{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:58:47Z","timestamp":1760234327686,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,4,30]],"date-time":"2021-04-30T00:00:00Z","timestamp":1619740800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Phase noise refers to the instability of an oscillator, which is the cause of instantaneous phase and frequency deviations in the carrier wave. This unavoidable instability adversely affects the performance of range\u2013velocity radar systems, including synthetic aperture radars (SARs) and ground-moving target indicator (GMTI) radars. Phase noise effects should be considered in high-resolution radar designs, operating in millimeter wavelengths and terahertz frequencies, due to their role in radar capability during the reliable identification of target location and velocity. In general, phase noise is a random process consisting of nonstationary terms. It has been shown that in order to optimize the coherent detection of stealthy, fast-moving targets with a low radar cross-section (RCS), it is required to evaluate the integration gain and to determine the incoherent noise effects for resolving target location and velocity. Here, we present an analytical expression for the coherent integration loss when a nonstationary phase noise is considered. A Wigner distribution was employed to derive the time\u2013frequency expression for the coherent loss when nonstationary conditions were considered. Up to now, no analytical expressions have been developed for coherent integration loss when dealing with real nonstationary phase noise mathematical models. The proposed expression will help radar systems estimate the nonstationary integration loss and adjust the decision threshold value in order to maximize the probability of detection. The effect of nonstationary phase noise is demonstrated for studying coherent integration loss of high-resolution radar operating in the W-band. The investigation indicates that major degradation in the time-frequency coherent integration due to short-term, nonstationary phase noise instabilities arises for targets moving at low velocities and increases with range. Opposed to the conventional model, which assumes stationarity, a significant difference of up to 25 dB is revealed in the integration loss for radars operating in the millimeter wave regime. Moreover, for supersonic moving targets, the loss peaks at intermediate distances and then reduces as the target moves away.<\/jats:p>","DOI":"10.3390\/rs13091755","type":"journal-article","created":{"date-parts":[[2021,4,30]],"date-time":"2021-04-30T10:53:29Z","timestamp":1619780009000},"page":"1755","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Coherent Integration Loss Due to Nonstationary Phase Noise in High-Resolution Millimeter-Wave Radars"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1687-6659","authenticated-orcid":false,"given":"Chagai","family":"Levy","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Ariel University, Ariel 40700, Israel"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1839-9489","authenticated-orcid":false,"given":"Monika","family":"Pinchas","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Ariel University, Ariel 40700, Israel"}]},{"given":"Yosef","family":"Pinhasi","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Ariel University, Ariel 40700, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,30]]},"reference":[{"key":"ref_1","unstructured":"Bassem, R.M. (2013). Radar Systems Analysis and Design Using MATLAB deciBEL Research, Chapman and Hall\/CRC Inc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1109\/LSP.2008.2002724","article-title":"Upper Bound of Coherent Integration Loss for Symmetrically Distributed Phase Noise","volume":"15","author":"Yu","year":"2008","journal-title":"Signal Process. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Doerry, A.W. (2018). Radar Receiver Oscillator Phase Noise, Sandia National Laboratories. Sandia Report SAND2018-3614.","DOI":"10.2172\/1528837"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1109\/LSP.2003.811589","article-title":"Coherent Integration Loss Due to White Gaussian Phase Noise","volume":"10","author":"Richards","year":"2003","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Nebel, M., and Lankl, B. (2010, January 8\u201310). Oscillator phase noise as a limiting factor in stand-alone GPS-indoor navigation. Proceedings of the 2015 IEEE International Conference on Information and Automation, Lijiang, China.","DOI":"10.1109\/NAVITEC.2010.5708038"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/TUFFC.2012.2221","article-title":"Detection of Atomic Clock Frequency Jumps With the Kalman Filter","volume":"59","author":"Galleani","year":"2012","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_7","unstructured":"Galleani, L., and Tavella, P. (2003, January 4\u20138). The characterization of clock behavior with the dynamic Allan variance. Proceedings of the IEEE International Frequency Control Symposium and PDA Exhibition Jointly with the 17th European Frequency and Time Forum, Tampa, FL, USA."},{"key":"ref_8","first-page":"2","article-title":"Application of the Dynamic Allan Variance for the Characterization of Space Clock Behavior","volume":"47","author":"Sesial","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_9","unstructured":"Keysight, T. (2014). Analyzing Frequency Stability in the Frequency and Time Domains, Keysight Technologies. Application Note."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1109\/TUFFC.2005.1406554","article-title":"The clock model and its relationship with the Allan and related variances","volume":"52","author":"Zucca","year":"2005","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zucca, C. (2015). A mathematical model for the atomic clock error in case of jumps. arXiv.","DOI":"10.1088\/0026-1394\/52\/4\/514"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Rubiola, E. (2009). Phase Noise and Frequency Stability in Oscillators, Cambridge University Press.","DOI":"10.1017\/CBO9780511812798"},{"key":"ref_13","unstructured":"Cohen, L. (1994). Time-Frequency Analysis, Prentice Hall."},{"key":"ref_14","first-page":"61","article-title":"Theorie et applications de la notion de signal analytique","volume":"2","author":"Ville","year":"1948","journal-title":"Cables Transm."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1103\/PhysRev.40.749","article-title":"On the quantum correction for thermodynamic equilibrium","volume":"40","author":"Wigner","year":"1932","journal-title":"Phys. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Balal, N., Balal, Y., Richter, Y., and Pinhasi, Y. (2020). Detection of Low RCS Supersonic Flying Targets with a High-Resolution MMW Radar. Sensors, 20.","DOI":"10.3390\/s20113284"},{"key":"ref_17","unstructured":"(2021, February 20). KEYSIGHT, 83623B High Power Swept-Signal Generator. Available online: https:\/\/www.keysight.com\/en\/pd-1000001863."},{"key":"ref_18","unstructured":"(2021, March 25). Analog Devices, ADF4371\u2014Microwave Wideband Synthesizer with Integrated VCO. Available online: https:\/\/www.analog.com\/en\/products\/adf4371.html#product-overview."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Valenta, V., Baudoin, G., and Villegas, M. (2008, January 15\u201317). Phase Noise Analysis of PLL Based Frequency Synthesizers for Multi-Radio Mobile Terminals. Proceedings of the Third International Conference on Cognitive Radio Oriented Wireless Networks and Communications, CrownCom 2008, Singapore.","DOI":"10.1109\/CROWNCOM.2008.4562555"},{"key":"ref_20","unstructured":"Fima, C.K. (1998). Introduction to Stochastic Calculus with Applications, Imperial College Press."},{"key":"ref_21","unstructured":"Steven, E.S. (2004). Stochastic Calculus for Finance II: Continuous-Time Models, Springer."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/9\/1755\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:56:18Z","timestamp":1760162178000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/9\/1755"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,30]]},"references-count":21,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,5]]}},"alternative-id":["rs13091755"],"URL":"https:\/\/doi.org\/10.3390\/rs13091755","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2021,4,30]]}}}