New results on the evaluation of equalizers performance (original) (raw)

Optimal delay estimation and performance evaluation in blind equalization

International Journal of Adaptive Control and Signal Processing, 1997

This paper deals with the problem of recovering the input signal applied to a linear time-invariant system from the measurements of its output and the a priori knowledge of the input statistics (blind equalization). Under the assumption of an i.i.d. non-Gaussian input sequence a new iterative procedure based on phase-sensitive high-order cumulants for adjusting the coefficients of a transversal equalizer is introduced. The main feature of the proposed technique is the automatic selection of the equalization delay so as to improve the equalization performance. A method for the a posteriori evaluation of the obtained accuracy in PAM systems is also introduced. It consists of the computation of an upper bound on the probability of error depending on certain moments of the equalizer output and the statistics of the channel input and therefore can be used in a blind equalization context. Based on the result of such a computation, it can be decided whether it is necessary to consider a longer equalization filter in the iterative procedure. 1997 by John Wiley & Sons, Ltd.

Convergence analysis of finite length blind adaptive equalizers

IEEE Transactions on Signal Processing, 1995

Abstracf-l'his paper presents some new analytical results on the convergence of two finite length blind adaptive channel equalizers, namely, the Godard equalizer and the Shalvi-Weinstein equalizer. First, a one-to-one correspondence in I d " a is shown to exist between Godard and Shalvi-Weinstein equalizers, hence establishing the equivalent relationship between the two algorithms. Convergence behaviors of finite length Godard and Shalvi-Weinstein equalizers are analyzed, and the potential stable equilibrium points are identified. The existence of undesirable stable equilibria for the finite length Shalvi-Weinstein equalizer is demonstrated through a simple example. It is proven that the points of convergence for both finite length equalizers depend on an initial kurtosis condition. It is also proven that when the length of equalizer is long enough and the initial equalizer setting satisfies the kurtosis condition, the equalizer will converge to a stable equilibrium near a desired global minimum. When the kurtosis condition is not satisfied, generally the equalizer will take longer to converge to a desired equilibrium given sufliciently many parameters and adequate initialization. The convergence analysis of the equalizers in PAM communication system can be easily extended to the equalizers in QAM communication systems.

New criteria for blind equalization based on PDF fitting

2014 IEEE 15th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2014

In this paper, we address M-QAM blind equalization based on information theoretic criteria. We propose two new cost functions that force the probability density functions (pdf) at the equalizer output to match the known constellation pdf. They involve kernel pdf approximation. The kernel bandwidth of a Parzen estimator is updated during iterations to improve the convergence speed and to decrease the residual error of the algorithms. Unlike related existing techniques, the new algorithms measure the distance error between observed and assumed pdfs for the real and imaginary parts of the equalizer output separately. We show performance and complexity gain against the CMA, the most popular blind equalization technique, and classical pdf fitting approaches.

A combination of statistical and structural approaches in blind equalization algorithms

Conference Record of the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers (Cat. No.00CH37154), 2000

This paper presents two ways of obtaining more robust a d o r eflcient blind equalization algorithms. The first one is based on the linear combination of Second Order Statistics Methods (SOS) and Higher Order Statistics methods (HOS) in such way that the advantages of both approaches are kept. The new algorithm has better performances than each of its constituents taken separately [pure HOS or SOS method) rather than peflormances "in between". The second idea consists in taking into account some deterministic knowledge of the input signal in the SOS methods. Results obtained show that this technique also enhances the perfamnee of the algorithm.

An efficient blind decision feedback equalizer

IEEE Communications Letters, 2000

Efficient and fully blind Decision Feedback Equalizer (DFE) remains an open issue, mainly because of the potential errors in the decision loop. Based on the Weighted Decision Feedback Equalizer (WDFE), our previous work aiming at decreasing the error propagation phenomena, we propose a new blind DFE called Blind Weighted

Blind equalisation in the presence of bounded noise

IET Signal Processing, 2018

This study addresses the blind equalisation problem in the presence of bounded noise using an optimal bounding ellipsoid algorithm. This provides an adequate blind equalisation algorithm with an accurate parameter estimation. A fundamental analysis of the involved equaliser is performed to emphasise its underlying properties. This fundamental result is corroborated by promising simulation results.

Blind equalization based on pdf distance criteria and performance analysis

In this report, we address M-QAM blind equalization by fitting the probability density functions (pdf) of the equalizer output with the constellation symbols. We propose two new cost functions, based on kernel pdf approximation, which force the pdf at the equalizer output to match the known constellation pdf. The kernel bandwidth of a Parzen estimator is updated during iterations to improve the convergence speed and to decrease the residual error of the algorithms. Unlike related existing techniques, the new algorithms measure the distance error between observed and assumed pdfs for the real and imaginary parts of the equalizer output separately. The advantage of proceeding this way is that the distributions show less modes, which facilitates equalizer convergence, while as for multi-modulus methods phase recovery keeps being preserved. The proposed approaches outperform CMA and classical pdf fitting methods in terms of convergence speed and residual error. We also analyse the convergence properties of the most efficient proposed equalizer via the ordinary differential equation (ODE) method.

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

IEEE Transactions on Signal Processing, 1996

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.