Supervised identification and equalization of transmission channel using reproducing kernel Hilbert space

The subject matter of the article is to identify and equalize the parameters of telecommunication channels. The goal is to develop a new mathematical approach based on positive definite kernels on a Hilbert space. The tasks to be solved are: (a) to formulate a mathematical procedure based on a kernel; a kernel is a function that maps pairs of data points to a scalar value, and positive definite kernels are widely used in machine learning and signal processing applications; (b) to identify the channel parameters using the proposed method; and (c) to apply the Zero Forcing and MMSE equalizer to measure the performance of the proposed system. This article introduces a new method to address the problem of supervised identification of transmission channel parameters based on the positive definite kernel on Hilbert space, which implements Gaussian kernels. The input sequence, used as an input for a system or process, is assumed to be independent, have a zero mean, a non-Gaussian distribution, and be identically distributed. These assumptions are made to simplify the analysis and modeling. The proposed method for estimating the parameters of the channel impulse response yields promising results, indicating that the estimated parameters are close to the measured parameters of the model for various channels. The convergence of the estimated parameters toward the measured parameters of the model is particularly noticeable for BRAN A (indoor) and BRAN E (outdoor) channels. The method has been tested with different channel models, and the results remain consistent. Overall, the proposed method appears to be a reliable and effective approach for estimating channel impulse response parameters. The accuracy of the estimated parameters is particularly noteworthy considering the challenges inherent in modeling wireless channels, which can be influenced by various factors such as obstacles and interference. These findings have important implications for the design and optimization of wireless communication systems. Accurate estimates of channel impulse response parameters are essential for predicting and mitigating the effects of channel distortion and interference, and the proposed method represents a promising tool for achieving this goal. Further research and testing are needed to validate and refine the method and to explore its potential applications in different settings and scenarios. We evaluated the performance of the system using the estimated parameters obtained from the proposed method. Two equalizers, MMSE and ZF, were used, and the results show that MMSE outperforms ZF. Both equalizers produced highly satisfactory outcomes.