{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T19:59:47Z","timestamp":1777579187980,"version":"3.51.4"},"reference-count":19,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2013,4,22]],"date-time":"2013-04-22T00:00:00Z","timestamp":1366588800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We study the Cramer-Rao bounds of parameter estimation and coherence performance for the next generation radar (NGR). In order to enhance the performance of NGR, the signal model of NGR with master-slave architecture based on a single pulse is extended to the case of pulse trains, in which multiple pulses are emitted from all sensors and then integrated spatially and temporally in a unique master sensor. For the MIMO mode of NGR where orthogonal waveforms are emitted, we derive the closed-form Cramer-Rao bound (CRB) for the estimates of generalized coherence parameters (GCPs), including the time delay differences, total phase differences and Doppler frequencies with respect to different sensors. For the coherent mode of NGR where the coherent waveforms are emitted after pre-compensation using the estimates of GCPs, we develop a performance bound of signal-to-noise ratio (SNR) gain for NGR based on the aforementioned CRBs, taking all the estimation errors into consideration. It is shown that greatly improved estimation accuracy and coherence performance can be obtained with pulse trains employed in NGR. Numerical examples demonstrate the validity of the theoretical results.<\/jats:p>","DOI":"10.3390\/s130405347","type":"journal-article","created":{"date-parts":[[2013,4,22]],"date-time":"2013-04-22T14:02:19Z","timestamp":1366639339000},"page":"5347-5367","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Cramer-Rao Bounds and Coherence Performance Analysis for Next Generation Radar with Pulse Trains"],"prefix":"10.3390","volume":"13","author":[{"given":"Xiaowei","family":"Tang","sequence":"first","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}]},{"given":"Jun","family":"Tang","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}]},{"given":"Qian","family":"He","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}]},{"given":"Shuang","family":"Wan","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}]},{"given":"Bo","family":"Tang","sequence":"additional","affiliation":[{"name":"Electronic Engineering Institute, Hefei 230037, China"}]},{"given":"Peilin","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}]},{"given":"Ning","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}]}],"member":"1968","published-online":{"date-parts":[[2013,4,22]]},"reference":[{"key":"ref_1","unstructured":"Brookner, E. (April, January 17\u2013). Phased-Array and Radar Breakthroughs. Boston, MA, USA."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Cuomo, K., Coutts, S.D., McHarg, J.C., Pulsone, N.B., and Robey, F.C. (2004). Wideband Aperture Coherence Processing for Next Generation Radar (NexGen), MIT Lincoln Laboratory. Technical Report ESC-TR-2004-087.","DOI":"10.21236\/ADA430577"},{"key":"ref_3","unstructured":"Coutts, S., Cuomo, K., McHarg, J., Robey, F., and Weikle, D. (July, January 12\u2013). Distributed Coherent Aperture Measurements for Next Generation BMD Radar. Waltham, MA, USA."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sun, P.L., Tang, J., He, Q., Tang, B., and Tang, X.W. (2013). Cramer-Rao bound of parameters estimation and coherence performance for next generation radar. IEE Proc. Radar Sonar Navig., in press.","DOI":"10.1049\/iet-rsn.2012.0139"},{"key":"ref_5","unstructured":"Fletcher, A.S., and Robey, F.C. Performance Bounds for Adaptive Coherence of Sparse Array Radar, MIT Lincoln Laboratory. Technical Report 02420-9108."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Li, J., and Stoica, P. (2008). MIMO Radar Signal Processing, Wiley Press. [1st ed.].","DOI":"10.1002\/9780470391488"},{"key":"ref_7","first-page":"968","article-title":"On parameter identification ability of MIMO radar","volume":"12","author":"Li","year":"2007","journal-title":"IEEE Signal Process. Lett"},{"key":"ref_8","unstructured":"Lehmann, N.H., Haimovich, A.M., Blum, R.S., and Cimini, L.J. (1, January 29). High resolution capabilities of MIMO radar. Pacific Grove, CA, USA."},{"key":"ref_9","unstructured":"Godrich, H., Haimovich, A.M., and Blum, R.S. (March, January 19\u2013). Cramer Rao Bound on Target Localization Estimation in MIMO Radar Systems. Princeton, NJ, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2783","DOI":"10.1109\/TIT.2010.2046246","article-title":"Target localization accuracy gain in MIMO radar-based systems","volume":"6","author":"Godrich","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_11","first-page":"79","article-title":"Target velocity estimation and antenna placement for MIMO radar with widely separated antennas","volume":"4","author":"He","year":"2010","journal-title":"IEEE Trans. Signal Process"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3661","DOI":"10.1109\/TSP.2010.2044613","article-title":"Noncoherent MIMO radar for location and velocity estimation: More antennas means better performance","volume":"4","author":"He","year":"2010","journal-title":"IEEE Trans. Signal Process"},{"key":"ref_13","unstructured":"Wei, C.M., He, Q., and Blum, R.S. (March, January 17\u2013). Cramer-Rao Bound for Joint Location and Velocity Estimation in Multi-Target Non-Coherent MIMO Radars. Princeton, NJ, USA."},{"key":"ref_14","unstructured":"Godrich, H., and Haimovich, A.M. (March, January 3\u2013). Localization Performance of Coherent MIMO Radar Systems Subject to Phase Synchronization Errors. Cyprus."},{"key":"ref_15","first-page":"83","article-title":"Cramer-Rao bound for MIMO radar target localization with phase errors","volume":"1","author":"He","year":"2010","journal-title":"IEEE Signal Process. Lett"},{"key":"ref_16","first-page":"5538","article-title":"Phase synchronization for coherent MIMO radar: algorithms and their analysis","volume":"11","author":"Yang","year":"2010","journal-title":"IEEE Trans. Signal Process"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"848","DOI":"10.3390\/s130100848","article-title":"Hybrid radar emitter recognition based on rough k-means classifier and relevance vector machine","volume":"13","author":"Yang","year":"2013","journal-title":"Sensors"},{"key":"ref_18","unstructured":"Kay, S.M. (1993). Fundamentals of Statistical Signal Processing Volume I: Estimation Theory, Prentice Hall. [1st ed.]."},{"key":"ref_19","unstructured":"Zhang, X.D. (2004). Matrix Analysis and Applications, Tsinghua University Press. [1st ed.]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/4\/5347\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:46:17Z","timestamp":1760219177000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/4\/5347"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,22]]},"references-count":19,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,4]]}},"alternative-id":["s130405347"],"URL":"https:\/\/doi.org\/10.3390\/s130405347","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,4,22]]}}}