Applications of Kernel Methods

Kernel Methods In Communications

There are four situations that make kernel methods good candidates for use in electromagnetics (Martínez-Ramon, 2006): 1) No close solutions exist, and the only approaches are trial and error methods. In these cases, kernel algorithms can be employed to solve the problem. 2) The application requires operating in real time, and the computation time is limited. In these cases, a kernel algorithm can be trained off-line, and used in test mode in real time. The algorithms can be embedded in any hardware device. 3) Faster convergence rates and smaller errors are required. Kernel algorithms have shown superior performance in generalization ability in many problems. Also, the block optimization and the uniqueness of solutions make kernelized versions of linear algorithms (as SVM) faster than many other methods. 4) Enough measured data exist to train a regression algorithm for prediction and no analytical tools exist. In this case, one can actually use an SVM to solve the part of the problem where no analytical solution exist and combine the solution with other existing analytical and closed form solutions.

The use of kernelized SVMs has been already proposed to solve a variety of digital communications problems. The decision feedback equalizer (Sebald & Buclew, 2000) and the adaptive multi-user detector for Code Division Multiple Access (CDMA) signals in multipath channels (Chen et al., 2001) are addressed by means of binary SVM nonlinear classifiers. In (Rahman et al., 2004) signal equalization and detection for a MultiCarrier (MC)-CDMA system is based on an SVM linear classification algorithm. Koutsogiannis et al. (2002) introduced the use of KPCA for classification and de-noising of communication signals.