{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T19:06:37Z","timestamp":1761419197155,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,14]],"date-time":"2018-01-14T00:00:00Z","timestamp":1515888000000},"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>Many modulated signals exhibit a cyclostationarity property, which can be exploited in direction-of-arrival (DOA) estimation to effectively eliminate interference and noise. In this paper, our aim is to integrate the cyclostationarity with the spatial domain and enable the algorithm to estimate more sources than sensors. However, DOA estimation with a sparse array is performed in the coarray domain and the holes within the coarray limit the usage of the complete coarray information. In order to use the complete coarray information to increase the degrees-of-freedom (DOFs), sparsity-aware-based methods and the difference coarray interpolation methods have been proposed. In this paper, the coarray interpolation technique is further explored with cyclostationary signals. Besides the difference coarray model and its corresponding Toeplitz completion formulation, we build up a sum coarray model and formulate a Hankel completion problem. In order to further improve the performance of the structured matrix completion, we define the spatial spectrum sampling operations and the derivative (conjugate) correlation subspaces, which can be exploited to construct orthogonal constraints for the autocorrelation vectors in the coarray interpolation problem. Prior knowledge of the source interval can also be incorporated into the problem. Simulation results demonstrate that the additional constraints contribute to a remarkable performance improvement.<\/jats:p>","DOI":"10.3390\/s18010219","type":"journal-article","created":{"date-parts":[[2018,1,15]],"date-time":"2018-01-15T12:30:36Z","timestamp":1516019436000},"page":"219","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Improved Coarray Interpolation Algorithms with Additional Orthogonal Constraint for Cyclostationary Signals"],"prefix":"10.3390","volume":"18","author":[{"given":"Jinyang","family":"Song","sequence":"first","affiliation":[{"name":"College of Automation, Harbin Engineering University, No. 145 Nantong Street, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering &amp; Automation, Harbin Institute of Technology, No. 92 Xidazhi Street, Harbin 150006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Li, J., and Stoica, P. (2009). MIMO Radar Signal Processing, Wiley.","DOI":"10.1002\/9780470391488"},{"key":"ref_2","unstructured":"Haykin, S. (1984). Array Signal Processing, Prentice-Hall."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/79.526899","article-title":"Two decades of array signal processing research: The parametric approach","volume":"13","author":"Krim","year":"1996","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","article-title":"Multiple emitter location and signal parameter estimation","volume":"34","author":"Schmidt","year":"1986","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"984","DOI":"10.1109\/29.32276","article-title":"ESPRIT\u2014Estimation of signal parameters via rotation invariance techniques","volume":"17","author":"Roy","year":"1989","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_6","unstructured":"Gardner, W.A. (1994). Cyclostationarity in Communications and Signal Processing, Wiley."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1109\/5.7152","article-title":"Simplification of MUSIC and ESPRIT by exploitation of cyclostationarity","volume":"76","author":"Gardner","year":"1988","journal-title":"Proc. IEEE"},{"key":"ref_8","unstructured":"Schell, S.V., Calabretta, R.A., Gardner, W.A., and Agee, B.G. (1989, January 23\u201326). Cyclic MUSIC algorithms for signal-selective direction estimation. Proceedings of the 1989 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Glasgow, UK."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.1109\/78.143448","article-title":"Direction-of-arrival estimation via exploitation of cyclostationary-a combination of temporal and spatial processing","volume":"40","author":"Xu","year":"1992","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1109\/TSP.2003.812834","article-title":"An extended cyclic MUSIC algorithm","volume":"51","author":"Charge","year":"2003","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1109\/TAP.1968.1139138","article-title":"Minimum-redundancy linear arrays","volume":"16","author":"Moffet","year":"1968","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2605","DOI":"10.1109\/78.640730","article-title":"Minimum-redundancy linear arrays for cyclostationarity-based source location","volume":"45","author":"Gelli","year":"1997","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4167","DOI":"10.1109\/TSP.2010.2049264","article-title":"Nested arrays: A novel approach to array processing with enhanced degrees of freedom","volume":"58","author":"Pal","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3997","DOI":"10.1109\/TSP.2016.2558159","article-title":"Super nested arrays: Linear sparse arrays with reduced mutual coupling-part I: Fundamentals","volume":"64","author":"Liu","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/TSP.2010.2089682","article-title":"Sparse sensing with co-prime samplers and arrays","volume":"59","author":"Vaidyanathan","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1109\/TSP.2015.2393838","article-title":"Generalized coprime array configurations for direction-of-arrival estimation","volume":"63","author":"Qin","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1502","DOI":"10.1109\/78.765119","article-title":"Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. II. Partially augmentable arrays","volume":"47","author":"Abramovich","year":"1999","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1719","DOI":"10.1049\/iet-com.2016.1048","article-title":"Compressive sensing based coprime array direction-of-arrival estimation","volume":"11","author":"Zhou","year":"2017","journal-title":"IET Commun."