The Cost of Noncoherence: Avoiding Channel Estimation Through Differential Encoding in Phase Quantized Systems
This paper proposes a novel approach that utilizes differential encoding to overcome the channel estimation problem in communication systems with low-resolution quantization receivers. For differentially encoded data, we derive the maximum likelihood detection rule for the canonical block-2 detector...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Open Journal of the Communications Society |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10273613/ |
| _version_ | 1797644880860676096 |
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| author | Samiru Gayan Hazer Inaltekin Rajitha Senanayake Jamie Evans |
| author_facet | Samiru Gayan Hazer Inaltekin Rajitha Senanayake Jamie Evans |
| author_sort | Samiru Gayan |
| collection | DOAJ |
| description | This paper proposes a novel approach that utilizes differential encoding to overcome the channel estimation problem in communication systems with low-resolution quantization receivers. For differentially encoded data, we derive the maximum likelihood detection rule for the canonical block-2 detectors, employing just two consecutive quantized observations at the channel output and without any receiver-side channel state information. We establish the optimality of this maximum likelihood detection rule within the class of block-<inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> detectors, where <inline-formula> <tex-math notation="LaTeX">$L \geq 3$ </tex-math></inline-formula>, under the condition that <inline-formula> <tex-math notation="LaTeX">$n = \log _{2} M$ </tex-math></inline-formula>, with <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> denoting the number of quantization bits and input alphabet size, respectively. The derived detector has a simple and easily implementable structure, comparing the quantization region indices of consecutive observations to determine the transmitted message index. By leveraging the structure of the derived optimum detector, we obtain the expression for the message error probability in Rayleigh fading wireless channels. Through asymptotic analysis in the high signal-to-noise ratio regime, we reveal a crucial finding that achieving the same diversity order as infinite bit quantization with full channel knowledge requires an additional two bits at the quantizer, in addition to the minimum requirement of <inline-formula> <tex-math notation="LaTeX">$\log _{2} M$ </tex-math></inline-formula> bits. One bit compensates for the low-resolution effect, while the other addresses the lack of channel knowledge. Finally, we conduct an extensive simulation study to demonstrate the performance of the optimum detectors and quantify the performance loss resulting from the absence of channel knowledge at the receiver. |
| first_indexed | 2024-03-11T14:37:49Z |
| format | Article |
| id | doaj.art-32cf3943d5964b5c8858b2c8e7b10f9b |
| institution | Directory Open Access Journal |
| issn | 2644-125X |
| language | English |
| last_indexed | 2024-03-11T14:37:49Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of the Communications Society |
| spelling | doaj.art-32cf3943d5964b5c8858b2c8e7b10f9b2023-10-30T23:01:18ZengIEEEIEEE Open Journal of the Communications Society2644-125X2023-01-0142578259510.1109/OJCOMS.2023.332260310273613The Cost of Noncoherence: Avoiding Channel Estimation Through Differential Encoding in Phase Quantized SystemsSamiru Gayan0https://orcid.org/0000-0001-7561-1541Hazer Inaltekin1https://orcid.org/0000-0003-0147-4403Rajitha Senanayake2https://orcid.org/0000-0002-5960-4082Jamie Evans3https://orcid.org/0000-0003-4637-1037Department of Electronic and Telecommunication Engineering, University of Moratuwa, Katubedda, Sri LankaSchool of Engineering, Macquarie University, North Ryde, NSW, AustraliaDepartment of Electrical and Electronic Engineering, The University of Melbourne, Parkville, VIC, AustraliaDepartment of Electrical and Electronic Engineering, The University of Melbourne, Parkville, VIC, AustraliaThis paper proposes a novel approach that utilizes differential encoding to overcome the channel estimation problem in communication systems with low-resolution quantization receivers. For differentially encoded data, we derive the maximum likelihood detection rule for the canonical block-2 detectors, employing just two consecutive quantized observations at the channel output and without any receiver-side channel state information. We establish the optimality of this maximum likelihood detection rule within the class of block-<inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> detectors, where <inline-formula> <tex-math notation="LaTeX">$L \geq 3$ </tex-math></inline-formula>, under the condition that <inline-formula> <tex-math notation="LaTeX">$n = \log _{2} M$ </tex-math></inline-formula>, with <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> denoting the number of quantization bits and input alphabet size, respectively. The derived detector has a simple and easily implementable structure, comparing the quantization region indices of consecutive observations to determine the transmitted message index. By leveraging the structure of the derived optimum detector, we obtain the expression for the message error probability in Rayleigh fading wireless channels. Through asymptotic analysis in the high signal-to-noise ratio regime, we reveal a crucial finding that achieving the same diversity order as infinite bit quantization with full channel knowledge requires an additional two bits at the quantizer, in addition to the minimum requirement of <inline-formula> <tex-math notation="LaTeX">$\log _{2} M$ </tex-math></inline-formula> bits. One bit compensates for the low-resolution effect, while the other addresses the lack of channel knowledge. Finally, we conduct an extensive simulation study to demonstrate the performance of the optimum detectors and quantify the performance loss resulting from the absence of channel knowledge at the receiver.https://ieeexplore.ieee.org/document/10273613/Low-resolution quantizationML detectorsD-MPSK modulationsymbol error probabilitydiversity order |
| spellingShingle | Samiru Gayan Hazer Inaltekin Rajitha Senanayake Jamie Evans The Cost of Noncoherence: Avoiding Channel Estimation Through Differential Encoding in Phase Quantized Systems IEEE Open Journal of the Communications Society Low-resolution quantization ML detectors D-MPSK modulation symbol error probability diversity order |
| title | The Cost of Noncoherence: Avoiding Channel Estimation Through Differential Encoding in Phase Quantized Systems |
| title_full | The Cost of Noncoherence: Avoiding Channel Estimation Through Differential Encoding in Phase Quantized Systems |
| title_fullStr | The Cost of Noncoherence: Avoiding Channel Estimation Through Differential Encoding in Phase Quantized Systems |
| title_full_unstemmed | The Cost of Noncoherence: Avoiding Channel Estimation Through Differential Encoding in Phase Quantized Systems |
| title_short | The Cost of Noncoherence: Avoiding Channel Estimation Through Differential Encoding in Phase Quantized Systems |
| title_sort | cost of noncoherence avoiding channel estimation through differential encoding in phase quantized systems |
| topic | Low-resolution quantization ML detectors D-MPSK modulation symbol error probability diversity order |
| url | https://ieeexplore.ieee.org/document/10273613/ |
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