{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T16:33:20Z","timestamp":1775666000081,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T00:00:00Z","timestamp":1678752000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation of China","award":["62271386"],"award-info":[{"award-number":["62271386"]}]},{"name":"National Science Foundation of China","award":["61901357"],"award-info":[{"award-number":["61901357"]}]},{"name":"National Science Foundation of China","award":["U19B2015"],"award-info":[{"award-number":["U19B2015"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Unlike conventional phased array (PA), frequency diversity array (FDA) can perform the beampattern synthesis not only in an angle dimension but also in a range dimension by introducing an additional frequency offset (FO) across the array aperture, thus greatly enhancing the beamforming flexibility of an array antenna. Nevertheless, an FDA with uniform inter-element spacing that consists of a huge number of elements is required when a high resolution is needed, which results in a high cost. To substantially reduce the cost while almost maintaining the antenna resolution, it is important to conduct a sparse synthesis of FDA. Under these circumstances, this paper investigated the transmit\u2013receive beamforming of a sparse-fda in range and angle dimensions. In particular, the joint transmit\u2013receive signal formula was first derived and analyzed to resolve the inherent time-varying characteristics of FDA based on a cost-effective signal processing diagram. In the sequel, the GA-based low sidelobe level (SLL) transmit\u2013receive beamforming of the sparse-fda was proposed to generate a focused main lobe in a range-angle space, where the array element positions were incorporated into the optimization problem. Numerical results showed that 50% of the elements can be saved for the two linear FDAs with sinusoidally and logarithmically varying frequency offsets, respectively termed as sin-FO linear-FDA and log-FO linear-FDA, with only a less than 1 dB increment in SLL. The resultant SLLs are below \u22129.6 dB, and \u221212.9 dB for these two linear FDAs, respectively.<\/jats:p>","DOI":"10.3390\/s23063107","type":"journal-article","created":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T06:14:58Z","timestamp":1678774498000},"page":"3107","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Transmit\u2013Receive Sparse Synthesis of Linear Frequency Diverse Array in Range-Angle Space Using Genetic Algorithm"],"prefix":"10.3390","volume":"23","author":[{"given":"Yanhong","family":"Xu","sequence":"first","affiliation":[{"name":"Xi\u2019an Key Laboratory of Network Convergence Communication, College of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao","family":"Huang","sequence":"additional","affiliation":[{"name":"Xi\u2019an Key Laboratory of Network Convergence Communication, College of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anyi","family":"Wang","sequence":"additional","affiliation":[{"name":"Xi\u2019an Key Laboratory of Network Convergence Communication, College of Communication and Information Engineering, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,14]]},"reference":[{"key":"ref_1","unstructured":"Antonik, P., Wicks, M.C., Griffiths, H.D., and Baker, C.J. 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