A Survey on Low Complexity Detectors for OTFS Systems

doi:10.12142/ZTECOM.202104002

ZTE Communications ›› 2021, Vol. 19 ›› Issue (4): 3-15.DOI: 10.12142/ZTECOM.202104002

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A Survey on Low Complexity Detectors for OTFS Systems

ZHANG Zhengquan^1,²(), LIU Heng¹, WANG Qianli¹, FAN Pingzhi¹

^1.Key Lab of Information Coding and Transmission, Southwest Jiaotong University, Chengdu 611756, China
^2.State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an 710071, China

Received:2021-10-18 Online:2021-12-25 Published:2022-01-04
About author:ZHANG Zhengquan (zhangzqswjtu@163.com) received the Ph.D. degree in information and communication engineering from Southwest Jiaotong University, China in 2019. From 2008 to 2013, he was with ZTE Corporation as a communication engineer. From 2016 to 2017, he was a guest Ph.D. student with the KTH Royal Institute of Technology, Sweden. Since 2019, he has been with the Department of Communication Engineering, School of Information Science and Technology, Southwest Jiaotong University. His research interests include B5G and 6G wireless communication technologies. He is a member of IEEE.|LIU Heng received the Ph.D. degree in information and communication engineering from Southwest Jiaotong University, China in 2013. Since 2013, he has been with the Department of Communication Engineering, School of Information Science and Technology, Southwest Jiaotong University. His research interests include next-generation wireless communications, rail transit wireless communications, machine learning and intelligent wireless communications.|WANG Qianli received the B.S. and M.S. degrees in electronic and information engineering and the Ph.D. degree from the University of Electronic Science and Technology of China in 2013, 2016 and 2021, respectively. Since 2021, he has been with the Department of Communication Engineering, School of Information Science and Technology, Southwest Jiaotong University, China. His research interests include estimation theory, array signal processing, radar sensor network, and compressed sensing.|FAN Pingzhi is currently a distinguished professor of Southwest Jiaotong University, China, and a visiting professor of Leeds University, UK (1997–). He is a recipient of the UK ORS Award (1992), the National Science Fund for Distinguished Young Scholars (1998, NSFC), IEEE VT Society Jack Neubauer Memorial Award (2018), IEEE SP Society SPL Best Paper Award (2018), IEEE WCSP 10-Year Anniversary Excellent Paper Award (2009–2019), and IEEE/CIC ICCC Best Paper Award (2020). He served as a chief scientist of the National “973” Plan Project between January 2012 and December 2016. He is an IEEE VTS Distinguished Speaker (2019–2022), a fellow of IEEE, IET, CIE and CIC. His research interests include high mobility wireless communications, massive random-access techniques, and signal design and coding.
Supported by:
the NSFC Project(61871334);the open research fund of the State Key Laboratory of Integrated Services Networks, Xidian University(ISN21-15);the Fundamental Research Funds for the Central Universities, SWJTU(2682020CX79);FAN Pingzhi’s work is also supported by the NSFC project(61731017);the “111” project(111-2-14)

Abstract

Abstract:

The newly emerging orthogonal time frequency space (OTFS) modulation can obtain delay-Doppler diversity gain to significantly improve the system performance in high mobility wireless communication scenarios such as vehicle-to-everything (V2X), high-speed railway and unmanned aerial vehicles (UAV), by employing inverse symplectic finite Fourier transform (ISFFT) and symplectic finite Fourier transform (SFFT). However, OTFS modulation will dramatically increase system complexity, especially at the receiver side. Thus, designing low complexity OTFS receiver is a key issue for OTFS modulation to be adopted by new-generation wireless communication systems. In this paper, we review low complexity OTFS detectors and provide some insights on future researches. We firstly present the OTFS system model and basic principles, followed by an overview of OTFS detector structures, classifications and comparative discussion. We also survey the principles of OTFS detection algorithms. Furthermore, we discuss the design of hybrid OTFS and orthogonal frequency division multiplexing (OFDM) detectors in single user and multi-user multi-waveform communication systems. Finally, we address the main challenges in designing low complexity OTFS detectors and identify some future research directions.

Key words: high mobility wireless communications, OTFS, ISFFT, SFFT, delay-Doppler diversity, iterative maximum ratio combining (MRC) detection, message passing detection

ZHANG Zhengquan, LIU Heng, WANG Qianli, FAN Pingzhi. A Survey on Low Complexity Detectors for OTFS Systems[J]. ZTE Communications, 2021, 19(4): 3-15.

