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In this paper, we present a deep learning (DL) algorithm for channel estimation in communication systems. We consider the time-frequency response of a fast fading communication channel as a two-dimensional image. The aim is to find the unknown values of the channel response using some known values at the pilot locations. To this end, a general pipeline using deep image processing techniques, image super-resolution (SR) and image restoration (IR) is proposed. This scheme considers the pilot values, altogether, as a low-resolution image and uses an SR network cascaded with a denoising IR network to estimate the channel. Moreover, an implementation of the proposed pipeline is presented. The estimation error shows that the presented algorithm is comparable to the minimum mean square error (MMSE) with full knowledge of the channel statistics and it is better than ALMMSE (an approximation to linear MMSE). The results confirm that this pipeline can be used efficiently in channel estimation.

High-dimensional data in many machine learning applications leads to computational and analytical complexities. Feature selection provides an effective way for solving these problems by removing irrelevant and redundant features, thus reducing model complexity and improving accuracy and generalization capability of the model. In this paper, we present a novel teacher-student feature selection (TSFS) method in which a 'teacher' (a deep neural network or a complicated dimension reduction method) is first employed to learn the best representation of data in low dimension. Then a 'student' network (a simple neural network) is used to perform feature selection by minimizing the reconstruction error of low dimensional representation. Although the teacher-student scheme is not new, to the best of our knowledge, it is the first time that this scheme is employed for feature selection. The proposed TSFS can be used for both supervised and unsupervised feature selection. This method is evaluated on different datasets and is compared with state-of-the-art existing feature selection methods. The results show that TSFS performs better in terms of classification and clustering accuracies and reconstruction error. Moreover, experimental evaluations demonstrate a low degree of sensitivity to parameter selection in the proposed method.

In this paper, we present a downlink pilot design scheme for Deep Learning (DL) based channel estimation (ChannelNet) in orthogonal frequency-division multiplexing (OFDM) systems. Specifically, in the proposed scheme, a feature selection method named Concrete Autoencoder (ConcreteAE) is used to find the most informative locations for pilot transmission. This autoencoder consists of a concrete layer as the encoder and a multilayer perceptron (MLP) as the decoder. During the training, the concrete layer selects the most informative pilot locations, and the decoder reconstructs an approximate estimation of the channel. Eventually, the ChannelNet is trained on the output of the ConcreteAE aiming to reconstruct the ideal channel response. The estimation error results show that this approach outperforms the previously presented ChannelNet with a uniformly distributed pilot pattern, and its performance is comparable to the minimum mean square error (MMSE).

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