Communications in Information and Systems

Volume 20 (2020)

Number 3

Mathematical Engineering: A special issue at the occasion of the 85th birthday of Prof. Thomas Kailath

Guest Editors: Ali H. Sayed, Helmut Bölcskei, Patrick Dewilde, Vwani Roychowdhury, and Stephen Shing-Toung Yau

Data-driven symbol detection via model-based machine learning

Pages: 283 – 317



Nariman Farsad (Department of Computer Science, Ryerson University, Toronto, Canada)

Nir Shlezinger (School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Be’er-Sheva, Israel)

Andrea J. Goldsmith (Department of Electrical Engineering, Princeton University, Princeton, New Jersey, U.S.A.)

Yonina C. Eldar (Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot, Israel)


The design of symbol detectors in digital communication systems has traditionally relied on statistical channel models that describe the relation between the transmitted symbols and the observed signal at the receiver. Here we review a data-driven framework to symbol detection design which combines machine learning (ML) and model-based algorithms. In this hybrid approach, well-known channel-model-based algorithms such as the Viterbi method, BCJR detection, and multiple-input multiple-output (MIMO) soft interference cancellation (SIC) are augmented with ML-based algorithms to remove their channel-model-dependence, allowing the receiver to learn to implement these algorithms solely from data. The resulting data-driven receivers are most suitable for systems where the underlying channel models are poorly understood, highly complex, or do not well-capture the underlying physics. Our approach is unique in that it only replaces the channel-model-based computations with dedicated neural networks that can be trained from a small amount of data, while keeping the general algorithm intact. Our results demonstrate that these techniques can yield nearoptimal performance of model-based algorithms without knowing the exact channel input-output statistical relationship and in the presence of channel state information uncertainty.

This work was supported in part by the US - Israel Binational Science Foundation under grant No. 2026094, by the Israel Science Foundation under grant No. 0100101, by the Office of the Naval Research under grant No. 18-1-2191, and by NSERC Discovery Grant and CFI John Evans Leaders Funds.

Received 14 February 2020

Published 2 December 2020