Figures/Tables 12

Figure 1 OTFS system model

Figure 2 OTFS detector structures: (a) DD-domain non-iterative OTFS detector; (b) DD-domain iterative OTFS detector; (c) non-iterative joint TF- and DD-domain OTFS detector; (d) joint non-iterative TF-domain and iterative DD-domain OTFS detector; (e) iterative joint time- and DD-domain OTFS detector; (f) iterative joint TF- and DD-main OTFS detector; (g) iterative joint time-, TF- and DD-main OTFS detector; (h) learning-enabled OTFS detector

Figure 3 OTFS detector classifications: (a) non-iterative and iterative OTFS detectors; (b) single domain and multi-domain OTFS detectors; (c) conventional and learning-based OTFS detectors

Table 1 Summary of OTFS detector structures

Ref.	Detector Structure	Detector Structure Type	Domain	Basic Idea	Advantage	Disadvantage
Refs. [25]–[29]	Single- domain OTFS detector	DD-domain non-iterative OTFS detection	DD domain	Adopting non-iterative detection algorithms (e.g., MMSE/ZF) in DD domain	Signal detection is only performed in DD domain; Non-iterative signal detection algorithms are relatively low complexity.	Non-iterative signal detection algorithms suffer from some performance loss.
Refs. [30]–[35]	Single- domain OTFS detector	DD-domain iterative OTFS detection	DD domain	Adopting iterative detection algorithms, like MP/AMP and MRC etc., in DD domain	Iterative detection algorithms can achieve better performance.	Iterative detection will increase the complexity of algorithm design; the convergence of algorithms should be analyzed and ensured.
Ref. [17]	Joint multi- domain OTFS detector	Non-iterative joint TF- and DD-domain OTFS detection	TF domain and DD domain	Joint TF- and DD- domain processing with non-iterative detection algorithms	Joint multi-dimension processing can achieve better detection performance; Joint multi-dimension processing can relax the processing requirements in DD domain.	Joint multi-dimension processing increases the complexity of designing OTFS detector.
Refs. [15] and [16]		Joint non-iterative TF-domain and iterative DD-domain OTFS detection	TF domain and DD domain	Employing TF MMSE equalizer to provide good initials for DD-domain iterative MRC detector	Introducing non-iterative TF MMSE equalizer can accelerate the convergence of DD-domain iterative MRC detector; iterative MRC detector can fully merge separable taps to obtain better performance.	TF detection is needed to provide initial estimates; iteration processing increases the complexity; need to add null symbols to construct full channel matrix.
Ref. [18]		Iterative joint time- and DD-domain OTFS detection	Time domain and DD domain	Joint processing of time and DD domains to form a large iterative detection loop.	Iterative joint time- and DD-domain detection can achieve better performance and faster convergence by fully utilizing time- and DD-domain information.	Iterative joint time- and DD-domain detection increases the complexity of designing OTFS detector; a large amount external information exchange is inevitable.
Ref. [18]		Iterative joint TF- and DD-main OTFS detection	TF domain and DD domain	Joint TF and DD domains that form a large iterative detection loop.	Iterative joint TF- and DD-domain detection can achieve better performance and faster convergence by fully utilizing TF- and DD-domain information.	Iterative joint TF- and DD-domain detection increases the complexity of designing OTFS detector; a large amount external information exchange is inevitable.
Refs. [20]–[23]		Learning-based OTFS detection	DD domain	Using machine learning techniques to perform signal detection in DD domain or estimate some parameters in conventional OTFS detector.	It is relatively simple to design learning-based signal detection as a black box without understanding expert knowledge of OTFS detection; better detection performance is achieved.	Learning-based detection is un-explainable; more computing capability is required; massive training and testing datasets are necessary.

Table 1 Summary of OTFS detector structures

Ref.	Detector Structure	Detector Structure Type	Domain	Basic Idea	Advantage	Disadvantage
Refs. [25]–[29]	Single- domain OTFS detector	DD-domain non-iterative OTFS detection	DD domain	Adopting non-iterative detection algorithms (e.g., MMSE/ZF) in DD domain	Signal detection is only performed in DD domain; Non-iterative signal detection algorithms are relatively low complexity.	Non-iterative signal detection algorithms suffer from some performance loss.
Refs. [30]–[35]	Single- domain OTFS detector	DD-domain iterative OTFS detection	DD domain	Adopting iterative detection algorithms, like MP/AMP and MRC etc., in DD domain	Iterative detection algorithms can achieve better performance.	Iterative detection will increase the complexity of algorithm design; the convergence of algorithms should be analyzed and ensured.
Ref. [17]	Joint multi- domain OTFS detector	Non-iterative joint TF- and DD-domain OTFS detection	TF domain and DD domain	Joint TF- and DD- domain processing with non-iterative detection algorithms	Joint multi-dimension processing can achieve better detection performance; Joint multi-dimension processing can relax the processing requirements in DD domain.	Joint multi-dimension processing increases the complexity of designing OTFS detector.
Refs. [15] and [16]		Joint non-iterative TF-domain and iterative DD-domain OTFS detection	TF domain and DD domain	Employing TF MMSE equalizer to provide good initials for DD-domain iterative MRC detector	Introducing non-iterative TF MMSE equalizer can accelerate the convergence of DD-domain iterative MRC detector; iterative MRC detector can fully merge separable taps to obtain better performance.	TF detection is needed to provide initial estimates; iteration processing increases the complexity; need to add null symbols to construct full channel matrix.
Ref. [18]		Iterative joint time- and DD-domain OTFS detection	Time domain and DD domain	Joint processing of time and DD domains to form a large iterative detection loop.	Iterative joint time- and DD-domain detection can achieve better performance and faster convergence by fully utilizing time- and DD-domain information.	Iterative joint time- and DD-domain detection increases the complexity of designing OTFS detector; a large amount external information exchange is inevitable.
Ref. [18]		Iterative joint TF- and DD-main OTFS detection	TF domain and DD domain	Joint TF and DD domains that form a large iterative detection loop.	Iterative joint TF- and DD-domain detection can achieve better performance and faster convergence by fully utilizing TF- and DD-domain information.	Iterative joint TF- and DD-domain detection increases the complexity of designing OTFS detector; a large amount external information exchange is inevitable.
Refs. [20]–[23]		Learning-based OTFS detection	DD domain	Using machine learning techniques to perform signal detection in DD domain or estimate some parameters in conventional OTFS detector.	It is relatively simple to design learning-based signal detection as a black box without understanding expert knowledge of OTFS detection; better detection performance is achieved.	Learning-based detection is un-explainable; more computing capability is required; massive training and testing datasets are necessary.

