Adaptive blind equalizer for HF channels

In this paper, the problem of blind adaptive equalization of HF channel is considered using a state space approach. HF channel is multipath propagation channel due to multiple reflections on ionospheric layers, which causing intersymbol interference (ISI) at the receiver output. The problem of ISI suppression is referred to as deconvolution or channel equalization. At present, a family of methods for equalizing and estimating the channel based on the criterion of minimum mean-square error (MMSE) has become widespread in engineering practice. These methods assume the use of a training or pilot symbols known by the receiver to estimate the channel and “train” the equalizer. However, in order to increase the bandwidth efficiency blind deconvolution or channel equalization methods have been developing recently more actively. The essence of these methods is the task of equalization and estimation of the channel from sensors outputs without any a priory knowledge of the original signals. The classical criterion for blind equalization is the constant modulus (CM) criterion, which is an extension of the Godart algorithms family. However, this method has slow convergence, and is not applicable to all modulation methods used in the HF systems. The paper considers a learning algorithm based on information theory and natural gradient is used to solve the optimization problem. To effectively use the algorithm in a changing channel environment, it is suggested to use an additional optimization of the algorithm step size. The channel model is state-space description of a dynamic system. The main advantage of state-space model is that is flexible and can be used for internal description of system. Based on developed state-space model and measurement models, an adaptive optimum-size blind equalization algorithm is proposed to track the HF channel variation in time. Proposed algorithm is compared to CMA and classical stochastic gradient descent algorithms for blind deconvolution. In numerical simulations, it is observed that the proposed approach can track the channel variations with good performance. During computer simulations under good, moderate and poor HF ionospheric channel conditions, it is observed, that proposed adaptive equalization algorithm with adaptive step-size for blind deconvolution provides reliable equalization error and can track the variation of the channel in time with high accuracy.