{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:46:24Z","timestamp":1760240784209,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,9,3]],"date-time":"2019-09-03T00:00:00Z","timestamp":1567468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["HEUCFG201829"],"award-info":[{"award-number":["HEUCFG201829"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2018M631911"],"award-info":[{"award-number":["2018M631911"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012548","name":"Heilongjiang Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["LBH-Z18055"],"award-info":[{"award-number":["LBH-Z18055"]}],"id":[{"id":"10.13039\/100012548","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper establishes an optimal generic function model in order to obtain a continuous phase modulated (CPM) signal with a smoother phase modulation function. This is achieved by finding the solution to the symbol signals at different lengths of the CPM function. In the solution process, the unknown amount that needs to be solved is reduced by using the even function symmetry characteristic of the signal to be solved. For each different form of the signal, the time domain form of the CPM function and the corresponding normalized energy spectral density are compared under the influence of the phase modulation signal length and the generic function parameter n. The data transmission rate is improved by introducing inter-symbol interference, and the modulation process is realized using six-way parallel transmission when the CPM function is 6T. The simulation results show that the CPM function obtained by establishing an optimal generic function model has high-quality time-frequency characteristics. The real-time phase trajectory and the high-order derivative are both continuous, and the modulated signal has constant envelope characteristics. The CPM function has a fast rolling-off in the frequency domain and small out-of-band radiation, which greatly improves the characteristics of the frequency band utilization.<\/jats:p>","DOI":"10.3390\/sym11091114","type":"journal-article","created":{"date-parts":[[2019,9,4]],"date-time":"2019-09-04T08:28:13Z","timestamp":1567585693000},"page":"1114","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Research on an Optimization Method for a Partially Responsive Continuous Phase Modulated (CPM) Signal Based on an Optimal Generic Function"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2978-5676","authenticated-orcid":false,"given":"Junwei","family":"Qi","sequence":"first","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"College of Computer Science and Technology, Harbin Engineering University, Harbin 150001, China"}]},{"given":"Sergey B.","family":"Makarov","sequence":"additional","affiliation":[{"name":"Institute of Physics, Nanotechnology and Telecommunications, St. Petersburg State Polytechnical University, 195251 St. Petersburg, Russia"}]},{"given":"Mingxin","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}]},{"given":"Beiming","family":"Li","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}]},{"given":"Wei","family":"Xue","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"762","DOI":"10.1109\/TBC.2018.2835769","article-title":"Optimal Design of Cascade LDPC-CPM System Based on Bionic Swarm Optimization Algorithm","volume":"64","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Broadcast."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1564","DOI":"10.1109\/TWC.2009.080679","article-title":"Spectrally-Efficient Continuous Phase Modulations","volume":"8","author":"Barbieri","year":"2009","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_3","first-page":"1390","article-title":"Continuous Phase Modulation Classification via Baum-Welch Algorithm","volume":"22","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_4","unstructured":"Zhou, J., Pang, Q., Xu, D., Wu, W., and Yang, H. (2015). Minimum Frequency Shift Keying. Principle of Communication, Higher Education Press."},{"key":"ref_5","unstructured":"Fan, C., and Cao, L. (2015). Minimum Frequency Shift Keying and Gaussian Minimum Frequency Shift Keying. Principle of Communication, National Defense Industry Press."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3627","DOI":"10.1109\/JLT.2012.2224845","article-title":"Constant Envelop Minimum-Shift Keying OFDM Coherent Optical Communication System","volume":"30","author":"Yang","year":"2012","journal-title":"J. Lightw. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liu, W., and Santhanam, B. (2018). Wideband partial response CPM demodulation via multirate frequency transformations and decision feedback equalization. EURASIP J. Wireless Commun., 2018.","DOI":"10.1186\/s13638-018-1097-2"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1715","DOI":"10.1109\/TCOMM.2006.881340","article-title":"Analytical Solution for Optimum Partial-Response Target in Viterbi-Based Receivers","volume":"54","author":"Li","year":"2006","journal-title":"IEEE Trans. