On the Spectrum of OTFS/VOFDM Signals: PSD Analysis and Bandwidth Allocation

TL;DR

This paper analyzes the spectral properties of OTFS signals, revealing their periodic PSD structure, and proposes a null-space-based precoding method to enable flexible bandwidth allocation for OTFS/VOFDM systems.

Contribution

It provides a detailed PSD analysis of OTFS signals, establishes a relationship with OFDM PSDs, and introduces a novel precoding technique for bandwidth management.

Findings

OTFS PSD is periodic with a specific frequency interval.

The PSD of OTFS equals the sum of component OFDM PSDs under independence.

The proposed NSLP method effectively tailors OTFS spectral characteristics.

Abstract

Orthogonal time frequency space (OTFS)/vector OFDM (VOFDM) is widely regarded as a promising waveform for next-generation mobile communications. However, its spectral characteristics are not yet fully understood. The bandwidth allocation scheme, which is crucial for OTFS's integration into practical wireless standards, also remains unexplored. In this paper, we investigate the spectral characteristics of OTFS signals by analyzing their power spectral density (PSD). We demonstrate that the PSD of discrete-time OTFS signals is periodic with a period of $\frac{1}{MT_s}$, where $M$ is the size of the time/Doppler domain in OTFS, a.k.a., the vector size in VOFDM, and $T_s$ is the sampling interval length of digital to analog converter (DAC), resulting in $M$ identical spectral components within the spectral range $[-\frac{1}{2T_s}, \frac{1}{2T_s})$ of the continuous-time OTFS signal. The periodicity makes bandwidth allocation for OTFS/VOFDM signaling substantially challenging. Furthermore, we establish a relationship between the PSD of OFDM signals and that of OTFS signals, revealing that, when the information symbols are independent, the PSD of OTFS signals is equal to the sum of the PSDs of the component-expanded OFDM (CEP-OFDM) signals. Lastly, we derive a relationship between the information symbols and the corresponding OTFS spectrum, and based on which, we propose a null-space-based linear precoding (NSLP) method for OTFS signals to enable flexible bandwidth allocation. Numerical results validate our analytical results regarding the PSD of OTFS signals and show the effectiveness of our proposed NSLP method in tailoring the spectrum of OTFS signals.