Abstract
We study end-to-end learning-based frameworks for amplify-and-forward (AF) relay networks, with and without the channel state information (CSI) knowledge. The designed framework resembles an autoencoder (AE) where all the components of the neural network (NN)-based source and destination nodes are optimized together in an end-to-end manner, and the signal transmission takes place with an AF relay node. Unlike the literature that employs an NN-based relay node with full CSI knowledge, we consider a conventional relay node that only amplifies the received signal using CSI gains. Without the CSI knowledge, we employ power normalization-based amplification that normalizes the transmission power of each block of symbols. We propose and compare symbol-wise and bit-wise AE frameworks by minimizing categorical and binary cross-entropy loss that maximizes the symbol-wise and bit-wise mutual information (MI), respectively. We determine the estimated MI and examine the convergence of both AE frameworks with signal-to-noise ratio (SNR). For both these AE frameworks, we design coded modulation and differential coded modulation, depending upon the availability of CSI at the destination node, that obtains symbols in 2n-dimensions, where n is the block length. To explain the properties of the 2n-dimensional designs, we utilize various metrics like minimum Euclidean distance, normalized second-order and fourth-order moments, and constellation figures of merit. We show that both these AE frameworks obtain similar spherical coded-modulation designs in 2n-dimensions, and bit-wise AE that inherently obtains the optimal bit-labeling outperforms symbol-wise AE (with faster convergence under low SNR) and the conventional AF relay network with a considerable SNR margin.
Highlights
End-to-end learning has appeared as a promising solution for jointly optimizing all the components of the point-to-point (P2P) communication network consisting of a neural network (NN)-based encoder and decoder at the transmitter and receiver by employing an autoencoder (AE) framework [1]
We show the performance for additive white Gaussian noise (AWGN) and Rayleigh block fading (RBF) channels, where the channel remains constant during a transmission block of n symbols and changes randomly
We show that the NN-based encoder forms 2k constellation points as a spherical code for both symbol-wise or bit-wise AE frameworks
Summary
End-to-end learning has appeared as a promising solution for jointly optimizing all the components of the point-to-point (P2P) communication network consisting of a neural network (NN)-based encoder and decoder at the transmitter and receiver by employing an autoencoder (AE) framework [1]. To the best of the authors’ knowledge, no such comparative study between bit-wise and symbol-wise AE frameworks exists for relay networks or coded-modulation designs even for P2P networks. To the best of the authors’ knowledge, none of the previous works have studied bit-wise AE-based coded-modulation design, and/or, have considered a minimal complexity AF relay node with the fair CSI requirements as the conventional networks. To the best of the authors’ knowledge, none of the previous works have removed the necessity of the CSI knowledge without utilizing NN-based processing at the relay node either for a bit-wise or symbol-wise AE framework, and/or, have studied bit-wise AE-based differential coded-modulation designs for an AF relaying networks. LIST OF ABBREVIATIONS AND NOTATIONS To improve the readability of the paper, we have summarized the abbreviations in Table 1 and notations in Table 2, 3
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