{"references": ["Z. Ding, Y. Li, and K. D. Ding, \"Blind Equalization and\nIdentification.,-- Marcel Dekker, 2001.", "K. Pahlavan and A. Levesque, \"Wireless Information Networks,-- John\nWiley & Sons, 1995.", "A. Benveniste, M. Goursat, and G. Ruget, \"Robust identification of a\nnonminimum phase system : Blind adjustment of a linear equalizer in\ndata communications,\" IEEE Transactions on Automatic Control, vol.\n25, no. 3, pp. 385-398, June 1980.", "O. Macchi and E. Eweda, \"Convergence analysis of self-adaptive\nequalizers,\" IEEE Transactions on Information Theory, vol. 30, no. 3,\npp. 161-176, Mar. 1984.", "O. Macchi and A. Hachicha, \"Self-adaptive equalization based on a\nprediction principle,\" in IEEE Global Telecommunication Conference,\nDec. 1986, pp. 1641-1645.", "E. Bai and Z. Ding, \"Blind decision feedback equalization of\ntimevarying channels with DPSK inputs,\" IEEE Transactions on Signal\nProcessing, vol. 49, no. 7, pp. 1533-1542, July 2001.", "A. Rontogiannis and K. Berberidis, \"Efficient decision feedback\nequalization for sparse wireless channels,\" Efficient Decision Feedback\nEqualization for Sparse Wireless Channels, vol. 2, no. 3, pp. 570-581,\nMay 2003.", "Y. Li and Z. Ding, \"Global convergence of fractionally spaced godard\nadaptive equalizers,\" 28th Asilomar COnference on Signals, Systems and\nComputers, pp. 617-621, Nov. 1994.", "I. Fijalkow, C. E. Manlove, and J. C. R. Johnson, \"Adaptive fractionally\nspaced blind cma equalization: Excess mse,\" IEEE Transactions on\nSignal Processing, vol. 46, no. 1, pp. 227-231, Jan. 1998.\n[10] Z. Ding, R. Kennedy, B. Anderson, and C. Johnson, \"Local convergence\nof the sato blind equalizer and generalizations under practical\nconstraints,\" IEEE Transactions on Information Theory, vol. 39, no. 1,\npp. 129-144, Jan. 1993.\n[11] R. Kennedy, B. Anderson, and R. Bitmead, \"Blind adaptation of decision\nfeedback equalizers : Gross convergence properties,\" International\nJournal of Adaptive Control and Signal Processing, vol. 7, pp. 497-523,\n1993.\n[12] D. Godard, \"Self-recovering equalization and carrier tracking in\ntwodimensional data communication systems,\" IEEE Transactions on\nCommunications, vol. 28, no. 11, pp. 1867-1875, Nov. 1980.\n[13] R. Kennedy and B. Anderson, \"Recovery times of decision feedback\nequalizers on noiseless channels,\" IEEE Transactions on\nCommunications, vol. 35, no. 10, pp. 1012-1021, Oct. 1987.\n[14] P. Feintuch, \"An adaptive recursive LMS filter,\" Proc. IEEE, pp. 1622-\n1624, 1976.\n[15] J. Proakis, \"Digital Communications,-- McGraw-Hill, 2000."]}

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.