Blind adaptation of decision feedback equalizers: Gross convergence properties

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.

Maximum-likelihood sequence estimation in dispersive optical channels

“…Convergence in decision-directed mode is not guaranteed, but in practice it is found to be very robust. Conditions for convergence of decision-directed training of various equalizer structures have been studied in [17] and references thereof. It is also possible, although less convenient, to train the channel estimator using a special training sequence known by the receiver and sent by the transmitter during startup [18] or using blind equalization techniques [19].…”

“…The integral is hard to compute, but an approximation can easily be found using the method of steepest descent as follows. Define (17) Let be the vector in that minimizes . Then, we can define the "distance" between sequences and as (18) When the noise is Gaussian and signal independent, is the traditional Euclidean distance between sequences and .…”

On The Convergence of Blind DD-LMS Decision-Feedback Equalizers Using a Joint Equalization & Decoding Procedure

“…Analysis of convergence properties of the DD-DFE can be found in [1], [4], [6] and [7]. References [1] and [6] provide a class of channels that results in ill convergence when the feedback filter coefficients are initialized with zeros.…”

“…Therefore we can restrict our analysis to the feedback (FB) filter and to local minima associated with error propagation. Nevertheless the assumption is justified since a full theoretical analysis was developed in [4], where both FF and FB filters were considered,. However, this work did not take into account the impact of error correcting codes in the joint adaptation, which is the interest point of our work.…”

Analysis and performance of CMA blind deconvolution for image restoration

“…Vural et al have further developed their research on image processing with CMA in [10][11][12], where it was advanced into recursive deconvolution, resolution enhancement and an extensive analysis on the convergence of image deconvolution via dispersion minimization. 1136 P. D. SAMARASINGHE AND R. A. KENNEDY While algorithms from the Godard class have achieved considerable success in channel equalization, they have the potential to converge to undesirable equilibria, and this has been studied by many researchers [13][14][15][16][17]. Some cases of the ill-convergence of CMA in channel equalization can be attributed to noise in the channel and the violation of the assumptions made on the source signal, namely, the source is assumed to be zero mean, white, uniformly distributed and constant-modulus (CM) (circularly symmetric when complex) [18,19].…”