Figure 4 Iterative MRC detector[15]

Table 2 Summary of computational complexity and performance

Reference	Detection Algorithm	Algorithm Characteristic	Computational Complexity	Performance
Ref. [39]	Classical MMSE	Non-iterative	$Ο (M 3 N 3)$	UAMP>EP>AEP >MRC-rake >VB >MP >Classical MMSE ≥low complexity MMSE
Ref. [27]	Low complexity MMSE	Non-iterative	$Ο (M N l o g (M N))$
Ref. [25]	lower-upper factorization -based MMSE	Non-iterative	$Ο (M N l o g (N))$
Refs. [31] and [32]	MP	Iterative	$Ο (2 Q I M N S)$
Ref. [33]	MF-MP-PC	Iterative	$Ο (I M N (2 Q / 2 + S))$
Ref. [34]	GAMP	Iterative	$Ο (2 Q I M N S)$
Ref. [35]	UAMP	Iterative	$Ο (I M N l o g (M N)) + Ο (2 Q I M N)$
Ref. [36]	ICMP	Iterative	$Ο (2 Q I M N G S)$
Refs. [15] and [16]	MRC-rake	Iterative	$Ο (I M N (L + l o g (N))) + Ο (M N (L + l o g (M)))$
Ref. [39]	EP	Iterative	$Ο (I M N (2 Q + S))$
Ref. [39]	AEP	Iterative	$Ο (I M N (2 Q + S))$
Ref. [40]	VB	Iterative	$Ο (2 Q I M N S)$

Table 2 Summary of computational complexity and performance

Reference	Detection Algorithm	Algorithm Characteristic	Computational Complexity	Performance
Ref. [39]	Classical MMSE	Non-iterative	$Ο (M 3 N 3)$	UAMP>EP>AEP >MRC-rake >VB >MP >Classical MMSE ≥low complexity MMSE
Ref. [27]	Low complexity MMSE	Non-iterative	$Ο (M N l o g (M N))$
Ref. [25]	lower-upper factorization -based MMSE	Non-iterative	$Ο (M N l o g (N))$
Refs. [31] and [32]	MP	Iterative	$Ο (2 Q I M N S)$
Ref. [33]	MF-MP-PC	Iterative	$Ο (I M N (2 Q / 2 + S))$
Ref. [34]	GAMP	Iterative	$Ο (2 Q I M N S)$
Ref. [35]	UAMP	Iterative	$Ο (I M N l o g (M N)) + Ο (2 Q I M N)$
Ref. [36]	ICMP	Iterative	$Ο (2 Q I M N G S)$
Refs. [15] and [16]	MRC-rake	Iterative	$Ο (I M N (L + l o g (N))) + Ο (M N (L + l o g (M)))$
Ref. [39]	EP	Iterative	$Ο (I M N (2 Q + S))$
Ref. [39]	AEP	Iterative	$Ο (I M N (2 Q + S))$
Ref. [40]	VB	Iterative	$Ο (2 Q I M N S)$

Figure 5 LU factorization-based low complexity minimum-mean-square-error (MMSE) detection[25]

Figure 6 Hybrid OTFS-OFDM multi-waveform detector structure: (a) single user OTFS system; (b) multi-user OTFS system

Figure 7 Downlink waveform selection procedure

Figure 8 Uplink waveform selection procedure

Figure 9 Multiple access schemes for downlink hybrid OFDM-OTFS systems in multi-user scenario: (a) hybrid orthogonal frequency division multiple access (OFDMA) and orthogonal time frequency space multiple access (OTFSMA) in both DD and TF domains; (b) hybrid OFDMA and OTFSMA with overlap in the TF domain

Figure 10 BLER performance: (a) two-user orthogonal time frequency space (OTFS) systems without inter-user interference (IUI); (b) two-user hybrid OTFS-orthogonal frequency division multiplexing (OFDM) systems

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A Survey on Low Complexity Detectors for OTFS Systems

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