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ishkaev, I.R., Shevelev, A.E., Ovsyannikova, A.S., Zavjalov, S.V., Volvenko, S.V., and Makarov, S.B. (2018, January 22\u201323). Possibility of Peak-to-Avegare Power Ratio Reduction by Application of Optimal Signal for Transmitter Based on SDR HackRF One. Proceedings of the 2018 IEEE International Conference on Electrical Engineering and Photonics (EExPolytech), St. Petersburg, Russia.","DOI":"10.1109\/EExPolytech.2018.8564411"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Makarov, S.B., Ovsyannikova, A.S., Lavrenyuk, I.I., Zavjalov, S.V., and Volvenko, S.V. (2018, January 11\u201312). Distributions of Probability of Power Values for Random Sequences of Optimal FTN Signals. Proceedings of the 2018 International Symposium on Consumer Technologies (ISCT), St. Petersburg, Russia.","DOI":"10.1109\/ISCE.2018.8408919"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2041","DOI":"10.1109\/TCOMM.2004.838700","article-title":"An Efficient Algorithm to Compute the Euclidean Distance Spectrum of a General Intersymbol Interference Channel and Its Applications","volume":"52","author":"Li","year":"2004","journal-title":"IEEE Trans. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7664","DOI":"10.1109\/ACCESS.2018.2794959","article-title":"Estimation of Modulation Index for Partial Response CPM Signal","volume":"6","author":"Munawar","year":"2018","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1109\/TIT.2010.2096031","article-title":"The Error-Pattern-Correcting Turbo Equalizer: Spectrum Thinning at High SNRs","volume":"57","author":"Alhussien","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1109\/WCL.2013.092813.130622","article-title":"A Timing False Lock Detector for M-ary Partial-Response CPM","volume":"2","author":"Perrins","year":"2013","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1433","DOI":"10.1049\/iet-com.2009.0737","article-title":"Reduction of out of band radiation usingcarrier-by-carrier partial response signallingin orthogonal frequency division multiplexing","volume":"4","author":"Naghsh","year":"2010","journal-title":"IET Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1109\/TCOMM.2005.851614","article-title":"Simple CPM receivers based on a switched linear modulation model","volume":"53","author":"Huang","year":"2005","journal-title":"IEEE Trans. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"65901","DOI":"10.1109\/ACCESS.2018.2878310","article-title":"Mixed Norm Constrained Sparse APA Algorithm for Satellite and Network Echo Channel Estimation","volume":"6","author":"Li","year":"2018","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Shi, W., Li, Y., and Wang, Y. (2019). Noise-free Maximum Correntropy Criterion Algorithm in Non-Gaussian Environment. IEEE Trans. Circuits Syst. Ii Express Briefs, 2019.","DOI":"10.1109\/TCSII.2019.2914511"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6412","DOI":"10.1109\/ACCESS.2018.2889877","article-title":"Controllable Sparse Antenna Array for Adaptive Beamforming","volume":"7","author":"Shi","year":"2019","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Xu, Y., Xue, W., and Shang, W.A. (2014). Pan-Function Model for the Utilization of Bandwidth Improvement and PAPR Reduction. Math. Probl. Eng., 2014.","DOI":"10.1155\/2014\/658093"},{"key":"ref_21","unstructured":"Wu, D., Zhang, Y., Wang, S., and Guo, B. (2005). The Basic Properties of the Fourier Transform. Signal and Linear System Analysis, Higher Education Press."},{"key":"ref_22","first-page":"109","article-title":"Inter-code Interference and Symbol Cross-correlation Properties Affect the Signal","volume":"31","author":"Xue","year":"2010","journal-title":"J. Harb. Engin. Univ."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1109\/TEMC.2017.2749519","article-title":"A Passive Equalizer Optimization Method Based on Time-Domain Inter-Symbol Interference Cancellation Technique","volume":"60","author":"Song","year":"2018","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2095","DOI":"10.1109\/LPT.2018.2877723","article-title":"Inter-Symbol Differential Detection-Enabled Sampling Frequency Offset Compensation for DDO-OFDM","volume":"30","author":"Chen","year":"2018","journal-title":"IEEE Photon. Technol. Lett."},{"key":"ref_25","first-page":"1095","article-title":"A New GMSK Orthogonal Modulation Signal Generation Method","volume":"6","author":"Yang","year":"2005","journal-title":"Electr. J."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/9\/1114\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:16:29Z","timestamp":1760188589000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/9\/1114"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,3]]},"references-count":25,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["sym11091114"],"URL":"https:\/\/doi.org\/10.3390\/sym11091114","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,9,3]]}}}