{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:56:13Z","timestamp":1760151373691,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,3,18]],"date-time":"2022-03-18T00:00:00Z","timestamp":1647561600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Power inversion (PI) is a known adaptive beamforming algorithm that is widely used in wireless communication systems for anti-jamming purposes. The PI algorithm is typically implemented in a digital domain, which requires the radio-frequency signals to be down-converted into base-band signals, and then sampled by ADCs. In practice, the down-conversion circuit will introduce phase noises into the base-band signals, which may degrade the performance of the algorithm. At present, the impacts of phase noise on the PI algorithm have not been studied, according to the open literature, which is, however, important for practical design. Therefore, in this paper, we present a theoretical analysis on the impacts, provide a new mathematical model of the PI algorithm, and offer a closed-form formula of the interference cancellation ratio (ICR) to quantify the relations between the algorithm performance and the phase noise level, as well as the number of auxiliary antennas. We find that the ICR in decibel decreases logarithmically linearly with the phase noise variance. In addition, the ICR improves with an increasing number of auxiliary antennas, but the increment is upper-bounded. The above findings are verified with both simulated and measured phase noise data.<\/jats:p>","DOI":"10.3390\/s22062362","type":"journal-article","created":{"date-parts":[[2022,3,20]],"date-time":"2022-03-20T21:37:17Z","timestamp":1647812237000},"page":"2362","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Impacts of Phase Noise on the Anti-Jamming Performance of Power Inversion Algorithm"],"prefix":"10.3390","volume":"22","author":[{"given":"Minglei","family":"Zhou","sequence":"first","affiliation":[{"name":"National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan 430030, China"}]},{"given":"Qing","family":"Wang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan 430030, China"}]},{"given":"Fangmin","family":"He","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan 430030, China"}]},{"given":"Jin","family":"Meng","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Science and Technology on Vessel Integrated Power System, Naval University of Engineering, Wuhan 430030, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1109\/TASSP.1985.1164583","article-title":"Adaptive beamforming for coherent signals and interference","volume":"33","author":"Shan","year":"1985","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2905","DOI":"10.1109\/TAES.2021.3068439","article-title":"Adaptive Spatial Hybrid Nulling of Extremely Strong Interfering Signals","volume":"57","author":"Poberezhskiy","year":"2021","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wan, F., Xu, J., and Zhang, Z. (2022). Robust Beamforming Based on Covariance Matrix Reconstruction in FDA-MIMO Radar to Suppress Deceptive Jamming. Sensors, 22.","DOI":"10.3390\/s22041479"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"803","DOI":"10.1109\/TAES.1979.308765","article-title":"The power-inversion adaptive array: Concept and performance","volume":"AES-15","author":"Compton","year":"1979","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"25382","DOI":"10.1109\/ACCESS.2019.2900162","article-title":"A Novel Power Inversion Antenna Array for the Beidou Navigation Satellite System","volume":"7","author":"Jin","year":"2019","journal-title":"IEEE Access"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Liu, J., Li, L., Lv, Z., Chen, F., and Ni, S. (2019). Impact of Element Pattern on the Performance of GNSS Power-Inversion Adaptive Arrays. Electronics, 8.","DOI":"10.3390\/electronics8101120"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Lu, Y., Yan, Y., Yuan, J., Wu, D., Dai, C., and Yuan, H. (2006, January 16\u201319). The effect of channel mismatch and mutual coupling on GPS adaptive antenna array. Proceedings of the CIE International Conference on Radar, Shanghai, China.","DOI":"10.1109\/ICR.2006.343440"},{"key":"ref_8","unstructured":"Xiang, J., Guo, L., and Li, H. (2008, January 10\u201312). Study and simulating of adaptive array processing with effect of channel uniformity. Proceedings of the 2nd International Symposium on Systems and Control in Aerospace and Astronautics, Shenzhen, China."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"172","DOI":"10.26599\/TST.2018.9010019","article-title":"Effects of power inversion spatial only adaptive array on GNSS receiver measurements","volume":"23","author":"Xu","year":"2018","journal-title":"Tsinghua Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zeng, H., Zhao, Y., Fang, B., Ji, L., Li, S., and Dong, T. (2018, January 8\u201311). Influence of Channel Error on Nulling Antenna\u2019s Anti-Jamming Performance. Proceedings of the 18th International Conference on Communication Technology (ICCT), Chongqing, China.","DOI":"10.1109\/ICCT.2018.8599913"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6522","DOI":"10.1109\/TWC.2021.3074911","article-title":"Phase Noise in Modular Millimeter Wave Massive MIMO","volume":"20","author":"Rasekh","year":"2021","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1881","DOI":"10.1109\/TSP.2017.2652384","article-title":"Impacts of phase noise on digital self-interference cancellation in full-duplex communications","volume":"65","author":"Quan","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1607","DOI":"10.1109\/TCOMM.2007.902593","article-title":"Effects of phase noise on OFDM systems with and without PLL: Characterization and compensation","volume":"55","author":"Petrovic","year":"2007","journal-title":"IEEE Trans. