{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:18:50Z","timestamp":1760231930285,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2022,10,12]],"date-time":"2022-10-12T00:00:00Z","timestamp":1665532800000},"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>A novel framework for a low-cost coding digital receiving array based on machine learning (ML-CDRA) is proposed in this paper. The received full-array signals are encoded into a few radio frequency (RF) channels, and decoded by an artificial neural network in real-time. The encoding and decoding networks are studied in detail, including the implementation of the encoding network, the loss function and the complexity of the decoding network. A generalized form of loss function is presented by constraint with maximum likelihood, signal sparsity, and noise. Moreover, a feasible loss function is given as an example and the derivations for back propagation are successively derived. In addition, a real-time processing implementation architecture for ML-CDRA is presented based on the commercial chips. It is possible to implement by adding an additional FPGA on the hardware basis of full-channel DRA. ML-CDRA requires fewer RF channels than the traditional full-channel array, while maintaining a similar digital beamforming (DBF) performance. This provides a practical solution to the typical problems in the existing low-cost DBF systems, such as synchronization, moving target compensation, and being disabled at a low signal-to-noise ratio. The performance of ML-CDRA is evaluated in simulations.<\/jats:p>","DOI":"10.3390\/rs14205086","type":"journal-article","created":{"date-parts":[[2022,10,12]],"date-time":"2022-10-12T05:31:18Z","timestamp":1665552678000},"page":"5086","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Machine-Learning-Based Framework for Coding Digital Receiving Array with Few RF Channels"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5454-7648","authenticated-orcid":false,"given":"Lei","family":"Xiao","sequence":"first","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2705-3546","authenticated-orcid":false,"given":"Yubing","family":"Han","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3364-7145","authenticated-orcid":false,"given":"Zuxin","family":"Weng","sequence":"additional","affiliation":[{"name":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/62.990350","article-title":"Development of a Digital Array Radar (DAR)","volume":"17","author":"Cantrell","year":"2002","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/TSP.2021.3119768","article-title":"Direction-of-Arrival Estimation for Large Antenna Arrays with Hybrid Analog and Digital Architectures","volume":"70","author":"Zhang","year":"2022","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.sigpro.2017.03.013","article-title":"Design and analysis of compressive antenna arrays for direction of arrival estimation","volume":"138","author":"Ibrahim","year":"2017","journal-title":"Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"8865","DOI":"10.1109\/ACCESS.2016.2628869","article-title":"Underdetermined DOA Estimation Under the Compressive Sensing Framework: A Review","volume":"4","author":"Shen","year":"2016","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1109\/TAES.2014.120532","article-title":"Adaptive beamforming with compressed sensing for sparse receiving array","volume":"50","author":"Wang","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1109\/JSSC.2019.2900200","article-title":"A Flexible Phased-Array Architecture for Reception and Rapid Direction-of-Arrival Finding Utilizing Pseudo-Random Antenna Weight Modulation and Compressive Sampling","volume":"54","author":"Bajor","year":"2019","journal-title":"IEEE J. Solid-State Circuits"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Rahman, M.R., Bojja-Venkatakrishnan, S., Alwan, E.A., and Volakis, J.L. (2020, January 5\u201310). Spread Spectrum Techniques with Channel Coding for Wideband Secured Communication Links. Proceedings of the 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting, Toronto, ON, Canada.","DOI":"10.1109\/IEEECONF35879.2020.9329603"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Alwan, E.A., Khalil, W., and Volakis, J.L. (2013, January 7\u201313). Ultra-wideband on-site coding receiver (OSCR) for digital beamforming applications. Proceedings of the 2013 IEEE Antennas and Propagation Society International Symposium (APSURSI), Orlando, FL, USA.","DOI":"10.1109\/APS.2013.6710970"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ullah, K., Venkatakrishnan, S.B., and Volakis, J.L. (2021, January 9\u201313). Low Power and Low Cost Millimeter-Wave Digital Beamformer Using an Orthogonal Coding Scheme. Proceedings of the 2021 USNC-URSI Radio Science Meeting (USCN-URSI RSM), Honolulu, HI, USA.","DOI":"10.23919\/USNC-URSIRSM52661.2021.9552370"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1109\/LAWP.2011.2157073","article-title":"Single RF Channel Digital Beamforming Multibeam Antenna Array Based on Time Sequence Phase