Editing Phase-shift keying (section)

====SOQPSK====
The license-free '''[[Pulse shaping|shaped]]-offset QPSK''' (SOQPSK) is interoperable with Feher-patented QPSK ('''FQPSK'''), in the sense that an integrate-and-dump offset QPSK detector produces the same output no matter which kind of transmitter is used.<ref>
{{cite document | last1 = Nelson | first1 = T. | last2 = Perrins | first2 = E. | last3 = Rice | first3 = M. | title=Common detectors for Tier 1 modulations |publisher=International Foundation for Telemetering |date=2005 |hdl=10150/604890}}
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{{cite conference | last1 = Nelson | first1 = T. | last2 = Perrins | first2 = E. | last3 = Rice | first3 = M. | doi = 10.1109/GLOCOM.2005.1578470 | title = Common detectors for shaped offset QPSK (SOQPSK) and Feher-patented QPSK (FQPSK) | book-title = GLOBECOM '05. IEEE Global Telecommunications Conference, 2005 | pages = 5 pp | year = 2005 | isbn = 0-7803-9414-3 | s2cid = 11020777 |url=https://www.researchgate.net/publication/4213516_Common_detectors_for_shaped_offset_QPSK_(SOQPSK)_and_Feher-patented_QPSK_(FQPSK)}}
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These modulations carefully shape the I and Q waveforms such that they change very smoothly, and the signal stays constant-amplitude even during signal transitions. (Rather than traveling instantly from one symbol to another, or even linearly, it travels smoothly around the constant-amplitude circle from one symbol to the next.) SOQPSK modulation can be represented as the hybrid of QPSK and [[Minimum-shift keying|MSK]]: SOQPSK has the same signal constellation as QPSK, however the phase of SOQPSK is always stationary.<ref>{{cite conference |first=Terrance J. |last=Hill |title=A non-proprietary, constant envelope, variant of shaped offset QPSK (SOQPSK) for improved spectral containment and detection efficiency |book-title=MILCOM 2000 Proceedings. 21st Century Military Communications. Architectures and Technologies for Information Superiority |publisher=IEEE |volume=1 |date=2000 |isbn=0-7803-6521-6 |pages=347–352 |doi=10.1109/MILCOM.2000.904973}}</ref><ref>{{cite journal |last=Li |first=Lifang |first2=M.K. |last2=Simon |title=Performance of coded offset quadrature phase-shift keying (OQPSK) and MIL-STD shaped OQPSK (SOQPSK) with iterative decoding |journal=Interplanetary Network Prog. Rep. |volume=42 |page=156 |date=2004 |url=https://ipnpr.jpl.nasa.gov/progress_report/42-156/156A.pdf}}</ref>

The standard description of SOQPSK-TG involves [[ternary signal|ternary symbols]].<ref>{{cite conference |last=Sahin |first=C. |last2=Perrins |first2=E. |title=The capacity of SOQPSK-TG |book-title=2011-MILCOM 2011 Military Communications Conference |publisher=IEEE |date=2011 |isbn=978-1-4673-0081-0 |pages=555–560 |doi=10.1109/MILCOM.2011.6127730}}</ref> SOQPSK is one of the most spread modulation schemes in application to [[Low Earth orbit|LEO]] satellite communications.<ref>{{cite journal |last=Saeed |first=N. |last2=Elzanaty |first2=A. |last3=Almorad |first3=H. |last4=Dahrouj |first4=H. |last5=Al-Naffouri |first5=T.Y. |last6=Alouini |first6=M.S. |title=Cubesat communications: Recent advances and future challenges |journal=IEEE Communications Surveys & Tutorials |volume=22 |issue=3 |pages=1839–62 |date=2020 |doi=10.1109/COMST.2020.2990499 |arxiv=1908.09501}}</ref>