A Noniterative Radix-8 CORDIC Algorithm with Low Latency and High Efficiency
An efficient, noniterative Radix-8 (NR-8) coordinate rotation digital computer (CORDIC) algorithm is proposed for low-latency and high-efficiency computation of the functions of sine, cosine, or the phase shift, with which the values of the functions are precisely computed by only using the angle in...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Electronics |
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| Online Access: | https://www.mdpi.com/2079-9292/9/9/1521 |
| _version_ | 1797553384947974144 |
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| author | Wenming Tang Feng Xu |
| author_facet | Wenming Tang Feng Xu |
| author_sort | Wenming Tang |
| collection | DOAJ |
| description | An efficient, noniterative Radix-8 (NR-8) coordinate rotation digital computer (CORDIC) algorithm is proposed for low-latency and high-efficiency computation of the functions of sine, cosine, or the phase shift, with which the values of the functions are precisely computed by only using the angle in a narrow range of [0, π/12] rather than in a wide angle range of [0, π/2]. This algorithm is expressed by a formula that simplifies the traditional iterative processes by using a complex multiplier. The results obtained from the simulation and the experiment on an FPGA show that the NR-8 CORDIC algorithm operates well, with which the 16-bit precision output is extremely precise, with only 0.012% of the absolute error for computing the sine or cosine function with a step of 0.001°. Compared with the best conventional CORDIC algorithm, the clock latency of this algorithm significantly decreases down to less than 50%, only needs half of the logic resources and consumes half of the power. This algorithm also takes advantages over other newly improved CORDIC algorithms and requires less than half of the clock latency, even for a 23-bit precision output. Therefore, this algorithm could provide a potential application in real-time systems such as radar digital beamforming. |
| first_indexed | 2024-03-10T16:15:43Z |
| format | Article |
| id | doaj.art-789427952b7641d1a5f556eed1b42d2d |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-10T16:15:43Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-789427952b7641d1a5f556eed1b42d2d2023-11-20T14:05:53ZengMDPI AGElectronics2079-92922020-09-0199152110.3390/electronics9091521A Noniterative Radix-8 CORDIC Algorithm with Low Latency and High EfficiencyWenming Tang0Feng Xu1The Key Laboratory for Information Science of Electromagnetic Waves, School of Information Science and Technology, Fudan University, Shanghai 200433, ChinaThe Key Laboratory for Information Science of Electromagnetic Waves, School of Information Science and Technology, Fudan University, Shanghai 200433, ChinaAn efficient, noniterative Radix-8 (NR-8) coordinate rotation digital computer (CORDIC) algorithm is proposed for low-latency and high-efficiency computation of the functions of sine, cosine, or the phase shift, with which the values of the functions are precisely computed by only using the angle in a narrow range of [0, π/12] rather than in a wide angle range of [0, π/2]. This algorithm is expressed by a formula that simplifies the traditional iterative processes by using a complex multiplier. The results obtained from the simulation and the experiment on an FPGA show that the NR-8 CORDIC algorithm operates well, with which the 16-bit precision output is extremely precise, with only 0.012% of the absolute error for computing the sine or cosine function with a step of 0.001°. Compared with the best conventional CORDIC algorithm, the clock latency of this algorithm significantly decreases down to less than 50%, only needs half of the logic resources and consumes half of the power. This algorithm also takes advantages over other newly improved CORDIC algorithms and requires less than half of the clock latency, even for a 23-bit precision output. Therefore, this algorithm could provide a potential application in real-time systems such as radar digital beamforming.https://www.mdpi.com/2079-9292/9/9/1521CORDICsine and cosinephase shiftFPGAdigital beamforming |
| spellingShingle | Wenming Tang Feng Xu A Noniterative Radix-8 CORDIC Algorithm with Low Latency and High Efficiency Electronics CORDIC sine and cosine phase shift FPGA digital beamforming |
| title | A Noniterative Radix-8 CORDIC Algorithm with Low Latency and High Efficiency |
| title_full | A Noniterative Radix-8 CORDIC Algorithm with Low Latency and High Efficiency |
| title_fullStr | A Noniterative Radix-8 CORDIC Algorithm with Low Latency and High Efficiency |
| title_full_unstemmed | A Noniterative Radix-8 CORDIC Algorithm with Low Latency and High Efficiency |
| title_short | A Noniterative Radix-8 CORDIC Algorithm with Low Latency and High Efficiency |
| title_sort | noniterative radix 8 cordic algorithm with low latency and high efficiency |
| topic | CORDIC sine and cosine phase shift FPGA digital beamforming |
| url | https://www.mdpi.com/2079-9292/9/9/1521 |
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