ZTE Communications ›› 2021, Vol. 19 ›› Issue (4): 315.DOI: 10.12142/ZTECOM.202104002
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ZHANG Zhengquan^{1,}^{2}(), LIU Heng^{1}, WANG Qianli^{1}, FAN Pingzhi^{1}
Received:
20211018
Online:
20211225
Published:
20220104
About author:
ZHANG Zhengquan (Supported by:
ZHANG Zhengquan, LIU Heng, WANG Qianli, FAN Pingzhi. A Survey on Low Complexity Detectors for OTFS Systems[J]. ZTE Communications, 2021, 19(4): 315.
Figure 2 OTFS detector structures: (a) DDdomain noniterative OTFS detector; (b) DDdomain iterative OTFS detector; (c) noniterative joint TF and DDdomain OTFS detector; (d) joint noniterative TFdomain and iterative DDdomain OTFS detector; (e) iterative joint time and DDdomain OTFS detector; (f) iterative joint TF and DDmain OTFS detector; (g) iterative joint time, TF and DDmain OTFS detector; (h) learningenabled OTFS detector
Figure 3 OTFS detector classifications: (a) noniterative and iterative OTFS detectors; (b) single domain and multidomain OTFS detectors; (c) conventional and learningbased OTFS detectors
Ref.  Detector Structure  Detector Structure Type  Domain  Basic Idea  Advantage  Disadvantage 

Refs. [  Single domain OTFS detector  DDdomain noniterative OTFS detection  DD domain  Adopting noniterative detection algorithms (e.g., MMSE/ZF) in DD domain  Signal detection is only performed in DD domain; Noniterative signal detection algorithms are relatively low complexity.  Noniterative signal detection algorithms suffer from some performance loss. 
Refs. [  DDdomain 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. [  Joint multi domain OTFS detector  Noniterative joint TF and DDdomain OTFS detection  TF domain and DD domain  Joint TF and DD domain processing with noniterative detection algorithms  Joint multidimension processing can achieve better detection performance; Joint multidimension processing can relax the processing requirements in DD domain.  Joint multidimension processing increases the complexity of designing OTFS detector. 
Refs. [  Joint noniterative TFdomain and iterative DDdomain OTFS detection  TF domain and DD domain  Employing TF MMSE equalizer to provide good initials for DDdomain iterative MRC detector  Introducing noniterative TF MMSE equalizer can accelerate the convergence of DDdomain 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. [  Iterative joint time and DDdomain 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 DDdomain detection can achieve better performance and faster convergence by fully utilizing time and DDdomain information.  Iterative joint time and DDdomain detection increases the complexity of designing OTFS detector; a large amount external information exchange is inevitable.  
Iterative joint TF and DDmain OTFS detection  TF domain and DD domain  Joint TF and DD domains that form a large iterative detection loop.  Iterative joint TF and DDdomain detection can achieve better performance and faster convergence by fully utilizing TF and DDdomain information.  Iterative joint TF and DDdomain detection increases the complexity of designing OTFS detector; a large amount external information exchange is inevitable.  
Refs. [  Learningbased 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 learningbased signal detection as a black box without understanding expert knowledge of OTFS detection; better detection performance is achieved.  Learningbased detection is unexplainable; 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. [  Single domain OTFS detector  DDdomain noniterative OTFS detection  DD domain  Adopting noniterative detection algorithms (e.g., MMSE/ZF) in DD domain  Signal detection is only performed in DD domain; Noniterative signal detection algorithms are relatively low complexity.  Noniterative signal detection algorithms suffer from some performance loss. 
Refs. [  DDdomain 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. [  Joint multi domain OTFS detector  Noniterative joint TF and DDdomain OTFS detection  TF domain and DD domain  Joint TF and DD domain processing with noniterative detection algorithms  Joint multidimension processing can achieve better detection performance; Joint multidimension processing can relax the processing requirements in DD domain.  Joint multidimension processing increases the complexity of designing OTFS detector. 
Refs. [  Joint noniterative TFdomain and iterative DDdomain OTFS detection  TF domain and DD domain  Employing TF MMSE equalizer to provide good initials for DDdomain iterative MRC detector  Introducing noniterative TF MMSE equalizer can accelerate the convergence of DDdomain 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. [  Iterative joint time and DDdomain 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 DDdomain detection can achieve better performance and faster convergence by fully utilizing time and DDdomain information.  Iterative joint time and DDdomain detection increases the complexity of designing OTFS detector; a large amount external information exchange is inevitable.  
Iterative joint TF and DDmain OTFS detection  TF domain and DD domain  Joint TF and DD domains that form a large iterative detection loop.  Iterative joint TF and DDdomain detection can achieve better performance and faster convergence by fully utilizing TF and DDdomain information.  Iterative joint TF and DDdomain detection increases the complexity of designing OTFS detector; a large amount external information exchange is inevitable.  
Refs. [  Learningbased 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 learningbased signal detection as a black box without understanding expert knowledge of OTFS detection; better detection performance is achieved.  Learningbased detection is unexplainable; more computing capability is required; massive training and testing datasets are necessary. 
Reference  Detection Algorithm  Algorithm Characteristic  Computational Complexity  Performance 

Ref. [  Classical MMSE  Noniterative  UAMP>EP>AEP >MRCrake >VB >MP >Classical MMSE ≥low complexity MMSE  
Ref. [  Low complexity MMSE  Noniterative  
Ref. [  lowerupper factorization based MMSE  Noniterative  
Refs. [  MP  Iterative  
Ref. [  MFMPPC  Iterative  
Ref. [  GAMP  Iterative  
Ref. [  UAMP  Iterative  
Ref. [  ICMP  Iterative  
Refs. [  MRCrake  Iterative  
Ref. [  EP  Iterative  
AEP  Iterative  
Ref. [  VB  Iterative 
Table 2 Summary of computational complexity and performance
Reference  Detection Algorithm  Algorithm Characteristic  Computational Complexity  Performance 

Ref. [  Classical MMSE  Noniterative  UAMP>EP>AEP >MRCrake >VB >MP >Classical MMSE ≥low complexity MMSE  
Ref. [  Low complexity MMSE  Noniterative  
Ref. [  lowerupper factorization based MMSE  Noniterative  
Refs. [  MP  Iterative  
Ref. [  MFMPPC  Iterative  
Ref. [  GAMP  Iterative  
Ref. [  UAMP  Iterative  
Ref. [  ICMP  Iterative  
Refs. [  MRCrake  Iterative  
Ref. [  EP  Iterative  
AEP  Iterative  
Ref. [  VB  Iterative 
Figure 9 Multiple access schemes for downlink hybrid OFDMOTFS systems in multiuser 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) twouser orthogonal time frequency space (OTFS) systems without interuser interference (IUI); (b) twouser hybrid OTFSorthogonal frequency division multiplexing (OFDM) systems
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