Support vector machine techniques for nonlinear equalization

Abstract

The emerging machine learning technique called support vector machines is proposed as a method for performing nonlinear equalization in communication systems. The support vector machine has the advantage that a smaller number of parameters for the model can be identified in a manner that does not require the extent of prior information or heuristic assumptions that some previous techniques require. Furthermore, the optimization method of a support vector machine is quadratic programming, which is a well-studied and understood mathematical programming technique. Support vector machine simulations are carried out on nonlinear problems previously studied by other researchers using neural networks. This allows initial comparison against other techniques to determine the feasibility of using the proposed method for nonlinear detection. Results show that support vector machines perform as well as neural networks on the nonlinear problems investigated. A method is then proposed to introduce decision feedback processing to support vector machines to address the fact that intersymbol interference (ISI) data generates input vectors having temporal correlation, whereas a standard support vector machine assumes independent input vectors. Presenting the problem from the viewpoint of the pattern space illustrates the utility of a bank of support vector machines. This approach yields a nonlinear processing method that is somewhat different than the nonlinear decision feedback method whereby the linear feedback filter of the decision feedback equalizer is replaced by a Volterra filter. A simulation using a linear system shows that the proposed method performs equally to a conventional decision feedback equalizer for this problem.

Adaptive minimum error-rate filtering design: A review

“…Otherwise, nonlinear filtering is required in order to achieve an adequate performance. Examples of such nonlinear filtering include nonlinear single-user channel equalisation [89][90][91][92][93][94][95][96][97][98][99][100][101], nonlinear CDMA multiuser detection [102], nonlinear beamforming assisted detection [103][104][105][106], and nonlinear space-time equalisation [107]. Let us consider the generic nonlinear filter of the form y R ðkÞ ¼ f ðxðkÞ; wÞ,…”

Support vector machines for robust channel estimation in OFDM

“…In [8], the -Huber cost function is used, given by (4) where , is the insensitive parameter, and and control the trade-off between the regularization and the losses. Three different regions allow to deal with different kinds of noise: -insensitive zone ignores errors lower than ; quadratic cost zone uses the -norm of errors, which is appropriate for Gaussian noise; and linear cost zone limits the effect of subGaussian noise.…”

“…For simplicity, a linear dispersive channel with non-Gaussian noise is analyzed here. The extension of the proposed linear OFDM-SVM scheme to nonlinear scenarios can be easily introduced by using Mercer's kernels in a similar way as proposed for other communication schemes [4].…”

“…The decision feedback equalizer [3], [4] and adaptive multiuser detector for direct sequence code division multiple access (CDMA) signals in multipath channels [5] are addressed by means of binary SVM nonlinear classifiers. In [6], signal equalization and detection for a multicarrier (MC)-CDMA system are based on an SVM linear classification algorithm.…”

A Granular Classifier By Means of Context-based Similarity Clustering

“…Especially, one can extend SVM to obtain nonlinear decision hyperplanes by exploiting kernelization techniques [9][10][11][12]. Pioneering studies by Xue et al [13], Sebald et al [14], Alam et al [15], and Morsier et al [16] led to different improved SVM models. By now, the research has focused on the efficient of linear or nonlinear classification.…”