Convergence analysis of self-adaptive equalizers

Macchi, Odile; Eweda, E.

doi:10.1109/tit.1984.1056896

Cited by 163 publications

(58 citation statements)

References 13 publications

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“…A particular problem of the CMA, however, is that it only achieves a moderate level of mean square error (MSE) after convergence, which may not be sufficiently low for the system to obtain adequate performance. A possible solution is to switch to a decision directed (DD) adaptation which should be able to minimize the residual CMA steady state MSE [5]. However, as pointed out in [6], in order for such a transfer to be successful, the CMA steady state MSE should be sufficiently low.…”

Section: Introductionmentioning

confidence: 99%

Concurrent constant modulus algorithm and soft decision directed scheme for fractionally-spaced blind equalization

Chen

Chng

2004

2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577)

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The paper proposes a concurrent constant modulus algorithm (CMA) and soft decision-directed (SDD) scheme for lowcomplexity blind equalization of high-order quadrature amplitude modulation channels. Simulation using a fractionally-spaced equalization setting is used to compare the proposed scheme with the recently introduced state-of-art concurrent CMA and decisiondirected (DD) scheme. The proposed CMA+SDD blind equalizer is shown to have simpler computational complexity per weight update, faster convergence speed, and slightly improved steady-state equalization performance, compared with the CMA+DD blind equalizer.

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Section: Introductionmentioning

confidence: 99%

Concurrent constant modulus algorithm and soft decision directed scheme for fractionally-spaced blind equalization

Chen

Chng

2004

2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577)

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“…The local convergence of the DDE implemented with an FIR filter is demonstrated in [ l l ] , [14], and [15], which reveals the length-dependent local convergence of DDE. In this section, we will illustrate the cost-dependent local converg,ence of the DDE and the SGA by specifying their cost functions in some operating regions.…”

Section: Cost-dependent Local Minima Of Dde and Sgamentioning

confidence: 99%

“…It has been proved in [SI that both length and costdependent local minima exist for SA and the BCRA [SI. The local convergence of the decision directed equalizer (DDE) and the stop-and-go algorithm (SGA) [17] has been analyzed in [11], [14], and [IS]. Since the DDE and SGA are identical to the SA for channels with binary inputs, their cost-dependent local convergence is also given by [ 5 ] .…”

Section: Introductionmentioning

confidence: 99%

“…For equalizer filters without constraints, convergence analyzes of [3]- [5], [12], [14], and [I51 have shown LDLM to exist for many known algorithms such as BGRA, SA, GA, SWA, SGA, and DDE. Therefore, a natural question is whether or not it is possible to design good cost functions so that LDLM do not exist even for the common unconstrained FIR equalizer filters.…”

Section: Introductionmentioning

confidence: 99%

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Length- and cost-dependent local minima of unconstrained blind channel equalizers

Liu

Ding

1996

IEEE Trans. Signal Process.

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Abstract-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. In this paper, 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 shall be shown that several welldesigned 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 algorithms (GA's) and standard cumulant algorithms @CA's) under Gaussian noise is also presented here. Computer simulations are used to verify the analytical results.

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“…The auto-regressive part is introduced to beas general as possible without increasing the complexity. We will assume that the parameter variation can be modeled as a random walk so a total state space linear regression model is t+1 = t + v t y t = ' T t t + e t : (18) Here, ' t = (;y t;1 ;y t;n d a t a t;n b +1 ) T (19) …”

Section: Optimal Estimatesmentioning

confidence: 99%

Blind equalization by direct examination of the input sequences

Gustafsson

Wahlberg

1995

IEEE Trans. Commun.

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This paper presents a novel approach to blind equalization (deconvolution), which is based on direct examination of possible input sequences. In contrast to many other approaches, it does not rely on a model of the approximative inverse of the channel dynamics. To start with, the blind equalization identi ability problem for a noisefree nite impulse response channel model is investigated. A necessary condition for the input, which is algorithm independent, for blind deconvolution is derived. This condition is expressed in an information measure of the input sequence. A su cient condition for identi ability is also inferred, which imposes a constraint on the true channel dynamics. The analysis motivates a recursive algorithm where all permissible input sequences are examined. The exact solution is guaranteed to b e f o u n d a s s o o n as it is possible. An upper bound on the computional complexity of the algorithm is given. This algorithm is then generalized to cope with time-varying in nite impulse response channel models with additive noise. The estimated sequence is an arbitrary good approximation of the maximum a posteriori estimate. The proposed method is evaluated on a Rayleigh fading communication channel. The simulation results indicate fast convergence properties and good tracking abilities.

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Convergence analysis of self-adaptive equalizers

Cited by 163 publications

References 13 publications

Concurrent constant modulus algorithm and soft decision directed scheme for fractionally-spaced blind equalization

Concurrent constant modulus algorithm and soft decision directed scheme for fractionally-spaced blind equalization

Length- and cost-dependent local minima of unconstrained blind channel equalizers

Blind equalization by direct examination of the input sequences

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