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1109\/LCOMM.2018.2791590","article-title":"Extended Kalman Filter for MIMO Phase Noise Channels With Independent Oscillators","volume":"22","author":"Reggiani","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8238234","DOI":"10.1155\/2017\/8238234","article-title":"Phase noise effect on MIMO-OFDM systems with common and independent oscillators","volume":"2017","author":"Chen","year":"2017","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Chen, X., Fang, C., Zou, Y., Wolfgang, A., and Svensson, T. (2017, January 19\u201322). Beamforming MIMO-OFDM systems in the presence of phase noises at millimeter-wave frequencies. Proceedings of the Wireless Communications and Networking Conference Workshops (WCNCW), San Francisco, CA, USA.","DOI":"10.1109\/WCNCW.2017.7919036"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"10048","DOI":"10.1109\/TVT.2021.3100862","article-title":"Cell-Free Massive MIMO Systems With Oscillator Phase Noise: Performance Analysis and Power Control","volume":"70","author":"Fang","year":"2021","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2598","DOI":"10.1109\/TSP.2020.2986551","article-title":"Joint Channel and Location Estimation of Massive MIMO System with Phase Noise","volume":"68","author":"Zheng","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4494","DOI":"10.1109\/TVT.2013.2266359","article-title":"On the impact of phase noise on active cancelation in wireless full-duplex","volume":"62","author":"Sahai","year":"2013","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2977","DOI":"10.1109\/TWC.2014.041014.131171","article-title":"Analysis of oscillator phase-noise effects on self-interference cancellation in full-duplex OFDM radio transceivers","volume":"13","author":"Syrjala","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2118","DOI":"10.1109\/TVT.2017.2754489","article-title":"Self-Interference Cancellation with Nonlinearity and Phase-Noise Suppression in Full-Duplex Systems","volume":"67","author":"Li","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1109\/TVT.2019.2953623","article-title":"Analysis of Self-Interference Cancellation Under Phase Noise, CFO, and IQ Imbalance in GFDM Full-Duplex Transceivers","volume":"69","author":"Mohammadian","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Zhou, M., Wang, Q., He, F., Zhang, Y., Luo, K., and Meng, J. (2021, January 18\u201320). Impacts of Phase Noise on the Performance of Adaptive Side-lobe Cancellation System. Proceedings of the 4th International Conference on Electronic Information and Communication Technology (ICEICT), Xi\u2019an, China.","DOI":"10.1109\/ICEICT53123.2021.9531150"},{"key":"ref_24","first-page":"1788","article-title":"Design of multi-chip fractional frequency phase locked loop output signal phase synchronization","volume":"55","author":"Xu","year":"2021","journal-title":"J. Zhejiang Univ. (Eng. Sci.)"},{"key":"ref_25","unstructured":"Sun, Z.Z., Xiao, G.Y., and Quan, Y.H. (2021, January 28). Design and Implementation of a Digital Array Signal Processing Unit. Proceedings of the 13th National Conference on DSP Application Technology, Hangzhou, China."},{"key":"ref_26","unstructured":"LaCaille, G., Puglielli, A., and Alon, E. (2019). Optimizing the LO distribution architecture of mm-wave massive MIMO receivers. arXiv."},{"key":"ref_27","unstructured":"Delos, P. (2018). System-Level LO Phase Noise Model for Phased Arrays with Distributed Phase-Locked Loops, Analog Devices, Inc.. Tech. Rep."},{"key":"ref_28","unstructured":"Lin, B. (2018). Research on External Local Oscillator of Massive MIMO Communication Systems. [Master\u2019s Thesis, Southeast University]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1488","DOI":"10.1049\/iet-rsn.2017.0168","article-title":"Distortionless space-time adaptive processor based on MVDR beamformer for GNSS receiver","volume":"11","author":"Dai","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1109\/11.948268","article-title":"Understanding the effects of phase noise in orthogonal frequency division multiplexing (OFDM)","volume":"47","author":"Armada","year":"2001","journal-title":"IEEE Trans. Broadcasting"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1109\/5.381848","article-title":"Discrete simulation of colored noise and stochastic processes and 1\/f\/sup\/spl alpha\/\/power law noise generation","volume":"83","author":"Kasdin","year":"1995","journal-title":"Proc. IEEE"},{"key":"ref_32","unstructured":"Robertson, P., and Kaiser, S. (1995, January 18\u201322). Analysis of the effects of phase-noise in orthogonal frequency division multiplex (OFDM) systems. Proceedings of the International Conference on Communications, Seattle, WA, USA."},{"key":"ref_33","unstructured":"Yuan, L.S. (2014). Research of the Phase Noise Simulation Method and the Loss of Low-Frequency. [Master\u2019s Thesis, Xi\u2019an University of Electronic Science and Technology]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/6\/2362\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:39:12Z","timestamp":1760135952000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/6\/2362"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,18]]},"references-count":33,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["s22062362"],"URL":"https:\/\/doi.org\/10.3390\/s22062362","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,3,18]]}}}