Weighting","volume":"10","author":"Zhang","year":"2011","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4340","DOI":"10.1109\/ACCESS.2018.2800399","article-title":"Single RF Channel Digital Beamforming Array Antenna Based on Compressed Sensing for Large-Scale Antenna Applications","volume":"6","author":"Zhang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ma, Y., Miao, C., Wu, W., and Li, Y. (2020, January 8\u201311). Hyper Beamforming in Time Modulated Linear Arrays. Proceedings of the 2020 IEEE Asia-Pacific Microwave Conference (APMC), Hong Kong, China.","DOI":"10.1109\/APMC47863.2020.9331691"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1109\/TSP.2012.2222377","article-title":"Perturbation Analysis of Orthogonal Matching Pursuit","volume":"61","author":"Ding","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Bian, S., and Zhang, L. (2021, January 14\u201316). Overview of Match Pursuit Algorithms and Application Comparison in Image Reconstruction. Proceedings of the 2021 IEEE Asia-Pacific Conference on Image Processing, Electronics and Computers (IPEC), Dalian, China.","DOI":"10.1109\/IPEC51340.2021.9421295"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1109\/LSP.2015.2393637","article-title":"Fast Non-Negative Orthogonal Matching Pursuit","volume":"22","author":"Yaghoobi","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Han, B., and Jiang, H. (2019, January 26\u201328). An Improved Stagewise Orthogonal Matching Pursuit-Recursive Algorithm for Power Quality Signal Reconstruction. Proceedings of the 2019 Computing, Communications and IoT Applications (ComComAp), Shenzhen, China.","DOI":"10.1109\/ComComAp46287.2019.9018828"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Hanzo, L.L., Yang, L.L., Kuan, E.L., and Yen, K. (2004). CDMA Overview. Single and Multi-Carrier DS-CDMA: Multi-User Detection, Space-Time Spreading, Synchronisation, Networking and Standards, IEEE Press.","DOI":"10.1002\/0470863110"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1109\/TAP.2019.2938711","article-title":"Enhanced Single-Sideband Time-Modulated Phased Array with Lower Sideband Level and Loss","volume":"68","author":"Chen","year":"2020","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2302","DOI":"10.1109\/TSP.2021.3064183","article-title":"Adaptive Sparse Array Beamformer Design by Regularized Complementary Antenna Switching","volume":"69","author":"Wang","year":"2021","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"892","DOI":"10.1109\/JSTSP.2021.3071586","article-title":"Cognitive Antenna Selection for Automotive Radar Using Bobrovsky-Zakai Bound","volume":"15","author":"Tabrikian","year":"2021","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Garcia-Rodriguez, A., Masouros, C., and Rulikowski, P. (2017, January 5\u20139). Efficient large scale antenna selection by partial switching connectivity. Proceedings of the 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), New Orleans, LA, USA.","DOI":"10.1109\/ICASSP.2017.7953362"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1109\/LWC.2019.2943466","article-title":"Beamforming Design for Large-Scale Antenna Arrays Using Deep Learning","volume":"9","author":"Lin","year":"2020","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1109\/TVT.2019.2949122","article-title":"Fast Beamforming Design via Deep Learning","volume":"69","author":"Huang","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhao, X., Yang, Y., and Chen, K.S. (2021). Direction-of-Arrival Estimation over Sea Surface from Radar Scattering Based on Convolutional Neural Network. Remote Sens., 13.","DOI":"10.3390\/rs13142681"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1049\/iet-map.2018.5317","article-title":"SR-Crossbar topology for large-scale RF MEMS switch matrices","volume":"13","author":"Zhou","year":"2019","journal-title":"IET Microwaves Antennas Propag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"116961","DOI":"10.1109\/ACCESS.2020.3004174","article-title":"Smoothed L0-Constraint Dictionary Learning for Low-Dose X-Ray CT Reconstruction","volume":"8","author":"Komolafe","year":"2020","journal-title":"IEEE Access"},{"key":"ref_28","unstructured":"Xilinx (2020). 7 Series FPGAs Data Sheet: Overview, Xilinx. Rev. 2.6.1."},{"key":"ref_29","unstructured":"Xilinx (2022). UltraScale Architecture and Product Data Sheet: Overview, Xilinx. Rev. 4.1.1."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2740","DOI":"10.1109\/TSP.2007.893762","article-title":"Complex-Valued Matrix Differentiation: Techniques and Key Results","volume":"55","author":"Hjorungnes","year":"2007","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/20\/5086\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:50:23Z","timestamp":1760143823000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/20\/5086"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,12]]},"references-count":30,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["rs14205086"],"URL":"https:\/\/doi.org\/10.3390\/rs14205086","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,10,12]]}}}