[Paper Review] Receiver Design for OTFS with Fractionally Spaced Sampling Approach

Yao Ge, Qinwen Deng+2 more|arXiv (Cornell University)|Sep 2, 2020

PAPR reduction in OFDM43 references4 citations

TL;DR

This paper proposes a fractionally spaced sampling (FSS) receiver for orthogonal time-frequency space (OTFS) systems using practical rectangular pulses, avoiding impractical assumptions like ideal bi-orthogonal pulses or on-grid Doppler-delay shifts. By deriving a general input-output relationship in the delay-Doppler domain and employing iterative combining message passing (ICMP) and turbo message passing (TMP) algorithms, the FSS receiver achieves superior performance and robustness to imperfect channel state information, especially in high-mobility scenarios with time-varying channels.

ABSTRACT

The recent emergence of orthogonal time frequency space (OTFS) modulation as a novel PHY-layer mechanism is more suitable in high-mobility wireless communication scenarios than traditional orthogonal frequency division multiplexing (OFDM). Although multiple studies have analyzed OTFS performance using theoretical and ideal baseband pulseshapes, a challenging and open problem is the development of effective receivers for practical OTFS systems that must rely on non-ideal pulseshapes for transmission. This work focuses on the design of practical receivers for OTFS. We consider a fractionally spaced sampling (FSS) receiver in which the sampling rate is an integer multiple of the symbol rate. For rectangular pulses used in OTFS transmission, we derive a general channel input-output relationship of OTFS in delay-Doppler domain without the common reliance on impractical assumptions such as ideal bi-orthogonal pulses and on-the-grid delay/Doppler shifts. We propose two equalization algorithms: iterative combining message passing (ICMP) and turbo message passing (TMP) for symbol detection by exploiting delay-Doppler channel sparsity and the frequency diversity gain via FSS. We analyze the convergence performance of TMP receiver and propose simplified message passing (MP) receivers to further reduce complexity. Our FSS receivers demonstrate stronger performance than traditional receivers and robustness to the imperfect channel state information knowledge.

Motivation & Objective

• To address the lack of practical receiver designs for OTFS that rely on non-ideal, realizable pulse shapes such as rectangular pulses.
• To overcome the limitations of existing OTFS receivers that assume ideal bi-orthogonal pulses or on-grid delay/Doppler shifts, which are impractical due to the Heisenberg uncertainty principle.
• To develop a receiver architecture that fully exploits channel diversity and sparsity in the delay-Doppler domain using fractionally spaced sampling (FSS) with an integer multiple of the symbol rate.
• To design low-complexity, high-performance equalization algorithms—ICMP and TMP—that are robust to imperfect channel state information and suitable for real-world OTFS deployment.

Proposed method

• Derives a general input-output relationship for OTFS in the delay-Doppler domain using rectangular pulses and a single cyclic prefix per frame, without assuming ideal pulses or on-grid Doppler-delay shifts.
• Applies fractionally spaced sampling (FSS) at a rate that is an integer multiple of the symbol rate to preserve sufficient statistics and exploit channel diversity gain.
• Develops two message-passing-based equalization algorithms: iterative combining message passing (ICMP) and turbo message passing (TMP), leveraging channel sparsity and time-varying channel structure.
• Introduces simplified message passing (MP) variants to reduce computational complexity while maintaining performance.
• Uses cross-ambiguity functions and sampled channel impulse responses to model the effective channel matrix in the delay-Doppler domain.
• Derives closed-form expressions for the effective channel coefficients in the delay-Doppler domain, enabling efficient symbol detection via message passing.

Experimental results

Research questions

• RQ1 How can a practical OTFS receiver be designed using realizable rectangular pulses without relying on ideal bi-orthogonal pulse assumptions?
• RQ2 What is the input-output relationship of OTFS in the delay-Doppler domain when using rectangular pulses and a single cyclic prefix per frame?
• RQ3 Can fractionally spaced sampling (FSS) improve diversity gain and performance in high-mobility OTFS systems with time-varying channels?
• RQ4 How do ICMP and TMP equalization algorithms perform in terms of convergence and robustness under imperfect channel state information?
• RQ5 What is the impact of non-grid-aligned delay and Doppler shifts on OTFS system performance, and how can they be effectively mitigated?

Key findings

• The proposed FSS receiver achieves stronger performance than traditional symbol-spaced sampling receivers by exploiting channel diversity through increased sampling rate.
• The derived input-output relationship in the delay-Doppler domain is general and valid for rectangular pulses without requiring ideal pulse shapes or on-grid delay/Doppler shifts.
• The turbo message passing (TMP) receiver demonstrates good convergence performance and robustness to imperfect channel state information, making it suitable for practical deployment.
• Simplified message passing (MP) variants are proposed to reduce complexity while maintaining high detection accuracy.
• The FSS-based OTFS receiver effectively mitigates inter-symbol interference (ISI) and inter-carrier interference (ICI) in doubly dispersive channels.
• The use of a single cyclic prefix per OTFS frame maintains spectral efficiency while enabling effective interference cancellation through advanced equalization.