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhang, Y.D., Moeness, G.A., and Braham, H. (2013, January 26\u201331). Sparsity-based DOA estimation using co-prime arrays. Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638403"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1486","DOI":"10.1109\/TSP.2016.2645542","article-title":"DOA Estimation with enhanced DOFs by exploiting cyclostationarity","volume":"65","author":"Liu","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1109\/TSP.2011.2112650","article-title":"Sensitivity to Basis Mismatch in Compressed Sensing","volume":"59","author":"Chi","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"933","DOI":"10.1109\/TSP.2016.2626255","article-title":"Coarrays, MUSIC, and the Cram\u00e9r Rao Bound","volume":"65","author":"Wang","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1438","DOI":"10.1109\/LSP.2015.2409153","article-title":"Remarks on the spatial smoothing step in coarray MUSIC","volume":"22","author":"Liu","year":"2015","journal-title":"IEEE Signal Process Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zhou, C., and Zhou, J. (2017). Direction-of-Arrival Estimation with Coarray ESPRIT for Coprime Array. Sensors, 17.","DOI":"10.3390\/s17081779"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1109\/LSP.2014.2314175","article-title":"A grid-less approach to underdetermined direction of arrival estimation via low rank matrix denoising","volume":"21","author":"Pal","year":"2014","journal-title":"IEEE Signal Process Lett."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Liu, C.L., Vaidyanathan, P.P., and Piya, P. (2016, January 22\u201325). Coprime coarray interpolation for DOA estimation via nuclear norm minimization. Proceedings of the 2016 IEEE International Symposium on Circuits and Systems (ISCAS), Montreal, QC, Canada.","DOI":"10.1109\/ISCAS.2016.7539135"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1145\/2184319.2184343","article-title":"Exact matrix completion via convex optimization","volume":"55","author":"Recht","year":"2012","journal-title":"Commun. ACM"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1109\/TIT.2010.2044061","article-title":"The power of convex relaxation: Near-optimal matrix completion","volume":"56","author":"Tao","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Guo, M., Chen, T., and Wang, B. (2017). An improved DOA estimation approach using coarray interpolation and matrix denoising. Sensors, 17.","DOI":"10.3390\/s17051140"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Tao, C., Muran, G., and Limin, G. (2017). A direct coarray interpolation approach for direction finding. Sensors, 17.","DOI":"10.3390\/s17092149"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6576","DOI":"10.1109\/TIT.2014.2343623","article-title":"Robust Spectral Compressed Sensing via Structured Matrix Completion","volume":"60","author":"Chen","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.dsp.2016.04.011","article-title":"Cram\u00b4er-Rao bounds for coprime and other sparse arrays, which find more sources than sensors","volume":"61","author":"Liu","year":"2017","journal-title":"Digit. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/MSP.2015.2486805","article-title":"Compressive covariance sensing: Structure-based compressive sensing beyond sparsity","volume":"33","author":"Romero","year":"2016","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1511","DOI":"10.1109\/TASLP.2016.2560523","article-title":"Signal-Dependent Spatial Filtering Based on Weighted-Orthogonal Beamformers in the Spherical Harmonic Domain","volume":"24","author":"Delikaris","year":"2017","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Rahmani, M., and Atia, G.K. (2016, January 10\u201313). A subspace method for array covariance matrix estimation. Proceedings of the 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM), Rio de Janerio, Brazil.","DOI":"10.1109\/SAM.2016.7569686"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5006","DOI":"10.1109\/TSP.2017.2721915","article-title":"Correlation Subspaces: Generalizations and Connection to Difference Coarrays","volume":"65","author":"Liu","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Horn, R.A., and Johnson, C.R. (1985). Matrix Analysis, Cambridge University Press.","DOI":"10.1017\/CBO9780511810817"},{"key":"ref_38","unstructured":"Grant, M., and Boyd, S. (2018, January 14). CVX: MATLAB Software for Disciplined Convex Programming, Version 2.1. Available online: http:\/\/cvxr.com\/cvx."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/1\/219\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T14:51:13Z","timestamp":1760194273000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/1\/219"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,14]]},"references-count":38,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1]]}},"alternative-id":["s18010219"],"URL":"https:\/\/doi.org\/10.3390\/s18010219","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,1,14]]}}}