Length- and cost-dependent local minima of unconstrained blindchannel equalizers
Ye Li; Liu, K.J.R.; Zhi Ding
Signal Processing, IEEE Transactions on
Volume 44, Issue 11, Nov 1996 Page(s):2726 - 2735
Digital Object Identifier 10.1109/78.542179
Summary:Baud-rate linear blind equalizers may converge to undesirable
stable equilibria due to different mechanisms. One such mechanism is the
use of linear FIR filters as equalizers. It is shown that this type of
local minima exist for all unconstrained blind equalizers whose cost
functions satisfy two general conditions. The local minima generated by
this mechanism are thus called length-dependent local minima. Another
mechanism is generated by the cost function adopted by the blind
algorithm itself. This type of local minima are called cost-dependent
local minima. It is shown that several well-designed algorithms do not
have cost-dependent local minimum, whereas other algorithms, such as the
decision-directed equalizer and the stop-and-go algorithm (SGA), do.
Unlike many existing convergence analysis, the convergence of the Godard
(1980) algorithms (GAs) and standard cumulant algorithms (SCAs) under
Gaussian noise is also presented. Computer simulations are used to
verify the analytical results
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