modulus blind algorithms is presented. An analysis of the error
surface of the corresponding criterion cost functions is first
developed. With the intention of avoiding the ill-convergence of the
algorithm, the paper proposes to modify the shape of the cost
function error surface by using a soft decision instead of the hard
one. This was shown to reduce the influence of false decisions and to
smooth the undesirable minima. Modified algorithms using the soft
decision during a pseudo-training phase with an automatic switch to
the properly tracking phase are then derived. Computer simulations
show that these modified algorithms present better ability to avoid
local minima than conventional ones.", keywords = "Blind DFEs, decision-directed algorithm, constant
modulus algorithm, cost function analysis, convergence analysis, soft
decision.", volume = "2", number = "11", pages = "2618-7", }