Low Complexity Classification Approach for Faster-Than-Nyquist (FTN) Signaling Detection

Abstract

In this letter, we investigate the use of machine learning (ML) to reduce the detection complexity of faster-than-Nyquist (FTN) signaling. In particular, we view the FTN signaling detection problem as a classification task, where the received signal is considered as an unlabeled class sample that belongs to the set of all possible classes samples. We observe that by jointly considering <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{p}$ </tex-math></inline-formula> samples, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{p} \ll N$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> is the transmission block length, for the FTN signaling detection, the distance between the classes samples of any distance-based classifier increases, and hence, the detection performance improves. That said, we propose a low-complexity classifier (LCC) that exploits the ISI structure of FTN signaling to perform the classification task in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{p}$ </tex-math></inline-formula> -dimension space. The proposed LCC consists of two stages: 1) offline pre-classification that constructs the labeled classes samples in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{p}$ </tex-math></inline-formula> -dimensional space and 2) online classification where the detection of the received samples occurs. The proposed LCC is extended to produce soft-outputs as well. Simulation results show the effectiveness of the proposed LCC in balancing performance and complexity.